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http://rosettacode.org/wiki/Numerical_integration/Gauss-Legendre_Quadrature
Numerical integration/Gauss-Legendre Quadrature
In a general Gaussian quadrature rule, an definite integral of f ( x ) {\displaystyle f(x)} is first approximated over the interval [ − 1 , 1 ] {\displaystyle [-1,1]} by a polynomial approximable function g ( x ) {\displaystyle g(x)} and a known weighting function W ( x ) {\displaystyle W(x)} . ∫ − 1 1 f ( x ) d x = ∫ − 1 1 W ( x ) g ( x ) d x {\displaystyle \int _{-1}^{1}f(x)\,dx=\int _{-1}^{1}W(x)g(x)\,dx} Those are then approximated by a sum of function values at specified points x i {\displaystyle x_{i}} multiplied by some weights w i {\displaystyle w_{i}} : ∫ − 1 1 W ( x ) g ( x ) d x ≈ ∑ i = 1 n w i g ( x i ) {\displaystyle \int _{-1}^{1}W(x)g(x)\,dx\approx \sum _{i=1}^{n}w_{i}g(x_{i})} In the case of Gauss-Legendre quadrature, the weighting function W ( x ) = 1 {\displaystyle W(x)=1} , so we can approximate an integral of f ( x ) {\displaystyle f(x)} with: ∫ − 1 1 f ( x ) d x ≈ ∑ i = 1 n w i f ( x i ) {\displaystyle \int _{-1}^{1}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i})} For this, we first need to calculate the nodes and the weights, but after we have them, we can reuse them for numerious integral evaluations, which greatly speeds up the calculation compared to more simple numerical integration methods. The n {\displaystyle n} evaluation points x i {\displaystyle x_{i}} for a n-point rule, also called "nodes", are roots of n-th order Legendre Polynomials P n ( x ) {\displaystyle P_{n}(x)} . Legendre polynomials are defined by the following recursive rule: P 0 ( x ) = 1 {\displaystyle P_{0}(x)=1} P 1 ( x ) = x {\displaystyle P_{1}(x)=x} n P n ( x ) = ( 2 n − 1 ) x P n − 1 ( x ) − ( n − 1 ) P n − 2 ( x ) {\displaystyle nP_{n}(x)=(2n-1)xP_{n-1}(x)-(n-1)P_{n-2}(x)} There is also a recursive equation for their derivative: P n ′ ( x ) = n x 2 − 1 ( x P n ( x ) − P n − 1 ( x ) ) {\displaystyle P_{n}'(x)={\frac {n}{x^{2}-1}}\left(xP_{n}(x)-P_{n-1}(x)\right)} The roots of those polynomials are in general not analytically solvable, so they have to be approximated numerically, for example by Newton-Raphson iteration: x n + 1 = x n − f ( x n ) f ′ ( x n ) {\displaystyle x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}} The first guess x 0 {\displaystyle x_{0}} for the i {\displaystyle i} -th root of a n {\displaystyle n} -order polynomial P n {\displaystyle P_{n}} can be given by x 0 = cos ⁡ ( π i − 1 4 n + 1 2 ) {\displaystyle x_{0}=\cos \left(\pi \,{\frac {i-{\frac {1}{4}}}{n+{\frac {1}{2}}}}\right)} After we get the nodes x i {\displaystyle x_{i}} , we compute the appropriate weights by: w i = 2 ( 1 − x i 2 ) [ P n ′ ( x i ) ] 2 {\displaystyle w_{i}={\frac {2}{\left(1-x_{i}^{2}\right)[P'_{n}(x_{i})]^{2}}}} After we have the nodes and the weights for a n-point quadrature rule, we can approximate an integral over any interval [ a , b ] {\displaystyle [a,b]} by ∫ a b f ( x ) d x ≈ b − a 2 ∑ i = 1 n w i f ( b − a 2 x i + a + b 2 ) {\displaystyle \int _{a}^{b}f(x)\,dx\approx {\frac {b-a}{2}}\sum _{i=1}^{n}w_{i}f\left({\frac {b-a}{2}}x_{i}+{\frac {a+b}{2}}\right)} Task description Similar to the task Numerical Integration, the task here is to calculate the definite integral of a function f ( x ) {\displaystyle f(x)} , but by applying an n-point Gauss-Legendre quadrature rule, as described here, for example. The input values should be an function f to integrate, the bounds of the integration interval a and b, and the number of gaussian evaluation points n. An reference implementation in Common Lisp is provided for comparison. To demonstrate the calculation, compute the weights and nodes for an 5-point quadrature rule and then use them to compute: ∫ − 3 3 exp ⁡ ( x ) d x ≈ ∑ i = 1 5 w i exp ⁡ ( x i ) ≈ 20.036 {\displaystyle \int _{-3}^{3}\exp(x)\,dx\approx \sum _{i=1}^{5}w_{i}\;\exp(x_{i})\approx 20.036}
#Perl
Perl
use List::Util qw(sum); use constant pi => 3.14159265;   sub legendre_pair { my($n, $x) = @_; if ($n == 1) { return $x, 1 } my ($m1, $m2) = legendre_pair($n - 1, $x); my $u = 1 - 1 / $n; (1 + $u) * $x * $m1 - $u * $m2, $m1; }   sub legendre { my($n, $x) = @_; (legendre_pair($n, $x))[0] }   sub legendre_prime { my($n, $x) = @_; if ($n == 0) { return 0 } if ($n == 1) { return 1 } my ($m0, $m1) = legendre_pair($n, $x); ($m1 - $x * $m0) * $n / (1 - $x**2); }   sub approximate_legendre_root { my($n, $k) = @_; my $t = (4*$k - 1) / (4*$n + 2); (1 - ($n - 1) / (8 * $n**3)) * cos(pi * $t); }   sub newton_raphson { my($n, $r) = @_; while (abs(my $dr = - legendre($n,$r) / legendre_prime($n,$r)) >= 2e-16) { $r += $dr; } $r; }   sub legendre_root { my($n, $k) = @_; newton_raphson($n, approximate_legendre_root($n, $k)); }   sub weight { my($n, $r) = @_; 2 / ((1 - $r**2) * legendre_prime($n, $r)**2) }   sub nodes { my($n) = @_; my %node; $node{'0'} = weight($n, 0) if 0 != $n%2; for (1 .. int $n/2) { my $r = legendre_root($n, $_); my $w = weight($n, $r); $node{$r} = $w; $node{-$r} = $w; } return %node }   sub quadrature { our($n, $a, $b) = @_; sub scale { ($_[0] * ($b - $a) + $a + $b) / 2 } %nodes = nodes($n); ($b - $a) / 2 * sum map { $nodes{$_} * exp(scale($_)) } keys %nodes; }   printf("Gauss-Legendre %2d-point quadrature ∫₋₃⁺³ exp(x) dx ≈ %.13f\n", $_, quadrature($_, -3, +3) ) for 5 .. 10, 20;  
http://rosettacode.org/wiki/Old_lady_swallowed_a_fly
Old lady swallowed a fly
Task Present a program which emits the lyrics to the song   I Knew an Old Lady Who Swallowed a Fly,   taking advantage of the repetitive structure of the song's lyrics. This song has multiple versions with slightly different lyrics, so all these programs might not emit identical output. Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Logo
Logo
make "data [ ; animal inc comment [fly 2 [I don't know why she swallowed that fly]] [spider 2 [That wriggled and jiggled and tickled inside her]] [bird 1 [Quite absurd, to swallow a bird]] [cat 1 [How about that, to swallow a cat]] [dog 1 [What a hog, to swallow a dog]] [pig 1 [Her mouth was so big to swallow a pig]] [goat 1 [She just opened her throat to swallow a goat.]] [cow 1 [I don't know how she swallowed a cow.]] [donkey 1 [It was rather wonky to swallow a donkey]] [horse 0 [She's dead, of course!]] ]   foreach :data [ local "i make "i # (local "animal "include "comment) (foreach [animal include comment] ? "make) print se [There was an old lady who swallowed a] :animal print :comment if greater? :include 0 [ if greater? :i 1 [ repeat difference :i 1 [ local "j make "j difference :i repcount print (se [She swallowed the] (first item sum 1 :j :data) [to catch the] (first item :j :data)) if greater? item 2 item :j :data 1 [print item 3 item :j :data] ] ] print [Perhaps she'll die] print " ] ]   bye
http://rosettacode.org/wiki/Old_lady_swallowed_a_fly
Old lady swallowed a fly
Task Present a program which emits the lyrics to the song   I Knew an Old Lady Who Swallowed a Fly,   taking advantage of the repetitive structure of the song's lyrics. This song has multiple versions with slightly different lyrics, so all these programs might not emit identical output. Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Lua
Lua
animals = {"fly", "spider", "bird", "cat","dog", "goat", "cow", "horse"} phrases = { "", "That wriggled and jiggled and tickled inside her", "How absurd to swallow a bird", "Fancy that to swallow a cat", "What a hog, to swallow a dog", "She just opened her throat and swallowed a goat", "I don't know how she swallowed a cow", " ...She's dead of course" }   for i=0,7 do io.write(string.format("There was an old lady who swallowed a %s\n", animals[i+1])) if i>0 then io.write(phrases[i+1]) end if i==7 then break end if i>0 then io.write("\n") for j=i,1,-1 do io.write(string.format("She swallowed the %s to catch the %s", animals[j+1], animals[j])) -- if j<4 then p='.' else p=',' end -- io.write(string.format("%s\n", p)) io.write("\n") if j==2 then io.write(string.format("%s!\n", phrases[2])) end end end io.write("I don't know why she swallowed a fly - Perhaps she'll die!\n\n") end
http://rosettacode.org/wiki/OpenGL
OpenGL
Task Display a smooth shaded triangle with OpenGL. Triangle created using C example compiled with GCC 4.1.2 and freeglut3.
#Tcl
Tcl
package require Tk package require tcl3d   proc resizedWin {win w h} { glViewport 0 0 $w $h glMatrixMode GL_PROJECTION glLoadIdentity glOrtho -30.0 30.0 -30.0 30.0 -30.0 30.0 glMatrixMode GL_MODELVIEW } proc paintShape {win} { glClearColor 0.0 0.0 0.0 0.5 glClear [expr {$::GL_COLOR_BUFFER_BIT+$::GL_DEPTH_BUFFER_BIT}] glShadeModel GL_SMOOTH glLoadIdentity glTranslatef -15.0 -15.0 0.0 glBegin GL_TRIANGLES glColor3f 1.0 0.0 0.0 glVertex2f 5.0 5.0 glColor3f 0.0 1.0 0.0 glVertex2f 25.0 5.0 glColor3f 0.0 0.0 1.0 glVertex2f 5.0 25.0 glEnd $win swapbuffers }   togl .surface -width 640 -height 480 -double true -depth true \ -displayproc paintShape -reshapeproc resizedWin pack .surface -fill both -expand 1
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#REXX
REXX
/*REXX program simulates reading a ten─line file, count the selection randomness. */ N= 10 /*the number of lines in pseudo-file. */ @.= 0 /*zero all the (ten) "buckets". */ do 1000000 /*perform main loop one million times.*/  ?= 1 do k=1 for N /*N is the number of lines in the file*/ if random(0, 99999) / 100000 < 1/k then ?= k /*the criteria.*/ end /*k*/ @.?= @.? + 1 /*bump the count in a particular bucket*/ end /*1000000*/   do j=1 for N /*display randomness counts (buckets). */ say "number of times line" right(j, 2) "was selected:" right(@.j, 9) end /*j*/ /*stick a fork in it, we're all done. */
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#Ring
Ring
  cnt = list(10) for nr = 1 to 10000 cnt[oneofn(10)] += 1 next for m = 1 to 10 see "" + m + " : " + cnt[m] + nl next see nl   func oneofn n for i = 1 to n if random(1) <= 1/i d = i ok next return d  
http://rosettacode.org/wiki/Optional_parameters
Optional parameters
Task Define a function/method/subroutine which sorts a sequence ("table") of sequences ("rows") of strings ("cells"), by one of the strings. Besides the input to be sorted, it shall have the following optional parameters: ordering A function specifying the ordering of strings; lexicographic by default. column An integer specifying which string of each row to compare; the first by default. reverse Reverses the ordering. This task should be considered to include both positional and named optional parameters, as well as overloading on argument count as in Java or selector name as in Smalltalk, or, in the extreme, using different function names. Provide these variations of sorting in whatever way is most natural to your language. If the language supports both methods naturally, you are encouraged to describe both. Do not implement a sorting algorithm; this task is about the interface. If you can't use a built-in sort routine, just omit the implementation (with a comment). See also: Named Arguments
#XSLT
XSLT
<xsl:template name="sort"> <xsl:param name="table" /> <xsl:param name="ordering" select="'lexicographic'" /> <xsl:param name="column" select="1" /> <xsl:param name="reversed" select="false()" /> ... </xsl:template>
http://rosettacode.org/wiki/Optional_parameters
Optional parameters
Task Define a function/method/subroutine which sorts a sequence ("table") of sequences ("rows") of strings ("cells"), by one of the strings. Besides the input to be sorted, it shall have the following optional parameters: ordering A function specifying the ordering of strings; lexicographic by default. column An integer specifying which string of each row to compare; the first by default. reverse Reverses the ordering. This task should be considered to include both positional and named optional parameters, as well as overloading on argument count as in Java or selector name as in Smalltalk, or, in the extreme, using different function names. Provide these variations of sorting in whatever way is most natural to your language. If the language supports both methods naturally, you are encouraged to describe both. Do not implement a sorting algorithm; this task is about the interface. If you can't use a built-in sort routine, just omit the implementation (with a comment). See also: Named Arguments
#Yabasic
Yabasic
sub power(n, p) if numparams = 1 p = 2 return n^p end sub   print power(2) print power(2, 3)
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#Rascal
Rascal
rascal>[2,1,3] < [5,2,1,3] bool: true
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#REXX
REXX
/*REXX program determines if a list < previous list, and returns true or false. */ @.=; @.1 = 1 2 1 5 2 @.2 = 1 2 1 5 2 2 @.3 = 1 2 3 4 5 @.4 = 1 2 3 4 5 /* [↓] compare a list to previous list*/ do j=2 while @.j\==''; p= j - 1 /*P: points to previous value in list.*/ if FNorder(@.p, @.j)=='true' then is= " < " /*use a more familiar glyph.*/ else is= " ≥ " /* " " " " " */ say say right('['@.p"]", 40) is '['@.j"]" end /*i*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ FNorder: procedure; parse arg x,y wx= words(x); wy= words(y) do k=1 for min(wx, wy) a= word(x, k) /*get a value from X. */ b= word(y, k) /* " " " " Y. */ if a<b then return 'true' else if a>b then return 'false' end /*k*/ if wx<wy then return 'true' /*handle case of equal (so far). */ return 'false' /* " " " " " " */
http://rosettacode.org/wiki/Ordered_words
Ordered words
An   ordered word   is a word in which the letters appear in alphabetic order. Examples include   abbey   and   dirt. Task[edit] Find and display all the ordered words in the dictionary   unixdict.txt   that have the longest word length. (Examples that access the dictionary file locally assume that you have downloaded this file yourself.) The display needs to be shown on this page. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Phixmonti
Phixmonti
include ..\Utilitys.pmt   0 var maxlen ( ) var words 0 var f   def getword f fgets dup -1 == if drop false else -1 del endif enddef def ordered? dup dup sort == enddef def greater? len maxlen > enddef   "unixdict.txt" "r" fopen var f f -1 != while getword dup if ordered? if greater? if len var maxlen ( ) var words endif len maxlen == if words over 0 put var words endif endif endif endwhile f fclose words print
http://rosettacode.org/wiki/Ordered_words
Ordered words
An   ordered word   is a word in which the letters appear in alphabetic order. Examples include   abbey   and   dirt. Task[edit] Find and display all the ordered words in the dictionary   unixdict.txt   that have the longest word length. (Examples that access the dictionary file locally assume that you have downloaded this file yourself.) The display needs to be shown on this page. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Picat
Picat
go => Dict = "unixdict.txt", Words = new_map([Word=Word.length : Word in read_file_lines(Dict), Word == Word.sort()]), MaxLen = max([Len : _Word=Len in Words]), println([Word : Word=Len in Words, Len=MaxLen].sort).
http://rosettacode.org/wiki/Palindrome_detection
Palindrome detection
A palindrome is a phrase which reads the same backward and forward. Task[edit] Write a function or program that checks whether a given sequence of characters (or, if you prefer, bytes) is a palindrome. For extra credit: Support Unicode characters. Write a second function (possibly as a wrapper to the first) which detects inexact palindromes, i.e. phrases that are palindromes if white-space and punctuation is ignored and case-insensitive comparison is used. Hints It might be useful for this task to know how to reverse a string. This task's entries might also form the subjects of the task Test a function. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#REXX
REXX
/*REXX pgm checks if phrase is palindromic; ignores the case of the letters. */ parse arg y /*get (optional) phrase from the C.L. */ if y='' then y='In girum imus nocte et consumimur igni' /*[↓] translation.*/ /*We walk around in the night and we are burnt by the fire (of love).*/ say 'string = ' y if isTpal(y) then say 'The string is a true palindrome.' else if isPal(y) then say 'The string is an inexact palindrome.' else say "The string isn't palindromic." exit /*stick a fork in it, we're all done. */ /*────────────────────────────────────────────────────────────────────────────*/ isTpal: return reverse(arg(1))==arg(1) isPal: return isTpal(translate(space(x,0)))
http://rosettacode.org/wiki/Numeric_error_propagation
Numeric error propagation
If   f,   a,   and   b   are values with uncertainties   σf,   σa,   and   σb,   and   c   is a constant; then if   f   is derived from   a,   b,   and   c   in the following ways, then   σf   can be calculated as follows: Addition/Subtraction If   f = a ± c,   or   f = c ± a   then   σf = σa If   f = a ± b   then   σf2 = σa2 + σb2 Multiplication/Division If   f = ca   or   f = ac       then   σf = |cσa| If   f = ab   or   f = a / b   then   σf2 = f2( (σa / a)2 + (σb / b)2) Exponentiation If   f = ac   then   σf = |fc(σa / a)| Caution: This implementation of error propagation does not address issues of dependent and independent values.   It is assumed that   a   and   b   are independent and so the formula for multiplication should not be applied to   a*a   for example.   See   the talk page   for some of the implications of this issue. Task details Add an uncertain number type to your language that can support addition, subtraction, multiplication, division, and exponentiation between numbers with an associated error term together with 'normal' floating point numbers without an associated error term. Implement enough functionality to perform the following calculations. Given coordinates and their errors: x1 = 100 ± 1.1 y1 = 50 ± 1.2 x2 = 200 ± 2.2 y2 = 100 ± 2.3 if point p1 is located at (x1, y1) and p2 is at (x2, y2); calculate the distance between the two points using the classic Pythagorean formula: d = √   (x1 - x2)²   +   (y1 - y2)²   Print and display both   d   and its error. References A Guide to Error Propagation B. Keeney, 2005. Propagation of uncertainty Wikipedia. Related task   Quaternion type
#Wren
Wren
class Approx { construct new(nu, sigma) { _nu = nu _sigma = sigma }   static new(a) { if (a is Approx) return Approx.new(a.nu, a.sigma) if (a is Num) return Approx.new(a, 0) }   nu { _nu } sigma { _sigma }   +(a) { if (a is Approx) return Approx.new(_nu + a.nu, (_sigma *_sigma + a.sigma*a.sigma).sqrt) if (a is Num) return Approx.new(_nu + a, _sigma) }   -(a) { if (a is Approx) return Approx.new(_nu - a.nu, (_sigma *_sigma + a.sigma*a.sigma).sqrt) if (a is Num) return Approx.new(_nu - a, _sigma) }   *(a) { if (a is Approx) { var v = _nu * a.nu return Approx.new(v, (v*v*_sigma*_sigma/(_nu*_nu) + a.sigma*a.sigma/(a.nu*a.nu)).sqrt) } if (a is Num) return Approx.new(_nu*a, (a*_sigma).abs) }   /(a) { if (a is Approx) { var v = _nu / a.nu return Approx.new(v, (v*v*_sigma*_sigma/(_nu*_nu) + a.sigma*a.sigma/(a.nu*a.nu)).sqrt) } if (a is Num) return Approx.new(_nu/a, (a*_sigma).abs) }   pow(d) { var v = _nu.pow(d) return Approx.new(v, (v*d*_sigma/_nu).abs) }   toString { "%(_nu) ±%(_sigma)" } }   var x1 = Approx.new(100, 1.1) var y1 = Approx.new( 50, 1.2) var x2 = Approx.new(200, 2.2) var y2 = Approx.new(100, 2.3) System.print(((x1 - x2).pow(2) + (y1 - y2).pow(2)).pow(0.5))
http://rosettacode.org/wiki/Odd_word_problem
Odd word problem
Task Write a program that solves the odd word problem with the restrictions given below. Description You are promised an input stream consisting of English letters and punctuations. It is guaranteed that: the words (sequence of consecutive letters) are delimited by one and only one punctuation, the stream will begin with a word, the words will be at least one letter long,   and a full stop (a period, [.]) appears after, and only after, the last word. Example A stream with six words: what,is,the;meaning,of:life. The task is to reverse the letters in every other word while leaving punctuations intact, producing: what,si,the;gninaem,of:efil. while observing the following restrictions: Only I/O allowed is reading or writing one character at a time, which means: no reading in a string, no peeking ahead, no pushing characters back into the stream, and no storing characters in a global variable for later use; You are not to explicitly save characters in a collection data structure, such as arrays, strings, hash tables, etc, for later reversal; You are allowed to use recursions, closures, continuations, threads, co-routines, etc., even if their use implies the storage of multiple characters. Test cases Work on both the   "life"   example given above, and also the text: we,are;not,in,kansas;any,more.
