task_url stringlengths 30 116 | task_name stringlengths 2 86 | task_description stringlengths 0 14.4k | language_url stringlengths 2 53 | language_name stringlengths 1 52 | code stringlengths 0 61.9k |
|---|---|---|---|---|---|
http://rosettacode.org/wiki/Lychrel_numbers | Lychrel numbers | Take an integer n, greater than zero.
Form the next n of its series by reversing the digits of the current n and adding the result to the current n.
Stop when n becomes palindromic - i.e. the digits of n in reverse order == n.
The above recurrence relation when applied to most starting numbers n = 1, 2, ... terminates in a palindrome quite quickly.
Example
If n0 = 12 we get
12
12 + 21 = 33, a palindrome!
And if n0 = 55 we get
55
55 + 55 = 110
110 + 011 = 121, a palindrome!
Notice that the check for a palindrome happens after an addition.
Some starting numbers seem to go on forever; the recurrence relation for 196 has been calculated for millions of repetitions forming numbers with millions of digits, without forming a palindrome.
These numbers that do not end in a palindrome are called Lychrel numbers.
For the purposes of this task a Lychrel number is any starting number that does not form a palindrome within 500 (or more) iterations.
Seed and related Lychrel numbers
Any integer produced in the sequence of a Lychrel number is also a Lychrel number.
In general, any sequence from one Lychrel number might converge to join the sequence from a prior Lychrel number candidate; for example the sequences for the numbers 196 and then 689 begin:
196
196 + 691 = 887
887 + 788 = 1675
1675 + 5761 = 7436
7436 + 6347 = 13783
13783 + 38731 = 52514
52514 + 41525 = 94039
...
689
689 + 986 = 1675
1675 + 5761 = 7436
...
So we see that the sequence starting with 689 converges to, and continues with the same numbers as that for 196.
Because of this we can further split the Lychrel numbers into true Seed Lychrel number candidates, and Related numbers that produce no palindromes but have integers in their sequence seen as part of the sequence generated from a lower Lychrel number.
Task
Find the number of seed Lychrel number candidates and related numbers for n in the range 1..10000 inclusive. (With that iteration limit of 500).
Print the number of seed Lychrels found; the actual seed Lychrels; and just the number of relateds found.
Print any seed Lychrel or related number that is itself a palindrome.
Show all output here.
References
What's special about 196? Numberphile video.
A023108 Positive integers which apparently never result in a palindrome under repeated applications of the function f(x) = x + (x with digits reversed).
Status of the 196 conjecture? Mathoverflow.
| #zkl | zkl | var BN=Import("zklBigNum");
// 192-->"887\01675\07436\013783\0..." ~60k bytes
fcn lychrel(n,returnListof=False){ n=BN(n); //-->Bool|Data(==StringBuf)
sink:=(if(returnListof) Data(0,String) else Void);
nls:=(500).pump(sink,'wrap(){
ns:=n.add(BN(n.toString().reverse())).toString();
if(ns==ns.reverse()) return(Void.Stop,False); // not a Lychrel number
ns
});
if(nls) if(returnListof) return(sink.mode(Int).howza(2)) else return(True);
False;
}
fcn isPalindrome(n){ n==n.toString().reverse().toInt() }
fcn findSeeds(lychrels){
seeds:=List(lychrels[0]);
foreach n,lnns in ([1..].zip(lychrels[1,*])){ ln,seq:=lnns;
foreach _,s2 in (seeds){
foreach s3 in (seq){
if(Void!=(z:=s2.findString(s3)) and 0==s2[z-1]) break(2);
}
}
fallthrough{ seeds.append(lnns) }
}
seeds.apply("get",0)
} |
http://rosettacode.org/wiki/Mad_Libs | Mad Libs |
This page uses content from Wikipedia. The original article was at Mad Libs. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Mad Libs is a phrasal template word game where one player prompts another for a list of words to substitute for blanks in a story, usually with funny results.
Task;
Write a program to create a Mad Libs like story.
The program should read an arbitrary multiline story from input.
The story will be terminated with a blank line.
Then, find each replacement to be made within the story, ask the user for a word to replace it with, and make all the replacements.
Stop when there are none left and print the final story.
The input should be an arbitrary story in the form:
<name> went for a walk in the park. <he or she>
found a <noun>. <name> decided to take it home.
Given this example, it should then ask for a name, a he or she and a noun (<name> gets replaced both times with the same value).
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
| #Raku | Raku | print S:g[ '<' (.*?) '>' ] = %.{$0} //= prompt "$0? " given slurp; |
http://rosettacode.org/wiki/Loops/Increment_loop_index_within_loop_body | Loops/Increment loop index within loop body | Sometimes, one may need (or want) a loop which
its iterator (the index
variable) is modified within the
loop body in addition to the normal incrementation by the (do) loop structure index.
Goal
Demonstrate the best way to accomplish this.