#Python
Python
from sys import stdin, stdout   def char_in(): return stdin.read(1) def char_out(c): stdout.write(c)   def odd(prev = lambda: None): a = char_in() if not a.isalpha(): prev() char_out(a) return a != '.'   # delay action until later, in the shape of a closure def clos(): char_out(a) prev()   return odd(clos)   def even(): while True: c = char_in() char_out(c) if not c.isalpha(): return c != '.'   e = False while odd() if e else even(): e = not e
http://rosettacode.org/wiki/Odd_word_problem
Odd word problem
Task Write a program that solves the odd word problem with the restrictions given below. Description You are promised an input stream consisting of English letters and punctuations. It is guaranteed that: the words (sequence of consecutive letters) are delimited by one and only one punctuation, the stream will begin with a word, the words will be at least one letter long,   and a full stop (a period, [.]) appears after, and only after, the last word. Example A stream with six words: what,is,the;meaning,of:life. The task is to reverse the letters in every other word while leaving punctuations intact, producing: what,si,the;gninaem,of:efil. while observing the following restrictions: Only I/O allowed is reading or writing one character at a time, which means: no reading in a string, no peeking ahead, no pushing characters back into the stream, and no storing characters in a global variable for later use; You are not to explicitly save characters in a collection data structure, such as arrays, strings, hash tables, etc, for later reversal; You are allowed to use recursions, closures, continuations, threads, co-routines, etc., even if their use implies the storage of multiple characters. Test cases Work on both the   "life"   example given above, and also the text: we,are;not,in,kansas;any,more.
#Quackery
Quackery
[ upper dup lower != ] is letter ( c --> b )   forward is backwords ( $ --> $ )   [ [ behead dup letter while emit again ] dup emit char . != if backwords ] is forwords ( $ --> $ )   [ [ behead dup letter while swap recurse rot emit ] dup emit char . != if forwords ] resolves backwords ( $ --> $ )   [ forwords drop cr ] is oddwords ( $ --> )   $ "we,are;not,in,kansas;any,more." oddwords $ "what,is,the;meaning,of:life." oddwords
http://rosettacode.org/wiki/Number_names
Number names
Task Show how to spell out a number in English. You can use a preexisting implementation or roll your own, but you should support inputs up to at least one million (or the maximum value of your language's default bounded integer type, if that's less). Support for inputs other than positive integers (like zero, negative integers, and floating-point numbers) is optional. Related task   Spelling of ordinal numbers.
#C.23
C#
using System;   class NumberNamer { static readonly string[] incrementsOfOne = { "zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen" };   static readonly string[] incrementsOfTen = { "", "", "twenty", "thirty", "fourty", "fifty", "sixty", "seventy", "eighty", "ninety" };   const string millionName = "million", thousandName = "thousand", hundredName = "hundred", andName = "and";     public static string GetName( int i ) { string output = ""; if( i >= 1000000 ) { output += ParseTriplet( i / 1000000 ) + " " + millionName; i %= 1000000; if( i == 0 ) return output; }   if( i >= 1000 ) { if( output.Length > 0 ) { output += ", "; } output += ParseTriplet( i / 1000 ) + " " + thousandName; i %= 1000; if( i == 0 ) return output; }   if( output.Length > 0 ) { output += ", "; } output += ParseTriplet( i ); return output; }     static string ParseTriplet( int i ) { string output = ""; if( i >= 100 ) { output += incrementsOfOne[i / 100] + " " + hundredName; i %= 100; if( i == 0 ) return output; }   if( output.Length > 0 ) { output += " " + andName + " "; } if( i >= 20 ) { output += incrementsOfTen[i / 10]; i %= 10; if( i == 0 ) return output; }   if( output.Length > 0 ) { output += " "; } output += incrementsOfOne[i]; return output; } }     class Program { // Test class static void Main( string[] args ) { Console.WriteLine( NumberNamer.GetName( 1 ) ); Console.WriteLine( NumberNamer.GetName( 234 ) ); Console.WriteLine( NumberNamer.GetName( 31337 ) ); Console.WriteLine( NumberNamer.GetName( 987654321 ) ); } }  
http://rosettacode.org/wiki/Number_reversal_game
Number reversal game
Task Given a jumbled list of the numbers   1   to   9   that are definitely   not   in ascending order. Show the list,   and then ask the player how many digits from the left to reverse. Reverse those digits,   then ask again,   until all the digits end up in ascending order. The score is the count of the reversals needed to attain the ascending order. Note: Assume the player's input does not need extra validation. Related tasks   Sorting algorithms/Pancake sort   Pancake sorting.   Topswops
#COBOL
COBOL
  IDENTIFICATION DIVISION. PROGRAM-ID. REVERSAL. AUTHOR. Bill Gunshannon INSTALLATION. Home. DATE-WRITTEN. 11 December 2021 **************************************************************** ** Program Abstract: ** Use a Knuth Shuffle to reate our out ot sort array. ** Use a procedure called "reverse" to pancake sort the array. ****************************************************************   DATA DIVISION. WORKING-STORAGE SECTION.   01 RNUM PIC 9. 01 TRIES PIC 99 VALUE 0. 01 ANSWER PIC 9(9) VALUE 123456789. 01 TBL-LEN PIC 9 VALUE 9. 01 TBL. 05 TZ PIC 9(9). 05 TA REDEFINES TZ PIC 9 OCCURS 9 TIMES.   PROCEDURE DIVISION.   MAIN-pROGRAM. MOVE ANSWER TO TBL   CALL 'KNUTH-SHUFFLE' USING BY REFERENCE TBL END-CALL.   DISPLAY "TABLE after shuffle: " TBL.   PERFORM UNTIL TBL = ANSWER ADD 1 TO TRIES DISPLAY "How many to reverse? " ACCEPT RNUM   CALL 'REVERSE' USING BY CONTENT RNUM, BY REFERENCE TBL END-CALL   DISPLAY "Try #" TRIES " " TBL END-PERFORM. DISPLAY "Congratulations. You did it!"   STOP RUN. END PROGRAM REVERSAL.     IDENTIFICATION DIVISION. PROGRAM-ID. KNUTH-SHUFFLE.   DATA DIVISION. LOCAL-STORAGE SECTION. 01 I PIC 9(9). 01 J PIC 9(9). 01 TEMP PIC 9(9). 01 tABLE-lEN PIC 9 value 9.   LINKAGE SECTION. 01 TTABLE-AREA. 03 TTABLE PIC 9 OCCURS 9 TIMES.   PROCEDURE DIVISION USING ttable-area. MOVE FUNCTION RANDOM(FUNCTION CURRENT-DATE (11:6)) TO I   PERFORM VARYING i FROM Table-Len BY -1 UNTIL i = 0 COMPUTE j = FUNCTION MOD(FUNCTION RANDOM * 10000, Table-Len) + 1   MOVE ttable (i) TO temp MOVE ttable (j) TO ttable (i) MOVE temp TO ttable (j) END-PERFORM.   GOBACK. END PROGRAM KNUTH-SHUFFLE.     IDENTIFICATION DIVISION. PROGRAM-ID. REVERSE.   DATA DIVISION. LOCAL-STORAGE SECTION. 01 I PIC 9. 01 J PIC 9. 01 X PIC 9. 01 LOOP-IDX PIC 9.     LINKAGE SECTION. 01 IDX PIC 9. 01 TTABLE-AREA. 03 TTABLE PIC 9 OCCURS 9 TIMES.   PROCEDURE DIVISION USING IDX, TTABLE-AREA.   DIVIDE IDX BY 2 GIVING LOOP-IDx     MOVE 1 TO I MOVE IDX TO J   PERFORM LOOP-IDX TIMES MOVE TTABLE(I) TO X MOVE TTABLE(J) TO TTABLE(I) MOVE X TO TTABLE(J) ADD 1 TO I SUBTRACT 1 FROM J END-PERFORM.   GOBACK. END PROGRAM REVERSE.  
http://rosettacode.org/wiki/Null_object
Null object
Null (or nil) is the computer science concept of an undefined or unbound object. Some languages have an explicit way to access the null object, and some don't. Some languages distinguish the null object from undefined values, and some don't. Task Show how to access null in your language by checking to see if an object is equivalent to the null object. This task is not about whether a variable is defined. The task is about "null"-like values in various languages, which may or may not be related to the defined-ness of variables in your language.
#Eiffel
Eiffel
  class APPLICATION inherit ARGUMENTS create make   feature {NONE} -- Initialization   make local i: INTEGER s: detachable STRING do if i = Void then print("i = Void") end if s = Void then print("s = Void") end end end
http://rosettacode.org/wiki/Null_object
Null object
Null (or nil) is the computer science concept of an undefined or unbound object. Some languages have an explicit way to access the null object, and some don't. Some languages distinguish the null object from undefined values, and some don't. Task Show how to access null in your language by checking to see if an object is equivalent to the null object. This task is not about whether a variable is defined. The task is about "null"-like values in various languages, which may or may not be related to the defined-ness of variables in your language.
#Elixir
Elixir
iex(1)> nil == :nil true iex(2)> is_nil(nil) true
http://rosettacode.org/wiki/One-dimensional_cellular_automata
One-dimensional cellular automata
Assume an array of cells with an initial distribution of live and dead cells, and imaginary cells off the end of the array having fixed values. Cells in the next generation of the array are calculated based on the value of the cell and its left and right nearest neighbours in the current generation. If, in the following table, a live cell is represented by 1 and a dead cell by 0 then to generate the value of the cell at a particular index in the array of cellular values you use the following table: 000 -> 0 # 001 -> 0 # 010 -> 0 # Dies without enough neighbours 011 -> 1 # Needs one neighbour to survive 100 -> 0 # 101 -> 1 # Two neighbours giving birth 110 -> 1 # Needs one neighbour to survive 111 -> 0 # Starved to death.
#ERRE
ERRE
  PROGRAM ONEDIM_AUTOMATA   ! for rosettacode.org !   !VAR I,J,N,W,K   !$DYNAMIC DIM X[0],X2[0]   BEGIN   DATA(20,0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0)   PRINT(CHR$(12);) N=20  ! number of generation required READ(W)  !$DIM X[W+1],X2[W+1] FOR I=1 TO W DO READ(X[I]) END FOR FOR K=1 TO N DO PRINT("Generation";K;TAB(16);) FOR J=1 TO W DO IF X[J]=1 THEN PRINT("#";) ELSE PRINT("_";) END IF IF X[J-1]+X[J]+X[J+1]=2 THEN X2[J]=1 ELSE X2[J]=0 END IF END FOR PRINT FOR J=1 TO W DO X[J]=X2[J] END FOR END FOR END PROGRAM  
http://rosettacode.org/wiki/One-dimensional_cellular_automata
One-dimensional cellular automata
Assume an array of cells with an initial distribution of live and dead cells, and imaginary cells off the end of the array having fixed values. Cells in the next generation of the array are calculated based on the value of the cell and its left and right nearest neighbours in the current generation. If, in the following table, a live cell is represented by 1 and a dead cell by 0 then to generate the value of the cell at a particular index in the array of cellular values you use the following table: 000 -> 0 # 001 -> 0 # 010 -> 0 # Dies without enough neighbours 011 -> 1 # Needs one neighbour to survive 100 -> 0 # 101 -> 1 # Two neighbours giving birth 110 -> 1 # Needs one neighbour to survive 111 -> 0 # Starved to death.
#Euphoria
Euphoria
include machine.e   function rules(integer tri) return tri = 3 or tri = 5 or tri = 6 end function   function next_gen(atom gen) atom new, bit new = rules(and_bits(gen,3)*2) -- work with the first bit separately bit = 2 while gen > 0 do new += bit*rules(and_bits(gen,7)) gen = floor(gen/2) -- shift right bit *= 2 -- shift left end while return new end function   constant char_clear = '_', char_filled = '#'   procedure print_gen(atom gen) puts(1, int_to_bits(gen,32) * (char_filled - char_clear) + char_clear) puts(1,'\n') end procedure   function s_to_gen(sequence s) s -= char_clear return bits_to_int(s) end function   atom gen, prev integer n   n = 0 prev = 0 gen = bits_to_int(rand(repeat(2,32))-1) while gen != prev do printf(1,"Generation %d: ",n) print_gen(gen) prev = gen gen = next_gen(gen) n += 1 end while   printf(1,"Generation %d: ",n) print_gen(gen)
http://rosettacode.org/wiki/Numerical_integration
Numerical integration
Write functions to calculate the definite integral of a function ƒ(x) using all five of the following methods: rectangular left right midpoint trapezium Simpson's composite Your functions should take in the upper and lower bounds (a and b), and the number of approximations to make in that range (n). Assume that your example already has a function that gives values for ƒ(x) . Simpson's method is defined by the following pseudo-code: Pseudocode: Simpson's method, composite procedure quad_simpson_composite(f, a, b, n) h := (b - a) / n sum1 := f(a + h/2) sum2 := 0 loop on i from 1 to (n - 1) sum1 := sum1 + f(a + h * i + h/2) sum2 := sum2 + f(a + h * i)   answer := (h / 6) * (f(a) + f(b) + 4*sum1 + 2*sum2) Demonstrate your function by showing the results for:   ƒ(x) = x3,       where   x   is     [0,1],       with           100 approximations.   The exact result is     0.25               (or 1/4)   ƒ(x) = 1/x,     where   x   is   [1,100],     with        1,000 approximations.   The exact result is     4.605170+     (natural log of 100)   ƒ(x) = x,         where   x   is   [0,5000],   with 5,000,000 approximations.   The exact result is   12,500,000   ƒ(x) = x,         where   x   is   [0,6000],   with 6,000,000 approximations.   The exact result is   18,000,000 See also   Active object for integrating a function of real time.   Special:PrefixIndex/Numerical integration for other integration methods.
#Fortran
Fortran
elemental function elemf(x) real :: elemf, x elemf = f(x) end function elemf
http://rosettacode.org/wiki/Numerical_integration/Gauss-Legendre_Quadrature
Numerical integration/Gauss-Legendre Quadrature
In a general Gaussian quadrature rule, an definite integral of f ( x ) {\displaystyle f(x)} is first approximated over the interval [ − 1 , 1 ] {\displaystyle [-1,1]} by a polynomial approximable function g ( x ) {\displaystyle g(x)} and a known weighting function W ( x ) {\displaystyle W(x)} . ∫ − 1 1 f ( x ) d x = ∫ − 1 1 W ( x ) g ( x ) d x {\displaystyle \int _{-1}^{1}f(x)\,dx=\int _{-1}^{1}W(x)g(x)\,dx} Those are then approximated by a sum of function values at specified points x i {\displaystyle x_{i}} multiplied by some weights w i {\displaystyle w_{i}} : ∫ − 1 1 W ( x ) g ( x ) d x ≈ ∑ i = 1 n w i g ( x i ) {\displaystyle \int _{-1}^{1}W(x)g(x)\,dx\approx \sum _{i=1}^{n}w_{i}g(x_{i})} In the case of Gauss-Legendre quadrature, the weighting function W ( x ) = 1 {\displaystyle W(x)=1} , so we can approximate an integral of f ( x ) {\displaystyle f(x)} with: ∫ − 1 1 f ( x ) d x ≈ ∑ i = 1 n w i f ( x i ) {\displaystyle \int _{-1}^{1}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i})} For this, we first need to calculate the nodes and the weights, but after we have them, we can reuse them for numerious integral evaluations, which greatly speeds up the calculation compared to more simple numerical integration methods. The n {\displaystyle n} evaluation points x i {\displaystyle x_{i}} for a n-point rule, also called "nodes", are roots of n-th order Legendre Polynomials P n ( x ) {\displaystyle P_{n}(x)} . Legendre polynomials are defined by the following recursive rule: P 0 ( x ) = 1 {\displaystyle P_{0}(x)=1} P 1 ( x ) = x {\displaystyle P_{1}(x)=x} n P n ( x ) = ( 2 n − 1 ) x P n − 1 ( x ) − ( n − 1 ) P n − 2 ( x ) {\displaystyle nP_{n}(x)=(2n-1)xP_{n-1}(x)-(n-1)P_{n-2}(x)} There is also a recursive equation for their derivative: P n ′ ( x ) = n x 2 − 1 ( x P n ( x ) − P n − 1 ( x ) ) {\displaystyle P_{n}'(x)={\frac {n}{x^{2}-1}}\left(xP_{n}(x)-P_{n-1}(x)\right)} The roots of those polynomials are in general not analytically solvable, so they have to be approximated numerically, for example by Newton-Raphson iteration: x n + 1 = x n − f ( x n ) f ′ ( x n ) {\displaystyle x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}} The first guess x 0 {\displaystyle x_{0}} for the i {\displaystyle i} -th root of a n {\displaystyle n} -order polynomial P n {\displaystyle P_{n}} can be given by x 0 = cos ⁡ ( π i − 1 4 n + 1 2 ) {\displaystyle x_{0}=\cos \left(\pi \,{\frac {i-{\frac {1}{4}}}{n+{\frac {1}{2}}}}\right)} After we get the nodes x i {\displaystyle x_{i}} , we compute the appropriate weights by: w i = 2 ( 1 − x i 2 ) [ P n ′ ( x i ) ] 2 {\displaystyle w_{i}={\frac {2}{\left(1-x_{i}^{2}\right)[P'_{n}(x_{i})]^{2}}}} After we have the nodes and the weights for a n-point quadrature rule, we can approximate an integral over any interval [ a , b ] {\displaystyle [a,b]} by ∫ a b f ( x ) d x ≈ b − a 2 ∑ i = 1 n w i f ( b − a 2 x i + a + b 2 ) {\displaystyle \int _{a}^{b}f(x)\,dx\approx {\frac {b-a}{2}}\sum _{i=1}^{n}w_{i}f\left({\frac {b-a}{2}}x_{i}+{\frac {a+b}{2}}\right)} Task description Similar to the task Numerical Integration, the task here is to calculate the definite integral of a function f ( x ) {\displaystyle f(x)} , but by applying an n-point Gauss-Legendre quadrature rule, as described here, for example. The input values should be an function f to integrate, the bounds of the integration interval a and b, and the number of gaussian evaluation points n. An reference implementation in Common Lisp is provided for comparison. To demonstrate the calculation, compute the weights and nodes for an 5-point quadrature rule and then use them to compute: ∫ − 3 3 exp ⁡ ( x ) d x ≈ ∑ i = 1 5 w i exp ⁡ ( x i ) ≈ 20.036 {\displaystyle \int _{-3}^{3}\exp(x)\,dx\approx \sum _{i=1}^{5}w_{i}\;\exp(x_{i})\approx 20.036}
#Phix
Phix
with javascript_semantics integer order = 0 sequence legendreRoots = {}, legendreWeights = {} function legendre(integer term, atom z) if term=0 then return 1 elsif term=1 then return z else return ((2*term-1)*z*legendre(term-1,z)-(term-1)*legendre(term-2,z))/term end if end function function legendreDerivative(integer term, atom z) if term=0 or term=1 then return term end if return (term*(z*legendre(term,z)-legendre(term-1,z)))/(z*z-1) end function procedure getLegendreRoots() legendreRoots = {} for index=1 to order do atom y = cos(PI*(index-0.25)/(order+0.5)) while 1 do atom y1 = y y -= legendre(order,y)/legendreDerivative(order,y) if abs(y-y1)<2e-16 then exit end if end while legendreRoots &= y end for end procedure procedure getLegendreWeights() legendreWeights = {} for index=1 to order do atom lri = legendreRoots[index], diff = legendreDerivative(order,lri), weight = 2 / ((1-power(lri,2))*power(diff,2)) legendreWeights &= weight end for end procedure function gaussLegendreQuadrature(integer f, lowerLimit, upperLimit, n) order = n getLegendreRoots() getLegendreWeights() atom c1 = (upperLimit - lowerLimit) / 2 atom c2 = (upperLimit + lowerLimit) / 2 atom s = 0 for i = 1 to order do s += legendreWeights[i] * f(c1 * legendreRoots[i] + c2) end for return c1 * s end function string fmt = iff(machine_bits()=32?"%.13f":"%.14f"), res for i=5 to 11 by 6 do res = sprintf(fmt,{gaussLegendreQuadrature(exp, -3, 3, i)}) if i=5 then puts(1,"roots:") ?legendreRoots puts(1,"weights:") ?legendreWeights end if printf(1,"Gauss-Legendre %2d-point quadrature for exp over [-3..3] = %s\n",{order,res}) end for res = sprintf(fmt,{exp(3)-exp(-3)}) printf(1," compared to actual = %s\n",{res})
http://rosettacode.org/wiki/Old_lady_swallowed_a_fly
Old lady swallowed a fly
Task Present a program which emits the lyrics to the song   I Knew an Old Lady Who Swallowed a Fly,   taking advantage of the repetitive structure of the song's lyrics. This song has multiple versions with slightly different lyrics, so all these programs might not emit identical output. Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#MAD
MAD
NORMAL MODE IS INTEGER   INTERNAL FUNCTION(V) ENTRY TO VERSE. TRANSFER TO VS(V+1) VS(1) PRINT COMMENT$ I DON'T KNOW WHY SHE SWALLOWED THAT FLY$ PRINT COMMENT$ PERHAPS SHE'LL DIE$ PRINT COMMENT$ $ FUNCTION RETURN V VS(2) PRINT COMMENT 0 $ THAT WIGGLED AND JIGGLED AND TICKLED INSIDE HER$ FUNCTION RETURN V VS(3) PRINT COMMENT$ HOW ABSURD TO SWALLOW A BIRD!$ FUNCTION RETURN V VS(4) PRINT COMMENT$ IMAGINE THAT - SHE SWALLOWED A CAT!$ FUNCTION RETURN V VS(5) PRINT COMMENT$ WHAT A HOG TO SWALLOW A DOG$ FUNCTION RETURN V VS(6) PRINT COMMENT 0 $ SHE JUST OPENED HER THROAT AND SWALLOWED THAT GOAT$ FUNCTION RETURN V VS(7) PRINT COMMENT$ I DON'T KNOW HOW SHE SWALLOWED THAT COW$ FUNCTION RETURN V VS(8) PRINT COMMENT$ SHE'S DEAD, OF COURSE.$ END OF FUNCTION   VECTOR VALUES ANIMAL = 0 $FLY$,$SPIDER$,$BIRD$,$CAT$,$DOG$,$GOAT$,$COW$,$HORSE$   VECTOR VALUES LADY = 0 $38HTHERE WAS AN OLD LADY WHO SWALLOWED A ,C,1H,*$   VECTOR VALUES SWALLO = 0 $18HSHE SWALLOWED THE ,C,S1,13HTO CATCH THE ,C,1H,*$   THROUGH VERSE, FOR I=0, 1, I.G.7 PRINT FORMAT LADY, ANIMAL(I) VERSE.(I) THROUGH VERSE, FOR J=I, -1, J.E.0 .OR. I.GE.7 PRINT FORMAT SWALLO, ANIMAL(J), ANIMAL(J-1) VERSE WHENEVER J.LE.2, VERSE.(J-1)   END OF PROGRAM
http://rosettacode.org/wiki/Old_lady_swallowed_a_fly
Old lady swallowed a fly
Task Present a program which emits the lyrics to the song   I Knew an Old Lady Who Swallowed a Fly,   taking advantage of the repetitive structure of the song's lyrics. This song has multiple versions with slightly different lyrics, so all these programs might not emit identical output. Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Maple
Maple
swallowed := ["fly", "spider", "bird", "cat", "dog", "cow", "horse"]: phrases := ["I don't know why she swallowed a fly, perhaps she'll die!", "That wriggled and wiggled and tiggled inside her.", "How absurd to swallow a bird.", "Fancy that to swallow a cat!", "What a hog, to swallow a dog.", "I don't know how she swallowed a cow.", "She's dead, of course."]: for i to numelems(swallowed) do printf("There was an old lady who swallowed a %s.\n%s\n", swallowed[i], phrases[i]); if i > 1 and i < 7 then for j from i by -1 to 2 do printf("\tShe swallowed the %s to catch the %s.\n", swallowed[j], swallowed[j-1]); end do; printf("%s\n\n", phrases[1]); elif i = 1 then printf("\n"); end if; end do;
http://rosettacode.org/wiki/OpenGL
OpenGL
Task Display a smooth shaded triangle with OpenGL. Triangle created using C example compiled with GCC 4.1.2 and freeglut3.
#Wren
Wren
/* opengl.wren */   var GL_COLOR_BUFFER_BIT = 0x4000 var GL_DEPTH_BUFFER_BIT = 0x0100   var GL_SMOOTH = 0x1d01 var GL_MODELVIEW = 0x1700 var GL_PROJECTION = 0x1701   var GL_TRIANGLES = 0x0004   var GLUT_ACTION_ON_WINDOW_CLOSE = 0x01f9 var GLUT_ACTION_GLUTMAINLOOP_RETURNS = 0x0001   class GL { foreign static clearColor(red, green, blue, alpha)   foreign static clear(mask)   foreign static shadeModel(mode)   foreign static loadIdentity()   foreign static translatef(x, y, z)   foreign static begin(mode)   foreign static color3f(red, green, blue)   foreign static vertex2f(x, y)   foreign static end()   foreign static flush()   foreign static viewport(x, y, width, height)   foreign static matrixMode(mode)   foreign static ortho(left, right, bottom, top, nearVal, farVal) }   class Glut { foreign static initWindowSize(width, height)   foreign static createWindow(name)   foreign static displayFunc(clazz, signature)   foreign static reshapeFunc(clazz, signature)   foreign static setOption(eWhat, value) }   class GLCallbacks { static paint() { GL.clearColor(0.3, 0.3, 0.3, 0) GL.clear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT) GL.shadeModel(GL_SMOOTH) GL.loadIdentity() GL.translatef(-15, -15, 0) GL.begin(GL_TRIANGLES) GL.color3f(1, 0, 0) GL.vertex2f(0, 0) GL.color3f(0, 1, 0) GL.vertex2f(30, 0) GL.color3f(0, 0, 1) GL.vertex2f(0, 30) GL.end() GL.flush() }   static reshape(width, height) { GL.viewport(0, 0, width, height) GL.matrixMode(GL_PROJECTION) GL.loadIdentity() GL.ortho(-30, 30, -30, 30, -30, 30) GL.matrixMode(GL_MODELVIEW) } }   Glut.initWindowSize(640, 480) Glut.createWindow("Triangle") Glut.displayFunc("GLCallbacks", "paint()") Glut.reshapeFunc("GLCallbacks", "reshape(_,_)") Glut.setOption(GLUT_ACTION_ON_WINDOW_CLOSE, GLUT_ACTION_GLUTMAINLOOP_RETURNS)
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#Ruby
Ruby
# Returns a random line from _io_, or nil if _io_ has no lines. # # Get a random line from /etc/passwd # line = open("/etc/passwd") {|f| random_line(f) } def random_line(io) choice = io.gets; count = 1 while line = io.gets rand(count += 1).zero? and choice = line end choice end   def one_of_n(n) # Create a mock IO that provides line numbers instead of lines. # Assumes that #random_line calls #gets. (mock_io = Object.new).instance_eval do @count = 0 @last = n def self.gets (@count < @last) ? (@count += 1) : nil end end random_line(mock_io) end   chosen = Hash.new(0) 1_000_000.times { chosen[one_of_n(10)] += 1 } chosen.keys.sort.each do |key| puts "#{key} chosen #{chosen[key]} times" end
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#Run_BASIC
Run BASIC
for i1 = 1 to 1000000 c = oneOfN(10) chosen(c) = chosen(c) + 1 next   for i1 = 1 to 10 print i1;" ";chosen(i1) next   FUNCTION oneOfN(n) for i2 = 1 to n IF int(rnd(1) * i2) = 0 then choice = i2 next oneOfN = choice END FUNCTION
http://rosettacode.org/wiki/Optional_parameters
Optional parameters
Task Define a function/method/subroutine which sorts a sequence ("table") of sequences ("rows") of strings ("cells"), by one of the strings. Besides the input to be sorted, it shall have the following optional parameters: ordering A function specifying the ordering of strings; lexicographic by default. column An integer specifying which string of each row to compare; the first by default. reverse Reverses the ordering. This task should be considered to include both positional and named optional parameters, as well as overloading on argument count as in Java or selector name as in Smalltalk, or, in the extreme, using different function names. Provide these variations of sorting in whatever way is most natural to your language. If the language supports both methods naturally, you are encouraged to describe both. Do not implement a sorting algorithm; this task is about the interface. If you can't use a built-in sort routine, just omit the implementation (with a comment). See also: Named Arguments
#zkl
zkl
const lex="L"; fcn mystrySort(table,ordering=lex,column=0,reverse=False,other){ vm.arglist.println(); } mystrySort.prototype.println(); mystrySort("table"); mystrySort("table",lex,1); mystrySort("table",lex,1,True,D("row",35,"type","foobar"));    
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#Ring
Ring
  list1 = "1, 2, 1, 5, 2" list2 = "5, 2, 1, 5, 2, 2" list3 = "1, 2, 3, 4, 5" list4 = "1, 2, 3, 4, 5"   if order(list1, list2) = 0 see "list1=list2" + nl but order(list1, list2) < 0 see "list1<list2" + nl else see "list1>list2" + nl ok   if order(list2, list3) = 0 see "list2=list3" + nl but order(list2, list3) < 0 see "list2<list3" + nl else see "list2>list3" + nl ok   if order(list3, list4) = 0 see "list3=list4" + nl but order(list3, list4) < 0 see "list3<list4" + nl else see "list3>list4" + nl ok   func order alist, blist return strcmp(alist, blist)  
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#Ruby
Ruby
>> ([1,2,1,3,2] <=> [1,2,0,4,4,0,0,0]) < 0 => false
http://rosettacode.org/wiki/Ordered_words
Ordered words
An   ordered word   is a word in which the letters appear in alphabetic order. Examples include   abbey   and   dirt. Task[edit] Find and display all the ordered words in the dictionary   unixdict.txt   that have the longest word length. (Examples that access the dictionary file locally assume that you have downloaded this file yourself.) The display needs to be shown on this page. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#PicoLisp
PicoLisp
(in "unixdict.txt" (mapc prinl (maxi '((L) (length (car L))) (by length group (filter '((S) (apply <= S)) (make (while (line) (link @))) ) ) ) ) )
http://rosettacode.org/wiki/Palindrome_detection
Palindrome detection
A palindrome is a phrase which reads the same backward and forward. Task[edit] Write a function or program that checks whether a given sequence of characters (or, if you prefer, bytes) is a palindrome. For extra credit: Support Unicode characters. Write a second function (possibly as a wrapper to the first) which detects inexact palindromes, i.e. phrases that are palindromes if white-space and punctuation is ignored and case-insensitive comparison is used. Hints It might be useful for this task to know how to reverse a string. This task's entries might also form the subjects of the task Test a function. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Ring
Ring
  aString = "radar" bString = "" for i=len(aString) to 1 step -1 bString = bString + aString[i] next see aString if aString = bString see " is a palindrome." + nl else see " is not a palindrome" + nl ok  
http://rosettacode.org/wiki/Odd_word_problem
Odd word problem
Task Write a program that solves the odd word problem with the restrictions given below. Description You are promised an input stream consisting of English letters and punctuations. It is guaranteed that: the words (sequence of consecutive letters) are delimited by one and only one punctuation, the stream will begin with a word, the words will be at least one letter long,   and a full stop (a period, [.]) appears after, and only after, the last word. Example A stream with six words: what,is,the;meaning,of:life. The task is to reverse the letters in every other word while leaving punctuations intact, producing: what,si,the;gninaem,of:efil. while observing the following restrictions: Only I/O allowed is reading or writing one character at a time, which means: no reading in a string, no peeking ahead, no pushing characters back into the stream, and no storing characters in a global variable for later use; You are not to explicitly save characters in a collection data structure, such as arrays, strings, hash tables, etc, for later reversal; You are allowed to use recursions, closures, continuations, threads, co-routines, etc., even if their use implies the storage of multiple characters. Test cases Work on both the   "life"   example given above, and also the text: we,are;not,in,kansas;any,more.
#Racket
Racket
  #!/bin/sh #| exec racket -tm- "$0" "$@" |#   #lang racket   (define (even k) (define c (read-char)) (cond [(eq? c eof) (k)] [(not (char-alphabetic? c)) (k) (write-char c) (odd)] [else (even (λ() (write-char c) (k)))]))   (define (odd) (define c (read-char)) (unless (eq? c eof) (write-char c) (if (char-alphabetic? c) (odd) (even void))))   (provide main) (define (main) (odd) (newline))   ;; (with-input-from-string "what,is,the;meaning,of:life." main) ;; ;; -> what,si,the;gninaem,of:efil. ;; (with-input-from-string "we,are;not,in,kansas;any,more." main) ;; ;; -> we,era;not,ni,kansas;yna,more.  
http://rosettacode.org/wiki/Odd_word_problem
Odd word problem
Task Write a program that solves the odd word problem with the restrictions given below. Description You are promised an input stream consisting of English letters and punctuations. It is guaranteed that: the words (sequence of consecutive letters) are delimited by one and only one punctuation, the stream will begin with a word, the words will be at least one letter long,   and a full stop (a period, [.]) appears after, and only after, the last word. Example A stream with six words: what,is,the;meaning,of:life. The task is to reverse the letters in every other word while leaving punctuations intact, producing: what,si,the;gninaem,of:efil. while observing the following restrictions: Only I/O allowed is reading or writing one character at a time, which means: no reading in a string, no peeking ahead, no pushing characters back into the stream, and no storing characters in a global variable for later use; You are not to explicitly save characters in a collection data structure, such as arrays, strings, hash tables, etc, for later reversal; You are allowed to use recursions, closures, continuations, threads, co-routines, etc., even if their use implies the storage of multiple characters. Test cases Work on both the   "life"   example given above, and also the text: we,are;not,in,kansas;any,more.
#Raku
Raku
my &in = { $*IN.getc // last }   loop { ew(in); ow(in).print; }   multi ew ($_ where /\w/) { .print; ew(in); } multi ew ($_) { .print; next when "\n"; }   multi ow ($_ where /\w/) { ow(in) x .print; } multi ow ($_) { $_; }
http://rosettacode.org/wiki/Number_names
Number names
Task Show how to spell out a number in English. You can use a preexisting implementation or roll your own, but you should support inputs up to at least one million (or the maximum value of your language's default bounded integer type, if that's less). Support for inputs other than positive integers (like zero, negative integers, and floating-point numbers) is optional. Related task   Spelling of ordinal numbers.
#C.2B.2B
C++
#include <string> #include <iostream> using std::string;   const char* smallNumbers[] = { "zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen" };   string spellHundreds(unsigned n) { string res; if (n > 99) { res = smallNumbers[n/100]; res += " hundred"; n %= 100; if (n) res += " and "; } if (n >= 20) { static const char* Decades[] = { "", "", "twenty", "thirty", "forty", "fifty", "sixty", "seventy", "eighty", "ninety" }; res += Decades[n/10]; n %= 10; if (n) res += "-"; } if (n < 20 && n > 0) res += smallNumbers[n]; return res; }     const char* thousandPowers[] = { " billion", " million", " thousand", "" };   typedef unsigned long Spellable;   string spell(Spellable n) { if (n < 20) return smallNumbers[n]; string res; const char** pScaleName = thousandPowers; Spellable scaleFactor = 1000000000; // 1 billion while (scaleFactor > 0) { if (n >= scaleFactor) { Spellable h = n / scaleFactor; res += spellHundreds(h) + *pScaleName; n %= scaleFactor; if (n) res += ", "; } scaleFactor /= 1000; ++pScaleName; } return res; }   int main() { #define SPELL_IT(x) std::cout << #x " " << spell(x) << std::endl; SPELL_IT( 99); SPELL_IT( 300); SPELL_IT( 310); SPELL_IT( 1501); SPELL_IT( 12609); SPELL_IT( 512609); SPELL_IT(43112609); SPELL_IT(1234567890); return 0; }
http://rosettacode.org/wiki/Number_reversal_game
Number reversal game
Task Given a jumbled list of the numbers   1   to   9   that are definitely   not   in ascending order. Show the list,   and then ask the player how many digits from the left to reverse. Reverse those digits,   then ask again,   until all the digits end up in ascending order. The score is the count of the reversals needed to attain the ascending order. Note: Assume the player's input does not need extra validation. Related tasks   Sorting algorithms/Pancake sort   Pancake sorting.   Topswops
#Common_Lisp
Common Lisp
(defun shuffle! (vector) (loop for i from (1- (length vector)) downto 1 do (rotatef (aref vector i) (aref vector (random i)))))   (defun slice (vector start &optional end) (let ((end (or end (length vector)))) (make-array (- end start) :element-type (array-element-type vector) :displaced-to vector :displaced-index-offset start)))   (defun orderedp (seq) (apply #'<= (coerce seq 'list)))   (defun prompt-integer (prompt) (format t "~A: " prompt) (finish-output) (clear-input) (parse-integer (read-line)))   (defun game () (let ((numbers (vector 1 2 3 4 5 6 7 8 9))) (shuffle! numbers) (let ((score (do ((score 0 (1+ score))) ((orderedp numbers) score) (format t "~A~%" numbers) (let* ((n (prompt-integer "How many numbers to reverse")) (slice (slice numbers 0 n))) (replace slice (nreverse slice)))))) (format t "~A~%Congratulations, you did it in ~D reversals!~%" numbers score))))  
http://rosettacode.org/wiki/Null_object
Null object
Null (or nil) is the computer science concept of an undefined or unbound object. Some languages have an explicit way to access the null object, and some don't. Some languages distinguish the null object from undefined values, and some don't. Task Show how to access null in your language by checking to see if an object is equivalent to the null object. This task is not about whether a variable is defined. The task is about "null"-like values in various languages, which may or may not be related to the defined-ness of variables in your language.
#Erlang
Erlang
let sl : string list = [null; "abc"]   let f s = match s with | null -> "It is null!" | _ -> "It's non-null: " + s   for s in sl do printfn "%s" (f s)
http://rosettacode.org/wiki/Null_object
Null object
Null (or nil) is the computer science concept of an undefined or unbound object. Some languages have an explicit way to access the null object, and some don't. Some languages distinguish the null object from undefined values, and some don't. Task Show how to access null in your language by checking to see if an object is equivalent to the null object. This task is not about whether a variable is defined. The task is about "null"-like values in various languages, which may or may not be related to the defined-ness of variables in your language.
#F.23
F#
let sl : string list = [null; "abc"]   let f s = match s with | null -> "It is null!" | _ -> "It's non-null: " + s   for s in sl do printfn "%s" (f s)
http://rosettacode.org/wiki/One-dimensional_cellular_automata
One-dimensional cellular automata
Assume an array of cells with an initial distribution of live and dead cells, and imaginary cells off the end of the array having fixed values. Cells in the next generation of the array are calculated based on the value of the cell and its left and right nearest neighbours in the current generation. If, in the following table, a live cell is represented by 1 and a dead cell by 0 then to generate the value of the cell at a particular index in the array of cellular values you use the following table: 000 -> 0 # 001 -> 0 # 010 -> 0 # Dies without enough neighbours 011 -> 1 # Needs one neighbour to survive 100 -> 0 # 101 -> 1 # Two neighbours giving birth 110 -> 1 # Needs one neighbour to survive 111 -> 0 # Starved to death.
#Factor
Factor
USING: bit-arrays io kernel locals math sequences ; IN: cellular   : bool-sum ( bool1 bool2 -- sum ) [ [ 2 ] [ 1 ] if ] [ [ 1 ] [ 0 ] if ] if ; :: neighbours ( index world -- # ) index [ 1 - ] [ 1 + ] bi [ world ?nth ] bi@ bool-sum ; : count-neighbours ( world -- neighbours ) [ length iota ] keep [ neighbours ] curry map ;   : life-law ( alive? neighbours -- alive? ) swap [ 1 = ] [ 2 = ] if ; : step ( world -- world' ) dup count-neighbours [ life-law ] ?{ } 2map-as ; : print-cellular ( world -- ) [ CHAR: # CHAR: _ ? ] "" map-as print ; : main-cellular ( -- )  ?{ f t t t f t t f t f t f t f t f f t f f } 10 [ dup print-cellular step ] times print-cellular ; MAIN: main-cellular  
http://rosettacode.org/wiki/Numerical_integration
Numerical integration
Write functions to calculate the definite integral of a function ƒ(x) using all five of the following methods: rectangular left right midpoint trapezium Simpson's composite Your functions should take in the upper and lower bounds (a and b), and the number of approximations to make in that range (n). Assume that your example already has a function that gives values for ƒ(x) . Simpson's method is defined by the following pseudo-code: Pseudocode: Simpson's method, composite procedure quad_simpson_composite(f, a, b, n) h := (b - a) / n sum1 := f(a + h/2) sum2 := 0 loop on i from 1 to (n - 1) sum1 := sum1 + f(a + h * i + h/2) sum2 := sum2 + f(a + h * i)   answer := (h / 6) * (f(a) + f(b) + 4*sum1 + 2*sum2) Demonstrate your function by showing the results for:   ƒ(x) = x3,       where   x   is     [0,1],       with           100 approximations.   The exact result is     0.25               (or 1/4)   ƒ(x) = 1/x,     where   x   is   [1,100],     with        1,000 approximations.   The exact result is     4.605170+     (natural log of 100)   ƒ(x) = x,         where   x   is   [0,5000],   with 5,000,000 approximations.   The exact result is   12,500,000   ƒ(x) = x,         where   x   is   [0,6000],   with 6,000,000 approximations.   The exact result is   18,000,000 See also   Active object for integrating a function of real time.   Special:PrefixIndex/Numerical integration for other integration methods.
#FreeBASIC
FreeBASIC
' version 17-09-2015 ' compile with: fbc -s console   #Define screen_width 1024 #Define screen_height 256 ScreenRes screen_width, screen_height, 8 Width screen_width\8, screen_height\16   Function f1(x As Double) As Double Return x^3 End Function   Function f2(x As Double) As Double Return 1/x End Function   Function f3(x As Double) As Double Return x End Function   Function leftrect(a As Double, b As Double, n As Double, _ ByVal f As Function (ByVal As Double) As Double) As Double   Dim As Double sum, x = a, h = (b - a) / n   For i As UInteger = 1 To n sum = sum + h * f(x) x = x + h Next   leftrect = sum End Function   Function rightrect(a As Double, b As Double, n As Double, _ ByVal f As Function (ByVal As Double) As Double) As Double   Dim As Double sum, x = a, h = (b - a) / n   For i As UInteger = 1 To n x = x + h sum = sum + h * f(x) Next   rightrect = sum End Function   Function midrect(a As Double, b As Double, n As Double, _ ByVal f As Function (ByVal As Double) As Double) As Double   Dim As Double sum, h = (b - a) / n, x = a + h / 2   For i As UInteger = 1 To n sum = sum + h * f(x) x = x + h Next   midrect = sum End Function   Function trap(a As Double, b As Double, n As Double, _ ByVal f As Function (ByVal As Double) As Double) As Double   Dim As Double x = a, h = (b - a) / n Dim As Double sum = h * (f(a) + f(b)) / 2   For i As UInteger = 1 To n -1 x = x + h sum = sum + h * f(x) Next   trap = sum End Function   Function simpson(a As Double, b As Double, n As Double, _ ByVal f As Function (ByVal As Double) As Double) As Double   Dim As UInteger i Dim As Double sum1, sum2 Dim As Double h = (b - a) / n   For i = 0 To n -1 sum1 = sum1 + f(a + h * i + h / 2) Next i   For i = 1 To n -1 sum2 = sum2 + f(a + h * i) Next i   simpson = h / 6 * (f(a) + f(b) + 4 * sum1 + 2 * sum2) End Function   ' ------=< main >=------   Dim As Double y Dim As String frmt = " ##.##########"   Print Print "function range steps leftrect midrect " + _ "rightrect trap simpson "   Print "f(x) = x^3 0 - 1 100"; Print Using frmt; leftrect(0, 1, 100, @f1); midrect(0, 1, 100, @f1); _ rightrect(0, 1, 100, @f1); trap(0, 1, 100, @f1); simpson(0, 1, 100, @f1)   Print "f(x) = 1/x 1 - 100 1000"; Print Using frmt; leftrect(1, 100, 1000, @f2); midrect(1, 100, 1000, @f2); _ rightrect(1, 100, 1000, @f2); trap(1, 100, 1000, @f2); _ simpson(1, 100, 1000, @f2)   frmt = " #########.###" Print "f(x) = x 0 - 5000 5000000"; Print Using frmt; leftrect(0, 5000, 5000000, @f3); midrect(0, 5000, 5000000, @f3); _ rightrect(0, 5000, 5000000, @f3); trap(0, 5000, 5000000, @f3); _ simpson(0, 5000, 5000000, @f3)   Print "f(x) = x 0 - 6000 6000000"; Print Using frmt; leftrect(0, 6000, 6000000, @f3); midrect(0, 6000, 6000000, @f3); _ rightrect(0, 6000, 6000000, @f3); trap(0, 6000, 6000000, @f3); _ simpson(0, 6000, 6000000, @f3)   ' empty keyboard buffer While InKey <> "" : Wend Print : Print "hit any key to end program" Sleep End
http://rosettacode.org/wiki/Numerical_integration/Gauss-Legendre_Quadrature
Numerical integration/Gauss-Legendre Quadrature
In a general Gaussian quadrature rule, an definite integral of f ( x ) {\displaystyle f(x)} is first approximated over the interval [ − 1 , 1 ] {\displaystyle [-1,1]} by a polynomial approximable function g ( x ) {\displaystyle g(x)} and a known weighting function W ( x ) {\displaystyle W(x)} . ∫ − 1 1 f ( x ) d x = ∫ − 1 1 W ( x ) g ( x ) d x {\displaystyle \int _{-1}^{1}f(x)\,dx=\int _{-1}^{1}W(x)g(x)\,dx} Those are then approximated by a sum of function values at specified points x i {\displaystyle x_{i}} multiplied by some weights w i {\displaystyle w_{i}} : ∫ − 1 1 W ( x ) g ( x ) d x ≈ ∑ i = 1 n w i g ( x i ) {\displaystyle \int _{-1}^{1}W(x)g(x)\,dx\approx \sum _{i=1}^{n}w_{i}g(x_{i})} In the case of Gauss-Legendre quadrature, the weighting function W ( x ) = 1 {\displaystyle W(x)=1} , so we can approximate an integral of f ( x ) {\displaystyle f(x)} with: ∫ − 1 1 f ( x ) d x ≈ ∑ i = 1 n w i f ( x i ) {\displaystyle \int _{-1}^{1}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i})} For this, we first need to calculate the nodes and the weights, but after we have them, we can reuse them for numerious integral evaluations, which greatly speeds up the calculation compared to more simple numerical integration methods. The n {\displaystyle n} evaluation points x i {\displaystyle x_{i}} for a n-point rule, also called "nodes", are roots of n-th order Legendre Polynomials P n ( x ) {\displaystyle P_{n}(x)} . Legendre polynomials are defined by the following recursive rule: P 0 ( x ) = 1 {\displaystyle P_{0}(x)=1} P 1 ( x ) = x {\displaystyle P_{1}(x)=x} n P n ( x ) = ( 2 n − 1 ) x P n − 1 ( x ) − ( n − 1 ) P n − 2 ( x ) {\displaystyle nP_{n}(x)=(2n-1)xP_{n-1}(x)-(n-1)P_{n-2}(x)} There is also a recursive equation for their derivative: P n ′ ( x ) = n x 2 − 1 ( x P n ( x ) − P n − 1 ( x ) ) {\displaystyle P_{n}'(x)={\frac {n}{x^{2}-1}}\left(xP_{n}(x)-P_{n-1}(x)\right)} The roots of those polynomials are in general not analytically solvable, so they have to be approximated numerically, for example by Newton-Raphson iteration: x n + 1 = x n − f ( x n ) f ′ ( x n ) {\displaystyle x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}} The first guess x 0 {\displaystyle x_{0}} for the i {\displaystyle i} -th root of a n {\displaystyle n} -order polynomial P n {\displaystyle P_{n}} can be given by x 0 = cos ⁡ ( π i − 1 4 n + 1 2 ) {\displaystyle x_{0}=\cos \left(\pi \,{\frac {i-{\frac {1}{4}}}{n+{\frac {1}{2}}}}\right)} After we get the nodes x i {\displaystyle x_{i}} , we compute the appropriate weights by: w i = 2 ( 1 − x i 2 ) [ P n ′ ( x i ) ] 2 {\displaystyle w_{i}={\frac {2}{\left(1-x_{i}^{2}\right)[P'_{n}(x_{i})]^{2}}}} After we have the nodes and the weights for a n-point quadrature rule, we can approximate an integral over any interval [ a , b ] {\displaystyle [a,b]} by ∫ a b f ( x ) d x ≈ b − a 2 ∑ i = 1 n w i f ( b − a 2 x i + a + b 2 ) {\displaystyle \int _{a}^{b}f(x)\,dx\approx {\frac {b-a}{2}}\sum _{i=1}^{n}w_{i}f\left({\frac {b-a}{2}}x_{i}+{\frac {a+b}{2}}\right)} Task description Similar to the task Numerical Integration, the task here is to calculate the definite integral of a function f ( x ) {\displaystyle f(x)} , but by applying an n-point Gauss-Legendre quadrature rule, as described here, for example. The input values should be an function f to integrate, the bounds of the integration interval a and b, and the number of gaussian evaluation points n. An reference implementation in Common Lisp is provided for comparison. To demonstrate the calculation, compute the weights and nodes for an 5-point quadrature rule and then use them to compute: ∫ − 3 3 exp ⁡ ( x ) d x ≈ ∑ i = 1 5 w i exp ⁡ ( x i ) ≈ 20.036 {\displaystyle \int _{-3}^{3}\exp(x)\,dx\approx \sum _{i=1}^{5}w_{i}\;\exp(x_{i})\approx 20.036}
#PL.2FI
PL/I
(subscriptrange, size, fofl): Integration_Gauss: procedure options (main);   declare (n, k) fixed binary; declare r(*,*) float (18) controlled; declare (z, a, b, exact) float (18);   do n = 1 to 20; a = -3; b = 3; if allocation(r) > 0 then free r; allocate r(2, n); r = 0; call gaussquad(n, r); z = (b-a)/2 * sum(r(2,*) * exp((a+b)/2+r(1,*)*(b-a)/2)); exact = exp(3.0q0)-exp(-3.0q0); put skip edit (n, z, z-exact) (f(5), f(25,16), e(15,2)); end;   gaussquad: procedure(n, r); /*declare n fixed binary, r(2, n) float (18);*/ declare n fixed binary, r(2, *) float (18);/* corrected */ declare pi float (18) value (4*atan(1.0q0)); declare (x, f, df, dx) float (18); declare (i, iter, L) fixed binary; declare (p0(*), p1(*), tmp(*), tmp2(*)) float (18) controlled;   allocate p0(1) initial (1); allocate p1(2) initial (1, 0);   do k = 2 to n; allocate tmp(hbound(p1)+1); do L = 1 to hbound(p1); tmp(L) = p1(L); end; tmp(L) = 0; allocate tmp2(hbound(p0)+2); tmp2(1), tmp2(2) = 0; do L = 1 to hbound(p0); tmp2(L+2) = p0(L); end; tmp = ((2*k-1)*tmp - (k-1)*tmp2)/k; free p0; allocate p0(hbound(p1)); p0 = p1; free p1; allocate p1(hbound(tmp)); p1 = tmp; free tmp, tmp2; end; do i = 1 to n; x = cos(pi*(i-0.25q0)/(n+0.5q0)); do iter = 1 to 10; f = p1(1); df = 0; do k = 2 to hbound(p1); df = f + x*df; f = p1(k) + x * f; end; dx = f / df; x = x - dx; if abs(dx) < 10*epsilon(dx) then leave; end; r(1,i) = x; r(2,i) = 2/((1-x**2)*df**2); end; end gaussquad; end Integration_Gauss;  
http://rosettacode.org/wiki/Old_lady_swallowed_a_fly
Old lady swallowed a fly
Task Present a program which emits the lyrics to the song   I Knew an Old Lady Who Swallowed a Fly,   taking advantage of the repetitive structure of the song's lyrics. This song has multiple versions with slightly different lyrics, so all these programs might not emit identical output. Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Mathematica.2FWolfram_Language
Mathematica/Wolfram Language
animals = {"fly", "spider", "bird", "cat", "dog", "goat", "cow", "horse"}; notes = {"", "That wiggled and jiggled and tickled inside her.\n", "How absurd, to swallow a bird.\n", "Imagine that. She swallowed a cat.\n", "What a hog to swallow a dog.\n", "She just opened her throat and swallowed that goat.\n", "I don't know how she swallowed that cow.\n", "She's dead, of course.", "I don't know why she swallowed that fly.\nPerhaps she'll die.\n\n\ "}; Print[StringJoin @@ ("There was an old lady who swallowed a " <> animals[[#]] <> ".\n" <> notes[[#]] <> If[# == 8, "", StringJoin @@ ("She swallowed the " <> animals[[#]] <> " to catch the " <> animals[[# - 1]] <> ".\n" & /@ Range[#, 2, -1]) <> notes[[9]]] & /@ Range[8])];
http://rosettacode.org/wiki/Old_lady_swallowed_a_fly
Old lady swallowed a fly
Task Present a program which emits the lyrics to the song   I Knew an Old Lady Who Swallowed a Fly,   taking advantage of the repetitive structure of the song's lyrics. This song has multiple versions with slightly different lyrics, so all these programs might not emit identical output. Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Mercury
Mercury
:- module oldlady. :- interface. :- import_module io. :- pred main(io::di, io::uo) is det. :- implementation. :- import_module list, string.   :- type animal ---> horse  ; donkey  ; cow  ; goat  ; pig  ; dog  ; cat  ; bird  ; spider  ; fly.   :- func verse(animal) = string. verse(horse) = "She's dead, of course!". verse(donkey) = "It was rather wonky. To swallow a donkey.". verse(cow) = "I don't know how. To swallow a cow.". verse(goat) = "She just opened her throat. To swallow a goat.". verse(pig) = "Her mouth was so big. To swallow a pig.". verse(dog) = "What a hog. To swallow a dog.". verse(cat) = "Fancy that. To swallow a cat.". verse(bird) = "Quite absurd. To swallow a bird.". verse(spider) = "That wriggled and jiggled and tickled inside her.". verse(fly) = "I don't know why she swallowed the fly.".   :- pred tocatch(animal, animal). :- mode tocatch(in, out) is semidet. :- mode tocatch(out, in) is semidet. tocatch(horse, donkey). tocatch(donkey, cow). tocatch(cow, goat). tocatch(goat, pig). tocatch(pig, dog). tocatch(dog, cat). tocatch(cat, bird). tocatch(bird, spider). tocatch(spider, fly).   :- pred swallow(animal::in, io::di, io::uo) is det. swallow(A, !IO) :- ( if tocatch(A, B) then io.format("She swallowed the %s to catch the %s.\n", [s(string(A)), s(string(B))], !IO), swallow(B, !IO) else io.format("%s\nPerhaps she'll die.\n\n", [s(verse(fly))], !IO) ).   :- pred swallowed(animal::in, io::di, io::uo) is det. swallowed(A, !IO) :- io.format("I know an old lady who swallowed a %s.\n", [s(string(A))], !IO), ( if A = horse then io.write_string("She's dead, of course!\n", !IO) else if A = fly, tocatch(B, A) then swallow(A, !IO), swallowed(B, !IO) else if tocatch(B, A) then io.write_string(verse(A), !IO), io.nl(!IO), swallow(A, !IO), swallowed(B, !IO) else true ).   main(!IO) :- swallowed(fly, !IO).
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#Rust
Rust
extern crate rand;   use rand::{Rng, thread_rng};   fn one_of_n<R: Rng>(rng: &mut R, n: usize) -> usize { (1..n).fold(0, |keep, cand| { // Note that this will break if n is larger than u32::MAX if rng.gen_weighted_bool(cand as u32 + 1) { cand } else { keep } }) }   fn main() { const LINES: usize = 10;   let mut dist = [0; LINES]; let mut rng = thread_rng();   for _ in 0..1_000_000 { let num = one_of_n(&mut rng, LINES); dist[num] += 1; }   println!("{:?}", dist); }  
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#Scala
Scala
def one_of_n(n: Int, i: Int = 1, j: Int = 1): Int = if (n < 1) i else one_of_n(n - 1, if (scala.util.Random.nextInt(j) == 0) n else i, j + 1)   def simulate(lines: Int, iterations: Int) = { val counts = new Array[Int](lines) for (_ <- 1 to iterations; i = one_of_n(lines) - 1) counts(i) = counts(i) + 1 counts }   println(simulate(10, 1000000) mkString "\n")
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#Rust
Rust
vec![1, 2, 1, 3, 2] < vec![1, 2, 0, 4, 4, 0, 0, 0]
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#Scala
Scala
def lessThan1(a: List[Int], b: List[Int]): Boolean = if (b.isEmpty) false else if (a.isEmpty) true else if (a.head != b.head) a.head < b.head else lessThan1(a.tail, b.tail)
http://rosettacode.org/wiki/Ordered_words
Ordered words
An   ordered word   is a word in which the letters appear in alphabetic order. Examples include   abbey   and   dirt. Task[edit] Find and display all the ordered words in the dictionary   unixdict.txt   that have the longest word length. (Examples that access the dictionary file locally assume that you have downloaded this file yourself.) The display needs to be shown on this page. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#PL.2FI
PL/I
  order: procedure options (main); /* 24/11/2011 */ declare word character (20) varying; declare word_list character (20) varying controlled; declare max_length fixed binary; declare input file;   open file (input) title ('/ORDER.DAT,TYPE(TEXT),RECSIZE(100)');   on endfile (input) go to completed_search;   max_length = 0; do forever; get file (input) edit (word) (L); if length(word) > max_length then do; if in_order(word) then do; /* Get rid of any stockpiled shorter words. */ do while (allocation(word_list) > 0); free word_list; end; /* Add the eligible word to the stockpile. */ allocate word_list; word_list = word; max_length = length(word); end; end; else if max_length = length(word) then do; /* we have an eligle word of the same (i.e., maximum) length. */ if in_order(word) then do; /* Add it to the stockpile. */ allocate word_list; word_list = word; end; end; end; completed_search: put skip list ('There are ' || trim(allocation(word_list)) || ' eligible words of length ' || trim(length(word)) || ':'); do while (allocation(word_list) > 0); put skip list (word_list); free word_list; end;   /* Check that the letters of the word are in non-decreasing order of rank. */ in_order: procedure (word) returns (bit(1)); declare word character (*) varying; declare i fixed binary;   do i = 1 to length(word)-1; if substr(word, i, 1) > substr(word, i+1, 1) then return ('0'b); end; return ('1'b); end in_order; end order;  
http://rosettacode.org/wiki/Palindrome_detection
Palindrome detection
A palindrome is a phrase which reads the same backward and forward. Task[edit] Write a function or program that checks whether a given sequence of characters (or, if you prefer, bytes) is a palindrome. For extra credit: Support Unicode characters. Write a second function (possibly as a wrapper to the first) which detects inexact palindromes, i.e. phrases that are palindromes if white-space and punctuation is ignored and case-insensitive comparison is used. Hints It might be useful for this task to know how to reverse a string. This task's entries might also form the subjects of the task Test a function. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Ruby
Ruby
def palindrome?(s) s == s.reverse end
http://rosettacode.org/wiki/Odd_word_problem
Odd word problem
Task Write a program that solves the odd word problem with the restrictions given below. Description You are promised an input stream consisting of English letters and punctuations. It is guaranteed that: the words (sequence of consecutive letters) are delimited by one and only one punctuation, the stream will begin with a word, the words will be at least one letter long,   and a full stop (a period, [.]) appears after, and only after, the last word. Example A stream with six words: what,is,the;meaning,of:life. The task is to reverse the letters in every other word while leaving punctuations intact, producing: what,si,the;gninaem,of:efil. while observing the following restrictions: Only I/O allowed is reading or writing one character at a time, which means: no reading in a string, no peeking ahead, no pushing characters back into the stream, and no storing characters in a global variable for later use; You are not to explicitly save characters in a collection data structure, such as arrays, strings, hash tables, etc, for later reversal; You are allowed to use recursions, closures, continuations, threads, co-routines, etc., even if their use implies the storage of multiple characters. Test cases Work on both the   "life"   example given above, and also the text: we,are;not,in,kansas;any,more.
#REXX
REXX
/*REXX program solves the odd word problem by only using (single) byte input/output.*/ iFID_ = 'ODDWORD.IN' /*Note: numeric suffix is added later.*/ oFID_ = 'ODDWORD.' /* " " " " " " */ do case=1 for 2; #= 0 /*#: is the number of characters read.*/ iFID= iFID_ || case /*read ODDWORD.IN1 or ODDWORD.IN2 */ oFID= oFID_ || case /*write ODDWORD.1 or ODDWORD.2 */ say; say; say '════════ reading file: ' iFID "════════" /* ◄■■■■■■■■■ optional. */   do until x==. /* [↓] perform until reaching a period*/ do until \datatype(x, 'M') /* [↓] " " punctuation found*/ call rChar /*read a single character. */ call wChar /*write " " " */ end /*until \data···*/ /* [↑] read/write until punctuation. */ if x==. then leave /*is this the end─of─sentence (period)?*/ call readLetters; punct= # /*save the location of the punctuation.*/ do j=#-1 by -1 /*read some characters backwards. */ call rChar j /*read previous word (backwards). */ if \datatype(x, 'M') then leave /*Found punctuation? Then leave J. */ call wChar /*write a character (which is a letter)*/ end /*j*/ /* [↑] perform for "even" words. */ call rLett /*read letters until punctuation found.*/ call wChar; #= punct /*write a char; punctuation location. */ end /*until x==.*/ end /*case*/ /* [↑] process both of the input files*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ rLett: do until \datatype(x, 'M'); call rChar; end; return wChar: call charout , x /*console*/; call charout oFID, x /*file*/; return /*──────────────────────────────────────────────────────────────────────────────────────*/ rChar: if arg()==0 then do; x= charin(iFID); #= #+1; end /*read next char*/ else x= charin(iFID, arg(1) ); /* " specific " */ return
http://rosettacode.org/wiki/Number_names
Number names
Task Show how to spell out a number in English. You can use a preexisting implementation or roll your own, but you should support inputs up to at least one million (or the maximum value of your language's default bounded integer type, if that's less). Support for inputs other than positive integers (like zero, negative integers, and floating-point numbers) is optional. Related task   Spelling of ordinal numbers.
#Clojure
Clojure
(clojure.pprint/cl-format nil "~R" 1234) => "one thousand, two hundred thirty-four"
http://rosettacode.org/wiki/Number_reversal_game
Number reversal game
Task Given a jumbled list of the numbers   1   to   9   that are definitely   not   in ascending order. Show the list,   and then ask the player how many digits from the left to reverse. Reverse those digits,   then ask again,   until all the digits end up in ascending order. The score is the count of the reversals needed to attain the ascending order. Note: Assume the player's input does not need extra validation. Related tasks   Sorting algorithms/Pancake sort   Pancake sorting.   Topswops
#Crystal
Crystal
  SIZE = 9 ordered = (1..SIZE).to_a shuffled = (1..SIZE).to_a   while shuffled == ordered shuffled.shuffle! end   score = 0 until shuffled == ordered print "#{shuffled} Enter items to reverse: "   next unless guess = gets next unless num = guess.to_i? next if num < 2 || num > SIZE   shuffled[0, num] = shuffled[0, num].reverse score += 1 end   puts "#{shuffled} Your score: #{score}"  
http://rosettacode.org/wiki/Null_object
Null object
Null (or nil) is the computer science concept of an undefined or unbound object. Some languages have an explicit way to access the null object, and some don't. Some languages distinguish the null object from undefined values, and some don't. Task Show how to access null in your language by checking to see if an object is equivalent to the null object. This task is not about whether a variable is defined. The task is about "null"-like values in various languages, which may or may not be related to the defined-ness of variables in your language.
#Factor
Factor
: is-f? ( obj -- ? ) f = ;
http://rosettacode.org/wiki/Null_object
Null object
Null (or nil) is the computer science concept of an undefined or unbound object. Some languages have an explicit way to access the null object, and some don't. Some languages distinguish the null object from undefined values, and some don't. Task Show how to access null in your language by checking to see if an object is equivalent to the null object. This task is not about whether a variable is defined. The task is about "null"-like values in various languages, which may or may not be related to the defined-ness of variables in your language.
#Fantom
Fantom
  fansh> x := null fansh> x == null true fansh> x = 1 1 fansh> x == null false  
http://rosettacode.org/wiki/One-dimensional_cellular_automata
One-dimensional cellular automata
Assume an array of cells with an initial distribution of live and dead cells, and imaginary cells off the end of the array having fixed values. Cells in the next generation of the array are calculated based on the value of the cell and its left and right nearest neighbours in the current generation. If, in the following table, a live cell is represented by 1 and a dead cell by 0 then to generate the value of the cell at a particular index in the array of cellular values you use the following table: 000 -> 0 # 001 -> 0 # 010 -> 0 # Dies without enough neighbours 011 -> 1 # Needs one neighbour to survive 100 -> 0 # 101 -> 1 # Two neighbours giving birth 110 -> 1 # Needs one neighbour to survive 111 -> 0 # Starved to death.
#Fantom
Fantom
  class Automaton { static Int[] evolve (Int[] array) { return array.map |Int x, Int i -> Int| { if (i == 0) return ( (x + array[1] == 2) ? 1 : 0) else if (i == array.size-1) return ( (x + array[-2] == 2) ? 1 : 0) else if (x + array[i-1] + array[i+1] == 2) return 1 else return 0 } }   public static Void main () { Int[] array := [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] echo (array.join("")) Int[] newArray := evolve(array) while (newArray != array) { echo (newArray.join("")) array = newArray newArray = evolve(array) } } }  
http://rosettacode.org/wiki/Numerical_integration
Numerical integration
Write functions to calculate the definite integral of a function ƒ(x) using all five of the following methods: rectangular left right midpoint trapezium Simpson's composite Your functions should take in the upper and lower bounds (a and b), and the number of approximations to make in that range (n). Assume that your example already has a function that gives values for ƒ(x) . Simpson's method is defined by the following pseudo-code: Pseudocode: Simpson's method, composite procedure quad_simpson_composite(f, a, b, n) h := (b - a) / n sum1 := f(a + h/2) sum2 := 0 loop on i from 1 to (n - 1) sum1 := sum1 + f(a + h * i + h/2) sum2 := sum2 + f(a + h * i)   answer := (h / 6) * (f(a) + f(b) + 4*sum1 + 2*sum2) Demonstrate your function by showing the results for:   ƒ(x) = x3,       where   x   is     [0,1],       with           100 approximations.   The exact result is     0.25               (or 1/4)   ƒ(x) = 1/x,     where   x   is   [1,100],     with        1,000 approximations.   The exact result is     4.605170+     (natural log of 100)   ƒ(x) = x,         where   x   is   [0,5000],   with 5,000,000 approximations.   The exact result is   12,500,000   ƒ(x) = x,         where   x   is   [0,6000],   with 6,000,000 approximations.   The exact result is   18,000,000 See also   Active object for integrating a function of real time.   Special:PrefixIndex/Numerical integration for other integration methods.
#Go
Go
package main   import ( "fmt" "math" )   // specification for an integration type spec struct { lower, upper float64 // bounds for integration n int // number of parts exact float64 // expected answer fs string // mathematical description of function f func(float64) float64 // function to integrate }   // test cases per task description var data = []spec{ spec{0, 1, 100, .25, "x^3", func(x float64) float64 { return x * x * x }}, spec{1, 100, 1000, float64(math.Log(100)), "1/x", func(x float64) float64 { return 1 / x }}, spec{0, 5000, 5e5, 12.5e6, "x", func(x float64) float64 { return x }}, spec{0, 6000, 6e6, 18e6, "x", func(x float64) float64 { return x }}, }   // object for associating a printable function name with an integration method type method struct { name string integrate func(spec) float64 }   // integration methods implemented per task description var methods = []method{ method{"Rectangular (left) ", rectLeft}, method{"Rectangular (right) ", rectRight}, method{"Rectangular (midpoint)", rectMid}, method{"Trapezium ", trap}, method{"Simpson's ", simpson}, }   func rectLeft(t spec) float64 { var a adder r := t.upper - t.lower nf := float64(t.n) x0 := t.lower for i := 0; i < t.n; i++ { x1 := t.lower + float64(i+1)*r/nf // x1-x0 better than r/nf. // (with r/nf, the represenation error accumulates) a.add(t.f(x0) * (x1 - x0)) x0 = x1 } return a.total() }   func rectRight(t spec) float64 { var a adder r := t.upper - t.lower nf := float64(t.n) x0 := t.lower for i := 0; i < t.n; i++ { x1 := t.lower + float64(i+1)*r/nf a.add(t.f(x1) * (x1 - x0)) x0 = x1 } return a.total() }   func rectMid(t spec) float64 { var a adder r := t.upper - t.lower nf := float64(t.n) // there's a tiny gloss in the x1-x0 trick here. the correct way // would be to compute x's at division boundaries, but we don't need // those x's for anything else. (the function is evaluated on x's // at division midpoints rather than division boundaries.) so, we // reuse the midpoint x's, knowing that they will average out just // as well. we just need one extra point, so we use lower-.5. x0 := t.lower - .5*r/nf for i := 0; i < t.n; i++ { x1 := t.lower + (float64(i)+.5)*r/nf a.add(t.f(x1) * (x1 - x0)) x0 = x1 } return a.total() }   func trap(t spec) float64 { var a adder r := t.upper - t.lower nf := float64(t.n) x0 := t.lower f0 := t.f(x0) for i := 0; i < t.n; i++ { x1 := t.lower + float64(i+1)*r/nf f1 := t.f(x1) a.add((f0 + f1) * .5 * (x1 - x0)) x0, f0 = x1, f1 } return a.total() }   func simpson(t spec) float64 { var a adder r := t.upper - t.lower nf := float64(t.n) // similar to the rectangle midpoint logic explained above, // we play a little loose with the values used for dx and dx0. dx0 := r / nf a.add(t.f(t.lower) * dx0) a.add(t.f(t.lower+dx0*.5) * dx0 * 4) x0 := t.lower + dx0 for i := 1; i < t.n; i++ { x1 := t.lower + float64(i+1)*r/nf xmid := (x0 + x1) * .5 dx := x1 - x0 a.add(t.f(x0) * dx * 2) a.add(t.f(xmid) * dx * 4) x0 = x1 } a.add(t.f(t.upper) * dx0) return a.total() / 6 }   func sum(v []float64) float64 { var a adder for _, e := range v { a.add(e) } return a.total() }   type adder struct { sum, e float64 }   func (a *adder) total() float64 { return a.sum + a.e }   func (a *adder) add(x float64) { sum := a.sum + x e := sum - a.sum a.e += a.sum - (sum - e) + (x - e) a.sum = sum }   func main() { for _, t := range data { fmt.Println("Test case: f(x) =", t.fs) fmt.Println("Integration from", t.lower, "to", t.upper, "in", t.n, "parts") fmt.Printf("Exact result  %.7e Error\n", t.exact) for _, m := range methods { a := m.integrate(t) e := a - t.exact if e < 0 { e = -e } fmt.Printf("%s  %.7e  %.7e\n", m.name, a, e) } fmt.Println("") } }
http://rosettacode.org/wiki/Numerical_integration/Gauss-Legendre_Quadrature
Numerical integration/Gauss-Legendre Quadrature
In a general Gaussian quadrature rule, an definite integral of f ( x ) {\displaystyle f(x)} is first approximated over the interval [ − 1 , 1 ] {\displaystyle [-1,1]} by a polynomial approximable function g ( x ) {\displaystyle g(x)} and a known weighting function W ( x ) {\displaystyle W(x)} . ∫ − 1 1 f ( x ) d x = ∫ − 1 1 W ( x ) g ( x ) d x {\displaystyle \int _{-1}^{1}f(x)\,dx=\int _{-1}^{1}W(x)g(x)\,dx} Those are then approximated by a sum of function values at specified points x i {\displaystyle x_{i}} multiplied by some weights w i {\displaystyle w_{i}} : ∫ − 1 1 W ( x ) g ( x ) d x ≈ ∑ i = 1 n w i g ( x i ) {\displaystyle \int _{-1}^{1}W(x)g(x)\,dx\approx \sum _{i=1}^{n}w_{i}g(x_{i})} In the case of Gauss-Legendre quadrature, the weighting function W ( x ) = 1 {\displaystyle W(x)=1} , so we can approximate an integral of f ( x ) {\displaystyle f(x)} with: ∫ − 1 1 f ( x ) d x ≈ ∑ i = 1 n w i f ( x i ) {\displaystyle \int _{-1}^{1}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i})} For this, we first need to calculate the nodes and the weights, but after we have them, we can reuse them for numerious integral evaluations, which greatly speeds up the calculation compared to more simple numerical integration methods. The n {\displaystyle n} evaluation points x i {\displaystyle x_{i}} for a n-point rule, also called "nodes", are roots of n-th order Legendre Polynomials P n ( x ) {\displaystyle P_{n}(x)} . Legendre polynomials are defined by the following recursive rule: P 0 ( x ) = 1 {\displaystyle P_{0}(x)=1} P 1 ( x ) = x {\displaystyle P_{1}(x)=x} n P n ( x ) = ( 2 n − 1 ) x P n − 1 ( x ) − ( n − 1 ) P n − 2 ( x ) {\displaystyle nP_{n}(x)=(2n-1)xP_{n-1}(x)-(n-1)P_{n-2}(x)} There is also a recursive equation for their derivative: P n ′ ( x ) = n x 2 − 1 ( x P n ( x ) − P n − 1 ( x ) ) {\displaystyle P_{n}'(x)={\frac {n}{x^{2}-1}}\left(xP_{n}(x)-P_{n-1}(x)\right)} The roots of those polynomials are in general not analytically solvable, so they have to be approximated numerically, for example by Newton-Raphson iteration: x n + 1 = x n − f ( x n ) f ′ ( x n ) {\displaystyle x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}} The first guess x 0 {\displaystyle x_{0}} for the i {\displaystyle i} -th root of a n {\displaystyle n} -order polynomial P n {\displaystyle P_{n}} can be given by x 0 = cos ⁡ ( π i − 1 4 n + 1 2 ) {\displaystyle x_{0}=\cos \left(\pi \,{\frac {i-{\frac {1}{4}}}{n+{\frac {1}{2}}}}\right)} After we get the nodes x i {\displaystyle x_{i}} , we compute the appropriate weights by: w i = 2 ( 1 − x i 2 ) [ P n ′ ( x i ) ] 2 {\displaystyle w_{i}={\frac {2}{\left(1-x_{i}^{2}\right)[P'_{n}(x_{i})]^{2}}}} After we have the nodes and the weights for a n-point quadrature rule, we can approximate an integral over any interval [ a , b ] {\displaystyle [a,b]} by ∫ a b f ( x ) d x ≈ b − a 2 ∑ i = 1 n w i f ( b − a 2 x i + a + b 2 ) {\displaystyle \int _{a}^{b}f(x)\,dx\approx {\frac {b-a}{2}}\sum _{i=1}^{n}w_{i}f\left({\frac {b-a}{2}}x_{i}+{\frac {a+b}{2}}\right)} Task description Similar to the task Numerical Integration, the task here is to calculate the definite integral of a function f ( x ) {\displaystyle f(x)} , but by applying an n-point Gauss-Legendre quadrature rule, as described here, for example. The input values should be an function f to integrate, the bounds of the integration interval a and b, and the number of gaussian evaluation points n. An reference implementation in Common Lisp is provided for comparison. To demonstrate the calculation, compute the weights and nodes for an 5-point quadrature rule and then use them to compute: ∫ − 3 3 exp ⁡ ( x ) d x ≈ ∑ i = 1 5 w i exp ⁡ ( x i ) ≈ 20.036 {\displaystyle \int _{-3}^{3}\exp(x)\,dx\approx \sum _{i=1}^{5}w_{i}\;\exp(x_{i})\approx 20.036}
#Python
Python
from numpy import *   ################################################################## # Recursive generation of the Legendre polynomial of order n def Legendre(n,x): x=array(x) if (n==0): return x*0+1.0 elif (n==1): return x else: return ((2.0*n-1.0)*x*Legendre(n-1,x)-(n-1)*Legendre(n-2,x))/n   ################################################################## # Derivative of the Legendre polynomials def DLegendre(n,x): x=array(x) if (n==0): return x*0 elif (n==1): return x*0+1.0 else: return (n/(x**2-1.0))*(x*Legendre(n,x)-Legendre(n-1,x)) ################################################################## # Roots of the polynomial obtained using Newton-Raphson method def LegendreRoots(polyorder,tolerance=1e-20): if polyorder<2: err=1 # bad polyorder no roots can be found else: roots=[] # The polynomials are alternately even and odd functions. So we evaluate only half the number of roots. for i in range(1,int(polyorder)/2 +1): x=cos(pi*(i-0.25)/(polyorder+0.5)) error=10*tolerance iters=0 while (error>tolerance) and (iters<1000): dx=-Legendre(polyorder,x)/DLegendre(polyorder,x) x=x+dx iters=iters+1 error=abs(dx) roots.append(x) # Use symmetry to get the other roots roots=array(roots) if polyorder%2==0: roots=concatenate( (-1.0*roots, roots[::-1]) ) else: roots=concatenate( (-1.0*roots, [0.0], roots[::-1]) ) err=0 # successfully determined roots return [roots, err] ################################################################## # Weight coefficients def GaussLegendreWeights(polyorder): W=[] [xis,err]=LegendreRoots(polyorder) if err==0: W=2.0/( (1.0-xis**2)*(DLegendre(polyorder,xis)**2) ) err=0 else: err=1 # could not determine roots - so no weights return [W, xis, err] ################################################################## # The integral value # func : the integrand # a, b : lower and upper limits of the integral # polyorder : order of the Legendre polynomial to be used # def GaussLegendreQuadrature(func, polyorder, a, b): [Ws,xs, err]= GaussLegendreWeights(polyorder) if err==0: ans=(b-a)*0.5*sum( Ws*func( (b-a)*0.5*xs+ (b+a)*0.5 ) ) else: # (in case of error) err=1 ans=None return [ans,err] ################################################################## # The integrand - change as required def func(x): return exp(x) ################################################################## #   order=5 [Ws,xs,err]=GaussLegendreWeights(order) if err==0: print "Order  : ", order print "Roots  : ", xs print "Weights  : ", Ws else: print "Roots/Weights evaluation failed"   # Integrating the function [ans,err]=GaussLegendreQuadrature(func , order, -3,3) if err==0: print "Integral : ", ans else: print "Integral evaluation failed"
http://rosettacode.org/wiki/Old_lady_swallowed_a_fly
Old lady swallowed a fly
Task Present a program which emits the lyrics to the song   I Knew an Old Lady Who Swallowed a Fly,   taking advantage of the repetitive structure of the song's lyrics. This song has multiple versions with slightly different lyrics, so all these programs might not emit identical output. Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Modula-2
Modula-2
MODULE OldLady; FROM FormatString IMPORT FormatString; FROM Terminal IMPORT WriteString,WriteLn,ReadChar;   TYPE AA = ARRAY[0..7] OF ARRAY[0..7] OF CHAR; VA = ARRAY[0..7] OF ARRAY[0..63] OF CHAR; VAR buf : ARRAY[0..127] OF CHAR; animals : AA; verses : VA; i,j : INTEGER; BEGIN FormatString("I don't know why she swallowed that fly.\nPerhaps she'll die\n", buf);   animals := AA{"fly", "spider", "bird", "cat", "dog", "goat", "cow", "horse"}; verses := VA{ "I don't know why she swallowed that fly.", "That wiggled and jiggled and tickled inside her", "How absurd, to swallow a bird", "Imagine that. She swallowed a cat", "What a hog to swallow a dog", "She just opened her throat and swallowed that goat", "I don't know how she swallowed that cow", "She's dead of course" };   FOR i:=0 TO 7 DO FormatString("There was an old lady who swallowed a %s\n%s\n", buf, animals[i], verses[i]); WriteString(buf); IF i=0 THEN WriteString("Perhaps she'll die"); WriteLn; WriteLn; END; j := i; WHILE (j>0) AND (i<7) DO FormatString("She swallowed the %s to catch the %s\n", buf, animals[j], animals[j-1]); WriteString(buf); IF j=1 THEN WriteString(verses[0]); WriteLn; WriteString("Perhaps she'll die"); WriteLn; WriteLn END; DEC(j) END; END;   ReadChar END OldLady.
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#Seed7
Seed7
$ include "seed7_05.s7i";   const func integer: one_of_n (in integer: n) is func result var integer: r is 1; local var integer: i is 0; begin for i range 2 to n do if rand(1, i) = 1 then r := i; end if; end for; end func;   const proc: main is func local var array integer: r is 10 times 0; var integer: i is 0; begin for i range 1 to 1000000 do incr(r[one_of_n(10)]); end for; for i range 1 to 10 do write(r[i] <& " "); end for; writeln; end func;
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#Sidef
Sidef
func one_of_n(n) { var choice n.times { |i| choice = i if (1 > i.rand) } choice - 1 }   func one_of_n_test(n = 10, trials = 1_000_000) { var bins = [] trials.times { bins[one_of_n(n)] := 0 ++ } bins }   say one_of_n_test()
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#Scheme
Scheme
(define (lex<? a b) (cond ((null? b) #f) ((null? a) #t) ((= (car a) (car b)) (lex<? (cdr a) (cdr b))) (else (< (car a) (car b)))))
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#Seed7
Seed7
$ include "seed7_05.s7i";   const proc: main is func begin writeln([] (1) < [] (1, 2)); # If the first list runs out of elements the result is TRUE. writeln([] (1, 2) < [] (1)); # If the second list runs out of elements the result is FALSE. writeln([] (1, 2) < [] (1, 2)); # If both lists run out of elements the result is FALSE. writeln([] (1, 2, 3) < [] (1, 1, 3)); # The second element is greater than --> FALSE writeln([] (1, 2, 3) < [] (1, 3, 3)); # The second element is less than --> TRUE writeln(0 times 0 < [] (1)); # The empty list is less than any nonempty list --> TRUE writeln([] (1) < 0 times 0); # Any nonempty list is not less than the empty list --> FALSE writeln(0 times 0 < 0 times 0); # The empty list is not less than the empty list --> FALSE end func;
http://rosettacode.org/wiki/Ordered_words
Ordered words
An   ordered word   is a word in which the letters appear in alphabetic order. Examples include   abbey   and   dirt. Task[edit] Find and display all the ordered words in the dictionary   unixdict.txt   that have the longest word length. (Examples that access the dictionary file locally assume that you have downloaded this file yourself.) The display needs to be shown on this page. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#PowerShell
PowerShell
  $url = 'http://www.puzzlers.org/pub/wordlists/unixdict.txt'   (New-Object System.Net.WebClient).DownloadFile($url, "$env:TEMP\unixdict.txt")   $ordered = Get-Content -Path "$env:TEMP\unixdict.txt" | ForEach-Object {if (($_.ToCharArray() | Sort-Object) -join '' -eq $_) {$_}} | Group-Object -Property Length | Sort-Object -Property Name | Select-Object -Property @{Name="WordCount" ; Expression={$_.Count}}, @{Name="WordLength"; Expression={[int]$_.Name}}, @{Name="Words"  ; Expression={$_.Group}} -Last 1   "There are {0} ordered words of the longest word length ({1} characters):`n`n{2}" -f $ordered.WordCount, $ordered.WordLength, ($ordered.Words -join ", ") Remove-Item -Path "$env:TEMP\unixdict.txt" -Force -ErrorAction SilentlyContinue  
http://rosettacode.org/wiki/Palindrome_detection
Palindrome detection
A palindrome is a phrase which reads the same backward and forward. Task[edit] Write a function or program that checks whether a given sequence of characters (or, if you prefer, bytes) is a palindrome. For extra credit: Support Unicode characters. Write a second function (possibly as a wrapper to the first) which detects inexact palindromes, i.e. phrases that are palindromes if white-space and punctuation is ignored and case-insensitive comparison is used. Hints It might be useful for this task to know how to reverse a string. This task's entries might also form the subjects of the task Test a function. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Run_BASIC
Run BASIC
data "My dog has fleas", "Madam, I'm Adam.", "1 on 1", "In girum imus nocte et consumimur igni"   for i = 1 to 4 read w$ print w$;" is ";isPalindrome$(w$);" Palindrome" next   FUNCTION isPalindrome$(str$) for i = 1 to len(str$) a$ = upper$(mid$(str$,i,1)) if (a$ >= "A" and a$ <= "Z") or (a$ >= "0" and a$ <= "9") then b$ = b$ + a$: c$ = a$ + c$ next i if b$ <> c$ then isPalindrome$ = "not"
http://rosettacode.org/wiki/Odd_word_problem
Odd word problem
Task Write a program that solves the odd word problem with the restrictions given below. Description You are promised an input stream consisting of English letters and punctuations. It is guaranteed that: the words (sequence of consecutive letters) are delimited by one and only one punctuation, the stream will begin with a word, the words will be at least one letter long,   and a full stop (a period, [.]) appears after, and only after, the last word. Example A stream with six words: what,is,the;meaning,of:life. The task is to reverse the letters in every other word while leaving punctuations intact, producing: what,si,the;gninaem,of:efil. while observing the following restrictions: Only I/O allowed is reading or writing one character at a time, which means: no reading in a string, no peeking ahead, no pushing characters back into the stream, and no storing characters in a global variable for later use; You are not to explicitly save characters in a collection data structure, such as arrays, strings, hash tables, etc, for later reversal; You are allowed to use recursions, closures, continuations, threads, co-routines, etc., even if their use implies the storage of multiple characters. Test cases Work on both the   "life"   example given above, and also the text: we,are;not,in,kansas;any,more.
#Ring
Ring
  # Project : Odd word problem   test = "what,is,the;meaning,of:life." n1 = 1 testarr = [] testorigin = test test = substr(test, ",", " ") test = substr(test, ";", " ") test = substr(test, ":", " ") test = substr(test, ".", " ")   while true n2 = substring(test, " ", n1) n3 = substring(test, " ", n2 + 1) if n2>0 and n3>0 strcut = substr(test, n2 + 1, n3 - n2) strcut = trim(strcut) if strcut != "" add(testarr, strcut) n1 = n3 + 1 else exit ok ok end   for n = 1 to len(testarr) strrev = revstr(testarr[n]) testorigin = substr(testorigin, testarr[n], strrev) next see testorigin + nl   func Substring str,substr,n newstr=right(str,len(str)-n+1) nr = substr(newstr, substr) return n + nr -1   func revstr(cStr) cStr2 = "" for x = len(cStr) to 1 step -1 cStr2 += cStr[x] next return cStr2  
http://rosettacode.org/wiki/Odd_word_problem
Odd word problem
Task Write a program that solves the odd word problem with the restrictions given below. Description You are promised an input stream consisting of English letters and punctuations. It is guaranteed that: the words (sequence of consecutive letters) are delimited by one and only one punctuation, the stream will begin with a word, the words will be at least one letter long,   and a full stop (a period, [.]) appears after, and only after, the last word. Example A stream with six words: what,is,the;meaning,of:life. The task is to reverse the letters in every other word while leaving punctuations intact, producing: what,si,the;gninaem,of:efil. while observing the following restrictions: Only I/O allowed is reading or writing one character at a time, which means: no reading in a string, no peeking ahead, no pushing characters back into the stream, and no storing characters in a global variable for later use; You are not to explicitly save characters in a collection data structure, such as arrays, strings, hash tables, etc, for later reversal; You are allowed to use recursions, closures, continuations, threads, co-routines, etc., even if their use implies the storage of multiple characters. Test cases Work on both the   "life"   example given above, and also the text: we,are;not,in,kansas;any,more.
#Ruby
Ruby
f, r = nil fwd = proc {|c| c =~ /[[:alpha:]]/ ? [(print c), fwd[Fiber.yield f]][1] : c } rev = proc {|c| c =~ /[[:alpha:]]/ ? [rev[Fiber.yield r], (print c)][0] : c }   (f = Fiber.new { loop { print fwd[Fiber.yield r] }}).resume (r = Fiber.new { loop { print rev[Fiber.yield f] }}).resume   coro = f until $stdin.eof? coro = coro.resume($stdin.getc) end
http://rosettacode.org/wiki/Number_names
Number names
Task Show how to spell out a number in English. You can use a preexisting implementation or roll your own, but you should support inputs up to at least one million (or the maximum value of your language's default bounded integer type, if that's less). Support for inputs other than positive integers (like zero, negative integers, and floating-point numbers) is optional. Related task   Spelling of ordinal numbers.
#CoffeeScript
CoffeeScript
  spell_integer = (n) -> tens = [null, null, "twenty", "thirty", "forty", "fifty", "sixty", "seventy", "eighty", "ninety"]   small = ["zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen"]   bl = [null, null, "m", "b", "tr", "quadr", "quint", "sext", "sept", "oct", "non", "dec"]   divmod = (n, d) -> [Math.floor(n / d), n % d]   nonzero = (c, n) -> if n == 0 "" else c + spell_integer n   big = (e, n) -> if e == 0 spell_integer n else if e == 1 spell_integer(n) + " thousand" else spell_integer(n) + " " + bl[e] + "illion"   base1000_rev = (n) -> # generates the value of the digits of n in base 1000 # (i.e. 3-digit chunks), in reverse. chunks = [] while n != 0 [n, r] = divmod n, 1000 chunks.push r chunks   if n < 0 throw Error "spell_integer: negative input" else if n < 20 small[n] else if n < 100 [a, b] = divmod n, 10 tens[a] + nonzero("-", b) else if n < 1000 [a, b] = divmod n, 100 small[a] + " hundred" + nonzero(" ", b) else chunks = (big(exp, x) for x, exp in base1000_rev(n) when x) chunks.reverse().join ', '   # example console.log spell_integer 1278 console.log spell_integer 1752 console.log spell_integer 2010 console.log spell_integer 4000123007913  
http://rosettacode.org/wiki/Number_reversal_game
Number reversal game
Task Given a jumbled list of the numbers   1   to   9   that are definitely   not   in ascending order. Show the list,   and then ask the player how many digits from the left to reverse. Reverse those digits,   then ask again,   until all the digits end up in ascending order. The score is the count of the reversals needed to attain the ascending order. Note: Assume the player's input does not need extra validation. Related tasks   Sorting algorithms/Pancake sort   Pancake sorting.   Topswops
#D
D
import std.stdio, std.random, std.string, std.conv, std.algorithm, std.range;   void main() { auto data = iota(1, 10).array; do data.randomShuffle; while (data.isSorted);   int trial; while (!data.isSorted) { writef("%d: %s How many numbers to flip? ", ++trial, data); data[0 .. readln.strip.to!uint].reverse; } writefln("\nYou took %d attempts.", trial); }
http://rosettacode.org/wiki/Null_object
Null object
Null (or nil) is the computer science concept of an undefined or unbound object. Some languages have an explicit way to access the null object, and some don't. Some languages distinguish the null object from undefined values, and some don't. Task Show how to access null in your language by checking to see if an object is equivalent to the null object. This task is not about whether a variable is defined. The task is about "null"-like values in various languages, which may or may not be related to the defined-ness of variables in your language.
#Forth
Forth
'FB 1.05.0 Win64   ' FreeBASIC does not have a NULL keyword but it's possible to create one using a macro   #Define NULL CPtr(Any Ptr, 0) '' Any Ptr is implicitly convertible to pointers of other types   Type Dog name As String age As Integer End Type   Dim d As Dog Ptr = New Dog d->Name = "Rover" d->Age = 5 Print d->Name, d->Age Delete d d = NULL '' guard against 'd' being used accidentally in future   ' in practice many FB developers would simply have written: d = 0 above Sleep
http://rosettacode.org/wiki/Null_object
Null object
Null (or nil) is the computer science concept of an undefined or unbound object. Some languages have an explicit way to access the null object, and some don't. Some languages distinguish the null object from undefined values, and some don't. Task Show how to access null in your language by checking to see if an object is equivalent to the null object. This task is not about whether a variable is defined. The task is about "null"-like values in various languages, which may or may not be related to the defined-ness of variables in your language.
#FreeBASIC
FreeBASIC
'FB 1.05.0 Win64   ' FreeBASIC does not have a NULL keyword but it's possible to create one using a macro   #Define NULL CPtr(Any Ptr, 0) '' Any Ptr is implicitly convertible to pointers of other types   Type Dog name As String age As Integer End Type   Dim d As Dog Ptr = New Dog d->Name = "Rover" d->Age = 5 Print d->Name, d->Age Delete d d = NULL '' guard against 'd' being used accidentally in future   ' in practice many FB developers would simply have written: d = 0 above Sleep
http://rosettacode.org/wiki/One-dimensional_cellular_automata
One-dimensional cellular automata
Assume an array of cells with an initial distribution of live and dead cells, and imaginary cells off the end of the array having fixed values. Cells in the next generation of the array are calculated based on the value of the cell and its left and right nearest neighbours in the current generation. If, in the following table, a live cell is represented by 1 and a dead cell by 0 then to generate the value of the cell at a particular index in the array of cellular values you use the following table: 000 -> 0 # 001 -> 0 # 010 -> 0 # Dies without enough neighbours 011 -> 1 # Needs one neighbour to survive 100 -> 0 # 101 -> 1 # Two neighbours giving birth 110 -> 1 # Needs one neighbour to survive 111 -> 0 # Starved to death.
#FOCAL
FOCAL
1.1 S OLD(2)=1; S OLD(3)=1; S OLD(4)=1; S OLD(6)=1; S OLD(7)=1 1.2 S OLD(9)=1; S OLD(11)=1; S OLD(13)=1; S OLD(15)=1; S OLD(18)=1 1.3 F N=1,10; D 2 1.4 Q   2.1 F X=1,20; D 3 2.2 F X=1,20; D 6 2.3 F X=1,20; S OLD(X)=NEW(X) 2.4 T !   3.1 I (OLD(X-1)+OLD(X)+OLD(X+1)-2)4.1,5.1,4.1   4.1 S NEW(X)=0   5.1 S NEW(X)=1   6.1 I (-OLD(X))7.1,8.1,8.1   7.1 T "#"   8.1 T "."
http://rosettacode.org/wiki/One-dimensional_cellular_automata
One-dimensional cellular automata
Assume an array of cells with an initial distribution of live and dead cells, and imaginary cells off the end of the array having fixed values. Cells in the next generation of the array are calculated based on the value of the cell and its left and right nearest neighbours in the current generation. If, in the following table, a live cell is represented by 1 and a dead cell by 0 then to generate the value of the cell at a particular index in the array of cellular values you use the following table: 000 -> 0 # 001 -> 0 # 010 -> 0 # Dies without enough neighbours 011 -> 1 # Needs one neighbour to survive 100 -> 0 # 101 -> 1 # Two neighbours giving birth 110 -> 1 # Needs one neighbour to survive 111 -> 0 # Starved to death.
#Forth
Forth
: init ( bits count -- ) 0 do dup 1 and c, 2/ loop drop ;   20 constant size create state $2556e size init 0 c,   : .state cr size 0 do state i + c@ if ." #" else space then loop ;   : ctable create does> + c@ ; ctable rules $68 8 init   : gen state c@ ( window ) size 0 do 2* state i + 1+ c@ or 7 and dup rules state i + c! loop drop ;   : life1d ( n -- ) .state 1 do gen .state loop ;   10 life1d
http://rosettacode.org/wiki/Numerical_integration
Numerical integration
Write functions to calculate the definite integral of a function ƒ(x) using all five of the following methods: rectangular left right midpoint trapezium Simpson's composite Your functions should take in the upper and lower bounds (a and b), and the number of approximations to make in that range (n). Assume that your example already has a function that gives values for ƒ(x) . Simpson's method is defined by the following pseudo-code: Pseudocode: Simpson's method, composite procedure quad_simpson_composite(f, a, b, n) h := (b - a) / n sum1 := f(a + h/2) sum2 := 0 loop on i from 1 to (n - 1) sum1 := sum1 + f(a + h * i + h/2) sum2 := sum2 + f(a + h * i)   answer := (h / 6) * (f(a) + f(b) + 4*sum1 + 2*sum2) Demonstrate your function by showing the results for:   ƒ(x) = x3,       where   x   is     [0,1],       with           100 approximations.   The exact result is     0.25               (or 1/4)   ƒ(x) = 1/x,     where   x   is   [1,100],     with        1,000 approximations.   The exact result is     4.605170+     (natural log of 100)   ƒ(x) = x,         where   x   is   [0,5000],   with 5,000,000 approximations.   The exact result is   12,500,000   ƒ(x) = x,         where   x   is   [0,6000],   with 6,000,000 approximations.   The exact result is   18,000,000 See also   Active object for integrating a function of real time.   Special:PrefixIndex/Numerical integration for other integration methods.
#Groovy
Groovy
def assertBounds = { List bounds, int nRect -> assert (bounds.size() == 2) && (bounds[0] instanceof Double) && (bounds[1] instanceof Double) && (nRect > 0) }   def integral = { List bounds, int nRectangles, Closure f, List pointGuide, Closure integralCalculator-> double a = bounds[0], b = bounds[1], h = (b - a)/nRectangles def xPoints = pointGuide.collect { double it -> a + it*h } def fPoints = xPoints.collect { x -> f(x) } integralCalculator(h, fPoints) }   def leftRectIntegral = { List bounds, int nRect, Closure f -> assertBounds(bounds, nRect) integral(bounds, nRect, f, (0..<nRect)) { h, fPoints -> h*fPoints.sum() } }   def rightRectIntegral = { List bounds, int nRect, Closure f -> assertBounds(bounds, nRect) integral(bounds, nRect, f, (1..nRect)) { h, fPoints -> h*fPoints.sum() } }   def midRectIntegral = { List bounds, int nRect, Closure f -> assertBounds(bounds, nRect) integral(bounds, nRect, f, ((0.5d)..nRect)) { h, fPoints -> h*fPoints.sum() } }   def trapezoidIntegral = { List bounds, int nRect, Closure f -> assertBounds(bounds, nRect) integral(bounds, nRect, f, (0..nRect)) { h, fPoints -> def fLeft = fPoints[0..<nRect] def fRight = fPoints[1..nRect] h/2*(fLeft + fRight).sum() } }   def simpsonsIntegral = { List bounds, int nSimpRect, Closure f -> assertBounds(bounds, nSimpRect) integral(bounds, nSimpRect*2, f, (0..(nSimpRect*2))) { h, fPoints -> def fLeft = fPoints[(0..<nSimpRect*2).step(2)] def fMid = fPoints[(1..<nSimpRect*2).step(2)] def fRight = fPoints[(2..nSimpRect*2).step(2)] h/3*((fLeft + fRight).sum() + 4*(fMid.sum())) } }
http://rosettacode.org/wiki/Numerical_integration/Gauss-Legendre_Quadrature
Numerical integration/Gauss-Legendre Quadrature
In a general Gaussian quadrature rule, an definite integral of f ( x ) {\displaystyle f(x)} is first approximated over the interval [ − 1 , 1 ] {\displaystyle [-1,1]} by a polynomial approximable function g ( x ) {\displaystyle g(x)} and a known weighting function W ( x ) {\displaystyle W(x)} . ∫ − 1 1 f ( x ) d x = ∫ − 1 1 W ( x ) g ( x ) d x {\displaystyle \int _{-1}^{1}f(x)\,dx=\int _{-1}^{1}W(x)g(x)\,dx} Those are then approximated by a sum of function values at specified points x i {\displaystyle x_{i}} multiplied by some weights w i {\displaystyle w_{i}} : ∫ − 1 1 W ( x ) g ( x ) d x ≈ ∑ i = 1 n w i g ( x i ) {\displaystyle \int _{-1}^{1}W(x)g(x)\,dx\approx \sum _{i=1}^{n}w_{i}g(x_{i})} In the case of Gauss-Legendre quadrature, the weighting function W ( x ) = 1 {\displaystyle W(x)=1} , so we can approximate an integral of f ( x ) {\displaystyle f(x)} with: ∫ − 1 1 f ( x ) d x ≈ ∑ i = 1 n w i f ( x i ) {\displaystyle \int _{-1}^{1}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i})} For this, we first need to calculate the nodes and the weights, but after we have them, we can reuse them for numerious integral evaluations, which greatly speeds up the calculation compared to more simple numerical integration methods. The n {\displaystyle n} evaluation points x i {\displaystyle x_{i}} for a n-point rule, also called "nodes", are roots of n-th order Legendre Polynomials P n ( x ) {\displaystyle P_{n}(x)} . Legendre polynomials are defined by the following recursive rule: P 0 ( x ) = 1 {\displaystyle P_{0}(x)=1} P 1 ( x ) = x {\displaystyle P_{1}(x)=x} n P n ( x ) = ( 2 n − 1 ) x P n − 1 ( x ) − ( n − 1 ) P n − 2 ( x ) {\displaystyle nP_{n}(x)=(2n-1)xP_{n-1}(x)-(n-1)P_{n-2}(x)} There is also a recursive equation for their derivative: P n ′ ( x ) = n x 2 − 1 ( x P n ( x ) − P n − 1 ( x ) ) {\displaystyle P_{n}'(x)={\frac {n}{x^{2}-1}}\left(xP_{n}(x)-P_{n-1}(x)\right)} The roots of those polynomials are in general not analytically solvable, so they have to be approximated numerically, for example by Newton-Raphson iteration: x n + 1 = x n − f ( x n ) f ′ ( x n ) {\displaystyle x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}} The first guess x 0 {\displaystyle x_{0}} for the i {\displaystyle i} -th root of a n {\displaystyle n} -order polynomial P n {\displaystyle P_{n}} can be given by x 0 = cos ⁡ ( π i − 1 4 n + 1 2 ) {\displaystyle x_{0}=\cos \left(\pi \,{\frac {i-{\frac {1}{4}}}{n+{\frac {1}{2}}}}\right)} After we get the nodes x i {\displaystyle x_{i}} , we compute the appropriate weights by: w i = 2 ( 1 − x i 2 ) [ P n ′ ( x i ) ] 2 {\displaystyle w_{i}={\frac {2}{\left(1-x_{i}^{2}\right)[P'_{n}(x_{i})]^{2}}}} After we have the nodes and the weights for a n-point quadrature rule, we can approximate an integral over any interval [ a , b ] {\displaystyle [a,b]} by ∫ a b f ( x ) d x ≈ b − a 2 ∑ i = 1 n w i f ( b − a 2 x i + a + b 2 ) {\displaystyle \int _{a}^{b}f(x)\,dx\approx {\frac {b-a}{2}}\sum _{i=1}^{n}w_{i}f\left({\frac {b-a}{2}}x_{i}+{\frac {a+b}{2}}\right)} Task description Similar to the task Numerical Integration, the task here is to calculate the definite integral of a function f ( x ) {\displaystyle f(x)} , but by applying an n-point Gauss-Legendre quadrature rule, as described here, for example. The input values should be an function f to integrate, the bounds of the integration interval a and b, and the number of gaussian evaluation points n. An reference implementation in Common Lisp is provided for comparison. To demonstrate the calculation, compute the weights and nodes for an 5-point quadrature rule and then use them to compute: ∫ − 3 3 exp ⁡ ( x ) d x ≈ ∑ i = 1 5 w i exp ⁡ ( x i ) ≈ 20.036 {\displaystyle \int _{-3}^{3}\exp(x)\,dx\approx \sum _{i=1}^{5}w_{i}\;\exp(x_{i})\approx 20.036}
#Racket
Racket
  (define (LegendreP n x) (let compute ([n n] [Pn-1 x] [Pn-2 1]) (case n [(0) Pn-2] [(1) Pn-1] [else (compute (- n 1) (/ (- (* (- (* 2 n) 1) x Pn-1) (* (- n 1) Pn-2)) n) Pn-1)])))   (define (LegendreP′ n x) (* (/ n (- (* x x) 1)) (- (* x (LegendreP n x)) (LegendreP (- n 1) x))))  
http://rosettacode.org/wiki/Old_lady_swallowed_a_fly
Old lady swallowed a fly
Task Present a program which emits the lyrics to the song   I Knew an Old Lady Who Swallowed a Fly,   taking advantage of the repetitive structure of the song's lyrics. This song has multiple versions with slightly different lyrics, so all these programs might not emit identical output. Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Nanoquery
Nanoquery
reason = {"She swallowed the ", " to catch the "} creatures = {"fly", "spider", "bird", "cat", "dog", "goat", "cow", "horse"} comments = {"I don't know why she swallowed that fly.\nPerhaps she'll die\n",\ "That wiggled and jiggled and tickled inside her",\ "How absurd, to swallow a bird",\ "Imagine that. She swallowed a cat",\ "What a hog to swallow a dog",\ "She just opened her throat and swallowed that goat",\ "I don't know how she swallowed that cow",\ "She's dead of course"}   max = len(creatures) for i in range(0, max - 1) println "There was an old lady who swallowed a " + creatures[i] println comments[i] for (j = i) ((j > 0) && (i < (max - 1))) (j -= 1) println reason[0] + creatures[j] + reason[1] + creatures[j - 1] if j = 1 println comments[j - 1] end end end   input()
http://rosettacode.org/wiki/Old_lady_swallowed_a_fly
Old lady swallowed a fly
Task Present a program which emits the lyrics to the song   I Knew an Old Lady Who Swallowed a Fly,   taking advantage of the repetitive structure of the song's lyrics. This song has multiple versions with slightly different lyrics, so all these programs might not emit identical output. Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Nim
Nim
import zip/zlib, base64   const b64 = """ eNrtVE1rwzAMvedXaKdeRn7ENrb21rHCzmrs1m49K9gOJv9+cko/HBcGg0LHcpOfnq2np0QL 2FuKgBbICDAoeoiKwEc0hqIUgLAxfV0tQJCdhQM7qh68kheswKeBt5ROYetTemYMCC3rii// WMS3WkhXVyuFAaLT261JuBWwu4iDbvYp1tYzHVS68VEIObwFgaDB0KizuFs38aSdqKv3TgcJ uPYdn2B1opwIpeKE53qPftxRd88Y6uoVbdPzWxznrQ3ZUi3DudQ/bcELbevqM32iCIrj3IIh W6plOJf6L6xaajZjzqW/qAsKIvITBGs9Nm3glboZzkVP5l6Y+0bHLnedD0CttIyrpEU5Kv7N Mz3XkPBc/TSN3yxGiqMiipHRekycK0ZwMhM8jerGC9zuZaoTho3kMKSfJjLaF8v8wLzmXMqM zJvGew/jnZPzclA08yAkikegDTTUMfzwDXBcwoE="""   echo b64.decode.uncompress()
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#Swift
Swift
func one_of_n(n: Int) -> Int { var result = 1 for i in 2...n { if arc4random_uniform(UInt32(i)) < 1 { result = i } } return result }   var counts = [0,0,0,0,0,0,0,0,0,0] for _ in 1..1_000_000 { counts[one_of_n(10)-1]++ }   println(counts)
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#Tcl
Tcl
package require Tcl 8.5 proc 1ofN {n} { for {set line 1} {$line <= $n} {incr line} { if {rand() < 1.0/[incr fraction]} { set result $line } } return $result }   for {set i 0} {$i < 1000000} {incr i} { incr count([1ofN 10]) } parray count; # Alphabetic order, but convenient
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#Sidef
Sidef
func ordered(a, b) { (a <=> b) < 0 }   for p in [ Pair([1,2,4], [1,2,4]), Pair([1,2,4], [1,2] ), Pair([1,2], [1,2,4]), ] { var a = p.first var b = p.second var before = ordered(a, b) say "#{a} comes before #{b} : #{before}" }
http://rosettacode.org/wiki/Ordered_words
Ordered words
An   ordered word   is a word in which the letters appear in alphabetic order. Examples include   abbey   and   dirt. Task[edit] Find and display all the ordered words in the dictionary   unixdict.txt   that have the longest word length. (Examples that access the dictionary file locally assume that you have downloaded this file yourself.) The display needs to be shown on this page. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Prolog
Prolog
:- use_module(library( http/http_open )).   ordered_words :- % we read the URL of the words http_open('http://www.puzzlers.org/pub/wordlists/unixdict.txt', In, []), read_file(In, [], Out), close(In),   % we get a list of pairs key-value where key = Length and value = <list-of-its-codes> % this list must be sorted msort(Out, MOut),   group_pairs_by_key(MOut, POut),   % we sorted this list in decreasing order of the length of values predsort(my_compare, POut, [_N-V | _OutSort]), maplist(mwritef, V).     mwritef(V) :- writef('%s\n', [V]).   read_file(In, L, L1) :- read_line_to_codes(In, W), ( W == end_of_file -> % the file is read L1 = L ; % we sort the list of codes of the line % and keep only the "goods word" ( msort(W, W) -> length(W, N), L2 = [N-W | L], (len = 6 -> writef('%s\n', [W]); true) ; L2 = L ),   % and we have the pair Key-Value in the result list read_file(In, L2, L1)).   % predicate for sorting list of pairs Key-Values % if the lentgh of values is the same % we sort the keys in alhabetic order my_compare(R, K1-_V1, K2-_V2) :- ( K1 < K2 -> R = >; K1 > K2 -> R = <; =).  
http://rosettacode.org/wiki/Palindrome_detection
Palindrome detection
A palindrome is a phrase which reads the same backward and forward. Task[edit] Write a function or program that checks whether a given sequence of characters (or, if you prefer, bytes) is a palindrome. For extra credit: Support Unicode characters. Write a second function (possibly as a wrapper to the first) which detects inexact palindromes, i.e. phrases that are palindromes if white-space and punctuation is ignored and case-insensitive comparison is used. Hints It might be useful for this task to know how to reverse a string. This task's entries might also form the subjects of the task Test a function. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#Rust
Rust
fn is_palindrome(string: &str) -> bool { let half_len = string.len() / 2; string .chars() .take(half_len) .eq(string.chars().rev().take(half_len)) }   macro_rules! test { ( $( $x:tt ),* ) => { $( println!("'{}': {}", $x, is_palindrome($x)); )* }; }   fn main() { test!( "", "a", "ada", "adad", "ingirumimusnocteetconsumimurigni", "人人為我,我為人人", "Я иду с мечем, судия", "아들딸들아", "The quick brown fox" ); }
http://rosettacode.org/wiki/Odd_word_problem
Odd word problem
Task Write a program that solves the odd word problem with the restrictions given below. Description You are promised an input stream consisting of English letters and punctuations. It is guaranteed that: the words (sequence of consecutive letters) are delimited by one and only one punctuation, the stream will begin with a word, the words will be at least one letter long,   and a full stop (a period, [.]) appears after, and only after, the last word. Example A stream with six words: what,is,the;meaning,of:life. The task is to reverse the letters in every other word while leaving punctuations intact, producing: what,si,the;gninaem,of:efil. while observing the following restrictions: Only I/O allowed is reading or writing one character at a time, which means: no reading in a string, no peeking ahead, no pushing characters back into the stream, and no storing characters in a global variable for later use; You are not to explicitly save characters in a collection data structure, such as arrays, strings, hash tables, etc, for later reversal; You are allowed to use recursions, closures, continuations, threads, co-routines, etc., even if their use implies the storage of multiple characters. Test cases Work on both the   "life"   example given above, and also the text: we,are;not,in,kansas;any,more.
#Run_BASIC
Run BASIC
open "oddWord.txt" for input as #f ' read input stream while not(eof(#f)) line input #f, a$ oddW$ = "" ' begin the result oddW with blank px = 0 ' begin word search location with 0 count = 0 ' begin the word count to 0 while x < len(a$) ' look at each character x = instr(a$,",",px) ' search for comma (,) if x = 0 then x = len(a$) ' no more commas? x1 = instr(a$,";",px) ' search for (;) x2 = instr(a$,":",px) ' search for (:) if x1 <> 0 then x = min(x,x1) ' what came first the , ; or : if x2 <> 0 then x = min(x,x2)   w$ = mid$(a$,px,x - px) ' get the word seperated by , ; or :   if count and 1 then ' is it the odd word w1$ = "" for i = len(w$) to 1 step -1 w1$ = w1$ + mid$(w$,i,1) ' reverse odd words next i w$ = w1$ end if oddW$ = oddW$ + w$ + mid$(a$,x,1) ' add the word to the end of oddW$ px = x + 1 ' bump word search location for next while count = count + 1 ' count the words wend print a$;" -> ";oddW$ ' print the original and result next ii wend close #f
http://rosettacode.org/wiki/Odd_word_problem
Odd word problem
Task Write a program that solves the odd word problem with the restrictions given below. Description You are promised an input stream consisting of English letters and punctuations. It is guaranteed that: the words (sequence of consecutive letters) are delimited by one and only one punctuation, the stream will begin with a word, the words will be at least one letter long,   and a full stop (a period, [.]) appears after, and only after, the last word. Example A stream with six words: what,is,the;meaning,of:life. The task is to reverse the letters in every other word while leaving punctuations intact, producing: what,si,the;gninaem,of:efil. while observing the following restrictions: Only I/O allowed is reading or writing one character at a time, which means: no reading in a string, no peeking ahead, no pushing characters back into the stream, and no storing characters in a global variable for later use; You are not to explicitly save characters in a collection data structure, such as arrays, strings, hash tables, etc, for later reversal; You are allowed to use recursions, closures, continuations, threads, co-routines, etc., even if their use implies the storage of multiple characters. Test cases Work on both the   "life"   example given above, and also the text: we,are;not,in,kansas;any,more.
#Scala
Scala
import scala.io.Source import java.io.PrintStream   def process(s: Source, p: PrintStream, w: Int = 0): Unit = if (s.hasNext) s.next match { case '.' => p append '.' case c if !Character.isAlphabetic(c) => p append c; reverse(s, p, w + 1) case c => p append c; process(s, p, w) }   def reverse(s: Source, p: PrintStream, w: Int = 0, x: Char = '.'): Char = s.next match { case c if !Character.isAlphabetic(c) => p append x; c case c => val n = reverse(s, p, w, c); if (x == '.') {p append n; process(s, p, w + 1)} else p append x; n }   process(Source.fromString("what,is,the;meaning,of:life."), System.out); println process(Source.fromString("we,are;not,in,kansas;any,more."), System.out); println
http://rosettacode.org/wiki/Number_names
Number names
Task Show how to spell out a number in English. You can use a preexisting implementation or roll your own, but you should support inputs up to at least one million (or the maximum value of your language's default bounded integer type, if that's less). Support for inputs other than positive integers (like zero, negative integers, and floating-point numbers) is optional. Related task   Spelling of ordinal numbers.
#Commodore_BASIC
Commodore BASIC
10 print chr$(147);chr$(14) 20 dim s$(11),ts$(11),t$(11),o$(11):co=39 30 for i=0 to 11:read s$(i),ts$(i),t$(i),o$(i):next 40 print "Enter a number";:input n$ 45 ou$="" 50 if len(n$)>36 then print:print "Too long.":print:goto 40 51 print 55 rem check for negative 56 if left$(n$,1)="-" then n$=right$(n$,len(n$)-1):ou$="negative ":gosub 500 60 no=int((len(n$)-1)/3) 70 rem pad left side 71 p=(no+1)*3-len(n$) 75 if p>0 then n$="0"+n$:p=p-1:goto 75 77 if val(n$)=0 then ou$=s$(0):gosub 500:goto 125 80 rem calculate left to right 81 for i=no to 0 step -1:oi=no-i 85 ch$=mid$(n$,1+(oi*3),3) 90 h=val(mid$(ch$,1,1)):t=val(mid$(ch$,2,1)):s=val(mid$(ch$,3,1)) 93 if h=0 and t=0 and s=0 then goto 120 95 if h>0 then ou$=s$(h)+" hundred ":gosub 500 100 if t>1 then ou$=t$(t)+mid$("- ",abs(s=0)+1,1):gosub 500 105 if t=1 then ou$=ts$(s)+" ":gosub 500 110 if t<>1 and s>0 then ou$=s$(s)+" ":gosub 500 115 ou$=o$(i)+" ":gosub 500 120 next i 125 print:print 130 print "Another? (y/n) "; 140 get k$:ifk$<>"y" and k$<>"n" then 140 145 print k$ 150 if k$="y" then print:goto 40 200 end 500 rem print with word wrapping 505 cp=pos(0):nl=len(ou$) 510 if cp>co-nl then print 520 print ou$; 599 return 1000 data zero,ten,"","" 1001 data one,eleven,ten,thousand 1002 data two,twelve,twenty,million 1003 data three,thirteen,thirty,billion 1004 data four,fourteen,forty,trillion 1005 data five,fifteen,fifty,quadrillion 1006 data six,sixteen,sixty,quintillion 1007 data seven,seventeen,seventy,sextillion 1008 data eight,eighteen,eighty,septillion 1009 data nine,nineteen,ninety,octillion 1010 data "","","",nonillion 1011 data "","","",decillion
http://rosettacode.org/wiki/Number_reversal_game
Number reversal game
Task Given a jumbled list of the numbers   1   to   9   that are definitely   not   in ascending order. Show the list,   and then ask the player how many digits from the left to reverse. Reverse those digits,   then ask again,   until all the digits end up in ascending order. The score is the count of the reversals needed to attain the ascending order. Note: Assume the player's input does not need extra validation. Related tasks   Sorting algorithms/Pancake sort   Pancake sorting.   Topswops
#Egel
Egel
  import "prelude.eg" import "io.ego" import "random.ego"   using System using IO using List using Math   def swap = [ (I J) XX -> insert I (nth J XX) (insert J (nth I XX) XX) ]   def shuffle = [ XX -> let INDICES = reverse (fromto 0 ((length XX) - 1)) in let SWAPS = map [ I -> I (between 0 I) ] INDICES in foldr [I J -> swap I J] XX SWAPS ]   def prompt = [ XX TURN -> let _ = print TURN ". " in let _ = map [ X -> print X " " ] XX in let _ = print " : " in toint getline ]   def game = [ GOAL SHUFFLE TURN -> if SHUFFLE == GOAL then let _ = print "the goal was " in let _ = map [ X -> print X " " ] GOAL in print "\nit took you " TURN " turns\n" else let N = prompt SHUFFLE TURN in let YY = (reverse (take N SHUFFLE)) ++ (drop N SHUFFLE) in game GOAL YY (TURN + 1) ]   def main = let XX = fromto 1 9 in game XX (shuffle XX) 0
http://rosettacode.org/wiki/Null_object
Null object
Null (or nil) is the computer science concept of an undefined or unbound object. Some languages have an explicit way to access the null object, and some don't. Some languages distinguish the null object from undefined values, and some don't. Task Show how to access null in your language by checking to see if an object is equivalent to the null object. This task is not about whether a variable is defined. The task is about "null"-like values in various languages, which may or may not be related to the defined-ness of variables in your language.
#Go
Go
  package main   import "fmt"   var ( s []int // slice type p *int // pointer type f func() // function type i interface{} // interface type m map[int]int // map type c chan int // channel type )   func main() { fmt.Println(s == nil) fmt.Println(p == nil) fmt.Println(f == nil) fmt.Println(i == nil) fmt.Println(m == nil) fmt.Println(c == nil) }  
http://rosettacode.org/wiki/Null_object
Null object
Null (or nil) is the computer science concept of an undefined or unbound object. Some languages have an explicit way to access the null object, and some don't. Some languages distinguish the null object from undefined values, and some don't. Task Show how to access null in your language by checking to see if an object is equivalent to the null object. This task is not about whether a variable is defined. The task is about "null"-like values in various languages, which may or may not be related to the defined-ness of variables in your language.
#Haskell
Haskell
undefined -- undefined value provided by the standard library error "oops" -- another undefined value head [] -- undefined, you can't take the head of an empty list
http://rosettacode.org/wiki/One-dimensional_cellular_automata
One-dimensional cellular automata
Assume an array of cells with an initial distribution of live and dead cells, and imaginary cells off the end of the array having fixed values. Cells in the next generation of the array are calculated based on the value of the cell and its left and right nearest neighbours in the current generation. If, in the following table, a live cell is represented by 1 and a dead cell by 0 then to generate the value of the cell at a particular index in the array of cellular values you use the following table: 000 -> 0 # 001 -> 0 # 010 -> 0 # Dies without enough neighbours 011 -> 1 # Needs one neighbour to survive 100 -> 0 # 101 -> 1 # Two neighbours giving birth 110 -> 1 # Needs one neighbour to survive 111 -> 0 # Starved to death.
#Fortran
Fortran
PROGRAM LIFE_1D   IMPLICIT NONE   LOGICAL :: cells(20) = (/ .FALSE., .TRUE., .TRUE., .TRUE., .FALSE., .TRUE., .TRUE., .FALSE., .TRUE., .FALSE., & .TRUE., .FALSE., .TRUE., .FALSE., .TRUE., .FALSE., .FALSE., .TRUE., .FALSE., .FALSE. /) INTEGER :: i   DO i = 0, 9 WRITE(*, "(A,I0,A)", ADVANCE = "NO") "Generation ", i, ": " CALL Drawgen(cells) CALL Nextgen(cells) END DO   CONTAINS   SUBROUTINE Nextgen(cells) LOGICAL, INTENT (IN OUT) :: cells(:) LOGICAL :: left, centre, right INTEGER :: i   left = .FALSE. DO i = 1, SIZE(cells)-1 centre = cells(i) right = cells(i+1) IF (left .AND. right) THEN cells(i) = .NOT. cells(i) ELSE IF (.NOT. left .AND. .NOT. right) THEN cells(i) = .FALSE. END IF left = centre END DO cells(SIZE(cells)) = left .AND. right END SUBROUTINE Nextgen   SUBROUTINE Drawgen(cells) LOGICAL, INTENT (IN OUT) :: cells(:) INTEGER :: i   DO i = 1, SIZE(cells) IF (cells(i)) THEN WRITE(*, "(A)", ADVANCE = "NO") "#" ELSE WRITE(*, "(A)", ADVANCE = "NO") "_" END IF END DO WRITE(*,*) END SUBROUTINE Drawgen   END PROGRAM LIFE_1D
http://rosettacode.org/wiki/Numerical_integration
Numerical integration
Write functions to calculate the definite integral of a function ƒ(x) using all five of the following methods: rectangular left right midpoint trapezium Simpson's composite Your functions should take in the upper and lower bounds (a and b), and the number of approximations to make in that range (n). Assume that your example already has a function that gives values for ƒ(x) . Simpson's method is defined by the following pseudo-code: Pseudocode: Simpson's method, composite procedure quad_simpson_composite(f, a, b, n) h := (b - a) / n sum1 := f(a + h/2) sum2 := 0 loop on i from 1 to (n - 1) sum1 := sum1 + f(a + h * i + h/2) sum2 := sum2 + f(a + h * i)   answer := (h / 6) * (f(a) + f(b) + 4*sum1 + 2*sum2) Demonstrate your function by showing the results for:   ƒ(x) = x3,       where   x   is     [0,1],       with           100 approximations.   The exact result is     0.25               (or 1/4)   ƒ(x) = 1/x,     where   x   is   [1,100],     with        1,000 approximations.   The exact result is     4.605170+     (natural log of 100)   ƒ(x) = x,         where   x   is   [0,5000],   with 5,000,000 approximations.   The exact result is   12,500,000   ƒ(x) = x,         where   x   is   [0,6000],   with 6,000,000 approximations.   The exact result is   18,000,000 See also   Active object for integrating a function of real time.   Special:PrefixIndex/Numerical integration for other integration methods.
#Haskell
Haskell
approx f xs ws = sum [w * f x | (x,w) <- zip xs ws]
http://rosettacode.org/wiki/Numerical_integration/Gauss-Legendre_Quadrature
Numerical integration/Gauss-Legendre Quadrature
In a general Gaussian quadrature rule, an definite integral of f ( x ) {\displaystyle f(x)} is first approximated over the interval [ − 1 , 1 ] {\displaystyle [-1,1]} by a polynomial approximable function g ( x ) {\displaystyle g(x)} and a known weighting function W ( x ) {\displaystyle W(x)} . ∫ − 1 1 f ( x ) d x = ∫ − 1 1 W ( x ) g ( x ) d x {\displaystyle \int _{-1}^{1}f(x)\,dx=\int _{-1}^{1}W(x)g(x)\,dx} Those are then approximated by a sum of function values at specified points x i {\displaystyle x_{i}} multiplied by some weights w i {\displaystyle w_{i}} : ∫ − 1 1 W ( x ) g ( x ) d x ≈ ∑ i = 1 n w i g ( x i ) {\displaystyle \int _{-1}^{1}W(x)g(x)\,dx\approx \sum _{i=1}^{n}w_{i}g(x_{i})} In the case of Gauss-Legendre quadrature, the weighting function W ( x ) = 1 {\displaystyle W(x)=1} , so we can approximate an integral of f ( x ) {\displaystyle f(x)} with: ∫ − 1 1 f ( x ) d x ≈ ∑ i = 1 n w i f ( x i ) {\displaystyle \int _{-1}^{1}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i})} For this, we first need to calculate the nodes and the weights, but after we have them, we can reuse them for numerious integral evaluations, which greatly speeds up the calculation compared to more simple numerical integration methods. The n {\displaystyle n} evaluation points x i {\displaystyle x_{i}} for a n-point rule, also called "nodes", are roots of n-th order Legendre Polynomials P n ( x ) {\displaystyle P_{n}(x)} . Legendre polynomials are defined by the following recursive rule: P 0 ( x ) = 1 {\displaystyle P_{0}(x)=1} P 1 ( x ) = x {\displaystyle P_{1}(x)=x} n P n ( x ) = ( 2 n − 1 ) x P n − 1 ( x ) − ( n − 1 ) P n − 2 ( x ) {\displaystyle nP_{n}(x)=(2n-1)xP_{n-1}(x)-(n-1)P_{n-2}(x)} There is also a recursive equation for their derivative: P n ′ ( x ) = n x 2 − 1 ( x P n ( x ) − P n − 1 ( x ) ) {\displaystyle P_{n}'(x)={\frac {n}{x^{2}-1}}\left(xP_{n}(x)-P_{n-1}(x)\right)} The roots of those polynomials are in general not analytically solvable, so they have to be approximated numerically, for example by Newton-Raphson iteration: x n + 1 = x n − f ( x n ) f ′ ( x n ) {\displaystyle x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}} The first guess x 0 {\displaystyle x_{0}} for the i {\displaystyle i} -th root of a n {\displaystyle n} -order polynomial P n {\displaystyle P_{n}} can be given by x 0 = cos ⁡ ( π i − 1 4 n + 1 2 ) {\displaystyle x_{0}=\cos \left(\pi \,{\frac {i-{\frac {1}{4}}}{n+{\frac {1}{2}}}}\right)} After we get the nodes x i {\displaystyle x_{i}} , we compute the appropriate weights by: w i = 2 ( 1 − x i 2 ) [ P n ′ ( x i ) ] 2 {\displaystyle w_{i}={\frac {2}{\left(1-x_{i}^{2}\right)[P'_{n}(x_{i})]^{2}}}} After we have the nodes and the weights for a n-point quadrature rule, we can approximate an integral over any interval [ a , b ] {\displaystyle [a,b]} by ∫ a b f ( x ) d x ≈ b − a 2 ∑ i = 1 n w i f ( b − a 2 x i + a + b 2 ) {\displaystyle \int _{a}^{b}f(x)\,dx\approx {\frac {b-a}{2}}\sum _{i=1}^{n}w_{i}f\left({\frac {b-a}{2}}x_{i}+{\frac {a+b}{2}}\right)} Task description Similar to the task Numerical Integration, the task here is to calculate the definite integral of a function f ( x ) {\displaystyle f(x)} , but by applying an n-point Gauss-Legendre quadrature rule, as described here, for example. The input values should be an function f to integrate, the bounds of the integration interval a and b, and the number of gaussian evaluation points n. An reference implementation in Common Lisp is provided for comparison. To demonstrate the calculation, compute the weights and nodes for an 5-point quadrature rule and then use them to compute: ∫ − 3 3 exp ⁡ ( x ) d x ≈ ∑ i = 1 5 w i exp ⁡ ( x i ) ≈ 20.036 {\displaystyle \int _{-3}^{3}\exp(x)\,dx\approx \sum _{i=1}^{5}w_{i}\;\exp(x_{i})\approx 20.036}
#Raku
Raku
multi legendre-pair( 1 , $x) { $x, 1 } multi legendre-pair(Int $n, $x) { my ($m1, $m2) = legendre-pair($n - 1, $x); my \u = 1 - 1 / $n; (1 + u) * $x * $m1 - u * $m2, $m1; }   multi legendre( 0 , $ ) { 1 } multi legendre(Int $n, $x) { legendre-pair($n, $x)[0] }   multi legendre-prime( 0 , $ ) { 0 } multi legendre-prime( 1 , $ ) { 1 } multi legendre-prime(Int $n, $x) { my ($m0, $m1) = legendre-pair($n, $x); ($m1 - $x * $m0) * $n / (1 - $x**2); }   sub approximate-legendre-root(Int $n, Int $k) { # Approximation due to Francesco Tricomi my \t = (4*$k - 1) / (4*$n + 2); (1 - ($n - 1) / (8 * $n**3)) * cos(pi * t); }   sub newton-raphson(&f, &f-prime, $r is copy, :$eps = 2e-16) { while abs(my \dr = - f($r) / f-prime($r)) >= $eps { $r += dr; } $r; }   sub legendre-root(Int $n, Int $k) { newton-raphson(&legendre.assuming($n), &legendre-prime.assuming($n), approximate-legendre-root($n, $k)); }   sub weight(Int $n, $r) { 2 / ((1 - $r**2) * legendre-prime($n, $r)**2) }   sub nodes(Int $n) { flat gather { take 0 => weight($n, 0) if $n !%% 2; for 1 .. $n div 2 { my $r = legendre-root($n, $_); my $w = weight($n, $r); take $r => $w, -$r => $w; } } }   sub quadrature(Int $n, &f, $a, $b, :@nodes = nodes($n)) { sub scale($x) { ($x * ($b - $a) + $a + $b) / 2 } ($b - $a) / 2 * [+] @nodes.map: { .value * f(scale(.key)) } }   say "Gauss-Legendre $_.fmt('%2d')-point quadrature ∫₋₃⁺³ exp(x) dx ≈ ", quadrature($_, &exp, -3, +3) for flat 5 .. 10, 20;
http://rosettacode.org/wiki/Old_lady_swallowed_a_fly
Old lady swallowed a fly
Task Present a program which emits the lyrics to the song   I Knew an Old Lady Who Swallowed a Fly,   taking advantage of the repetitive structure of the song's lyrics. This song has multiple versions with slightly different lyrics, so all these programs might not emit identical output. Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#OCaml
OCaml
let d = [| "I know an old lady who swallowed a "; "fly"; ".\n"; "I don't know why she swallowed the fly.\nPerhaps she'll die.\n\n"; "spider"; "That wriggled and jiggled and tickled inside her"; "She swallowed the "; " to catch the "; "Bird"; "Quite absurd"; ". To swallow a "; "Cat"; "Fancy that"; "Dog"; "What a hog"; "Pig"; "Her mouth was so big"; "Goat"; "She just opened her throat"; "Cow"; "I don't know how"; "Donkey"; "It was rather wonky"; "I know an old lady who swallowed a Horse.\nShe's dead, of course!\n"; |]   let s0 = [6;4;7;1;2;3] let s1 = [6;8;7;4;2] @ s0 let s2 = [6;11;7;8;2] @ s1 let s3 = [6;13;7;11;2] @ s2 let s4 = [6;15;7;13;2] @ s3 let s5 = [6;17;7;15;2] @ s4 let s6 = [6;19;7;17;2] @ s5 let s7 = [6;21;7;19;2] @ s6   let s = [0;1;2;3;0;4;2;5;2] @ s0 @ [0;8;2;9;10;8;2] @ s1 @ [0;11;2;12;10;11;2] @ s2 @ [0;13;2;14;10;13;2] @ s3 @ [0;15;2;16;10;15;2] @ s4 @ [0;17;2;18;10;17;2] @ s5 @ [0;19;2;20;10;19;2] @ s6 @ [0;21;2;22;10;21;2] @ s7 @ [23] ;;   List.iter (fun i -> print_string d.(i)) s
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#VBScript
VBScript
  Dim chosen(10)   For j = 1 To 1000000 c = one_of_n(10) chosen(c) = chosen(c) + 1 Next   For k = 1 To 10 WScript.StdOut.WriteLine k & ". " & chosen(k) Next   Function one_of_n(n) Randomize For i = 1 To n If Rnd(1) < 1/i Then one_of_n = i End If Next End Function  
http://rosettacode.org/wiki/One_of_n_lines_in_a_file
One of n lines in a file
A method of choosing a line randomly from a file: Without reading the file more than once When substantial parts of the file cannot be held in memory Without knowing how many lines are in the file Is to: keep the first line of the file as a possible choice, then Read the second line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/2. Read the third line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/3. ... Read the Nth line of the file if possible and make it the possible choice if a uniform random value between zero and one is less than 1/N Return the computed possible choice when no further lines exist in the file. Task Create a function/method/routine called one_of_n that given n, the number of actual lines in a file, follows the algorithm above to return an integer - the line number of the line chosen from the file. The number returned can vary, randomly, in each run. Use one_of_n in a simulation to find what woud be the chosen line of a 10 line file simulated 1,000,000 times. Print and show how many times each of the 10 lines is chosen as a rough measure of how well the algorithm works. Note: You may choose a smaller number of repetitions if necessary, but mention this up-front. Note: This is a specific version of a Reservoir Sampling algorithm: https://en.wikipedia.org/wiki/Reservoir_sampling
#Wren
Wren
import "random" for Random import "/fmt" for Fmt   var rand = Random.new()   var oneOfN = Fn.new { |n| var choice = 1 for (i in 2..n) { if (rand.float() < 1/i) choice = i } return choice }   var n = 10 var freqs = List.filled(n, 0) var reps = 1e6 for (i in 0...reps) { var num = oneOfN.call(n) freqs[num-1] = freqs[num-1] + 1 } for (i in 1..n) Fmt.print("Line $-2d = $,7d", i, freqs[i-1])
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#Standard_ML
Standard ML
- List.collate Int.compare ([1,2,1,3,2], [1,2,0,4,4,0,0,0]) = LESS; val it = false : bool
http://rosettacode.org/wiki/Order_two_numerical_lists
Order two numerical lists
sorting Sorting Algorithm This is a sorting algorithm.   It may be applied to a set of data in order to sort it.     For comparing various sorts, see compare sorts.   For other sorting algorithms,   see sorting algorithms,   or: O(n logn) sorts Heap sort | Merge sort | Patience sort | Quick sort O(n log2n) sorts Shell Sort O(n2) sorts Bubble sort | Cocktail sort | Cocktail sort with shifting bounds | Comb sort | Cycle sort | Gnome sort | Insertion sort | Selection sort | Strand sort other sorts Bead sort | Bogo sort | Common sorted list | Composite structures sort | Custom comparator sort | Counting sort | Disjoint sublist sort | External sort | Jort sort | Lexicographical sort | Natural sorting | Order by pair comparisons | Order disjoint list items | Order two numerical lists | Object identifier (OID) sort | Pancake sort | Quickselect | Permutation sort | Radix sort | Ranking methods | Remove duplicate elements | Sleep sort | Stooge sort | [Sort letters of a string] | Three variable sort | Topological sort | Tree sort Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
#Swift
Swift
let a = [1,2,1,3,2] let b = [1,2,0,4,4,0,0,0] println(lexicographicalCompare(a, b)) // this is "less than"
http://rosettacode.org/wiki/Ordered_words
Ordered words
An   ordered word   is a word in which the letters appear in alphabetic order. Examples include   abbey   and   dirt. Task[edit] Find and display all the ordered words in the dictionary   unixdict.txt   that have the longest word length. (Examples that access the dictionary file locally assume that you have downloaded this file yourself.) The display needs to be shown on this page. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#PureBasic
PureBasic
Procedure.s sortLetters(*word.Character, wordLength) ;returns a string with the letters of a word sorted Protected Dim letters.c(wordLength) Protected *letAdr = @letters()   CopyMemoryString(*word, @*letAdr) SortArray(letters(), #PB_Sort_Ascending, 0, wordLength - 1) ProcedureReturn PeekS(@letters(), wordLength) EndProcedure   Structure orderedWord word.s length.i EndStructure   Define filename.s = "unixdict.txt", fileNum = 0, word.s   If OpenConsole() NewList orderedWords.orderedWord() If ReadFile(fileNum, filename) While Not Eof(fileNum) word = ReadString(fileNum) If word = sortLetters(@word, Len(word)) AddElement(orderedWords()) orderedWords()\word = word orderedWords()\length = Len(word) EndIf Wend Else MessageRequester("Error", "Unable to find dictionary '" + filename + "'") End EndIf   SortStructuredList(orderedWords(), #PB_Sort_Ascending, OffsetOf(orderedWord\word), #PB_String) SortStructuredList(orderedWords(), #PB_Sort_Descending, OffsetOf(orderedWord\length), #PB_Integer) Define maxLength FirstElement(orderedWords()) maxLength = orderedWords()\length ForEach orderedWords() If orderedWords()\length = maxLength Print(orderedWords()\word + " ") EndIf Next   Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input() CloseConsole() EndIf
http://rosettacode.org/wiki/Palindrome_detection
Palindrome detection
A palindrome is a phrase which reads the same backward and forward. Task[edit] Write a function or program that checks whether a given sequence of characters (or, if you prefer, bytes) is a palindrome. For extra credit: Support Unicode characters. Write a second function (possibly as a wrapper to the first) which detects inexact palindromes, i.e. phrases that are palindromes if white-space and punctuation is ignored and case-insensitive comparison is used. Hints It might be useful for this task to know how to reverse a string. This task's entries might also form the subjects of the task Test a function. Related tasks Word plays Ordered words Palindrome detection Semordnilap Anagrams Anagrams/Deranged anagrams Other tasks related to string operations: Metrics Array length String length Copy a string Empty string  (assignment) Counting Word frequency Letter frequency Jewels and stones I before E except after C Bioinformatics/base count Count occurrences of a substring Count how many vowels and consonants occur in a string Remove/replace XXXX redacted Conjugate a Latin verb Remove vowels from a string String interpolation (included) Strip block comments Strip comments from a string Strip a set of characters from a string Strip whitespace from a string -- top and tail Strip control codes and extended characters from a string Anagrams/Derangements/shuffling Word wheel ABC problem Sattolo cycle Knuth shuffle Ordered words Superpermutation minimisation Textonyms (using a phone text pad) Anagrams Anagrams/Deranged anagrams Permutations/Derangements Find/Search/Determine ABC words Odd words Word ladder Semordnilap Word search Wordiff  (game) String matching Tea cup rim text Alternade words Changeable words State name puzzle String comparison Unique characters Unique characters in each string Extract file extension Levenshtein distance Palindrome detection Common list elements Longest common suffix Longest common prefix Compare a list of strings Longest common substring Find common directory path Words from neighbour ones Change e letters to i in words Non-continuous subsequences Longest common subsequence Longest palindromic substrings Longest increasing subsequence Words containing "the" substring Sum of the digits of n is substring of n Determine if a string is numeric Determine if a string is collapsible Determine if a string is squeezable Determine if a string has all unique characters Determine if a string has all the same characters Longest substrings without repeating characters Find words which contains all the vowels Find words which contains most consonants Find words which contains more than 3 vowels Find words which first and last three letters are equals Find words which odd letters are consonants and even letters are vowels or vice_versa Formatting Substring Rep-string Word wrap String case Align columns Literals/String Repeat a string Brace expansion Brace expansion using ranges Reverse a string Phrase reversals Comma quibbling Special characters String concatenation Substring/Top and tail Commatizing numbers Reverse words in a string Suffixation of decimal numbers Long literals, with continuations Numerical and alphabetical suffixes Abbreviations, easy Abbreviations, simple Abbreviations, automatic Song lyrics/poems/Mad Libs/phrases Mad Libs Magic 8-ball 99 Bottles of Beer The Name Game (a song) The Old lady swallowed a fly The Twelve Days of Christmas Tokenize Text between Tokenize a string Word break problem Tokenize a string with escaping Split a character string based on change of character Sequences Show ASCII table De Bruijn sequences Self-referential sequences Generate lower case ASCII alphabet
#SAS
SAS
  The macro "palindro" has two parameters: string and ignorewhitespace. string is the expression to be checked. ignorewhitespace, (Y/N), determines whether or not to ignore blanks and punctuation. This macro was written in SAS 9.2. If you use a version before SAS 9.1.3, the compress function options will not work.  
http://rosettacode.org/wiki/Odd_word_problem
Odd word problem
Task Write a program that solves the odd word problem with the restrictions given below. Description You are promised an input stream consisting of English letters and punctuations. It is guaranteed that: the words (sequence of consecutive letters) are delimited by one and only one punctuation, the stream will begin with a word, the words will be at least one letter long,   and a full stop (a period, [.]) appears after, and only after, the last word. Example A stream with six words: what,is,the;meaning,of:life. The task is to reverse the letters in every other word while leaving punctuations intact, producing: what,si,the;gninaem,of:efil. while observing the following restrictions: Only I/O allowed is reading or writing one character at a time, which means: no reading in a string, no peeking ahead, no pushing characters back into the stream, and no storing characters in a global variable for later use; You are not to explicitly save characters in a collection data structure, such as arrays, strings, hash tables, etc, for later reversal; You are allowed to use recursions, closures, continuations, threads, co-routines, etc., even if their use implies the storage of multiple characters. Test cases Work on both the   "life"   example given above, and also the text: we,are;not,in,kansas;any,more.
#Scheme
Scheme
(define (odd) (let ((c (read-char))) (if (char-alphabetic? c) (let ((r (odd))) (write-char c) r) (lambda () (write-char c) (char=? c #\.)))))   (define (even) (let ((c (read-char))) (write-char c) (if (char-alphabetic? c) (even) (char=? c #\.))))   (let loop ((i #f)) (if (if i ((odd)) (even)) (exit) (loop (not i))))