Task
Write a loop which:
starts the index (variable) at 42
(at iteration time) increments the index by unity
if the index is prime:
displays the count of primes found (so far) and the prime (to the terminal)
increments the index such that the new index is now the (old) index plus that prime
terminates the loop when 42 primes are shown
Extra credit: because of the primes get rather large, use commas
within the displayed primes to ease comprehension.
Show all output here.
Note
Not all programming languages allow the modification of a
loop's index. If that is the case, then use whatever method that
is appropriate or idiomatic for that language. Please add a note
if the loop's index isn't modifiable.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Ksh | Ksh |
#!/bin/ksh
# Increment loop index within loop body
# # Variables:
#
integer INDX_START=42 N_PRIMES=42
# # Functions:
#
# # Function _isprime(n) return 1 for prime, 0 for not prime
#
function _isprime {
typeset _n ; integer _n=$1
typeset _i ; integer _i
(( _n < 2 )) && return 0
for (( _i=2 ; _i*_i<=_n ; _i++ )); do
(( ! ( _n % _i ) )) && return 0
done
return 1
}
######
# main #
######
integer i n=0
for ((i=INDX_START; n<N_PRIMES; i++)); do
_isprime ${i}
if (( $? )); then
printf "%,18d is prime, %2d primes found(so far)\n" ${i} $((++n))
(( i+=$i ))
fi
done |
http://rosettacode.org/wiki/Loops/Increment_loop_index_within_loop_body | Loops/Increment loop index within loop body | Sometimes, one may need (or want) a loop which
its iterator (the index
variable) is modified within the
loop body in addition to the normal incrementation by the (do) loop structure index.
Goal
Demonstrate the best way to accomplish this.
Task
Write a loop which:
starts the index (variable) at 42
(at iteration time) increments the index by unity
if the index is prime:
displays the count of primes found (so far) and the prime (to the terminal)
increments the index such that the new index is now the (old) index plus that prime
terminates the loop when 42 primes are shown
Extra credit: because of the primes get rather large, use commas
within the displayed primes to ease comprehension.
Show all output here.
Note
Not all programming languages allow the modification of a
loop's index. If that is the case, then use whatever method that
is appropriate or idiomatic for that language. Please add a note
if the loop's index isn't modifiable.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Lua | Lua | -- Returns boolean indicate whether x is prime
function isPrime (x)
if x < 2 then return false end
if x < 4 then return true end
if x % 2 == 0 then return false end
for d = 3, math.sqrt(x), 2 do
if x % d == 0 then return false end
end
return true
end
-- Main procedure
local n, i = 0, 42
while n < 42 do
if isPrime(i) then
n = n + 1
print("n = " .. n, i)
i = 2 * i - 1
end
i = i + 1
end |
http://rosettacode.org/wiki/Loops/Infinite | Loops/Infinite | Task
Print out SPAM followed by a newline in an infinite loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #C.23 | C# | while (true)
{
Console.WriteLine("SPAM");
} |
http://rosettacode.org/wiki/Loops/Infinite | Loops/Infinite | Task
Print out SPAM followed by a newline in an infinite loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #C.2B.2B | C++ | while (true)
std::cout << "SPAM\n"; |
http://rosettacode.org/wiki/Loops/With_multiple_ranges | Loops/With multiple ranges | Loops/With multiple ranges
You are encouraged to solve this task according to the task description, using any language you may know.
Some languages allow multiple loop ranges, such as the PL/I example (snippet) below.
/* all variables are DECLARED as integers. */
prod= 1; /*start with a product of unity. */
sum= 0; /* " " " sum " zero. */
x= +5;
y= -5;
z= -2;
one= 1;
three= 3;
seven= 7;
/*(below) ** is exponentiation: 4**3=64 */
do j= -three to 3**3 by three ,
-seven to +seven by x ,
555 to 550 - y ,
22 to -28 by -three ,
1927 to 1939 ,
x to y by z ,
11**x to 11**x + one;
/* ABS(n) = absolute value*/
sum= sum + abs(j); /*add absolute value of J.*/
if abs(prod)<2**27 & j¬=0 then prod=prod*j; /*PROD is small enough & J*/
end; /*not 0, then multiply it.*/
/*SUM and PROD are used for verification of J incrementation.*/
display (' sum= ' || sum); /*display strings to term.*/
display ('prod= ' || prod); /* " " " " */
Task
Simulate/translate the above PL/I program snippet as best as possible in your
language, with particular emphasis on the do loop construct.
The do index must be incremented/decremented in the same order shown.
If feasible, add commas to the two output numbers (being displayed).
Show all output here.
A simple PL/I DO loop (incrementing or decrementing) has the construct of:
DO variable = start_expression {TO ending_expression] {BY increment_expression} ;
---or---
DO variable = start_expression {BY increment_expression} {TO ending_expression] ;
where it is understood that all expressions will have a value. The variable is normally a
scaler variable, but need not be (but for this task, all variables and expressions are declared
to be scaler integers). If the BY expression is omitted, a BY value of unity is used.
All expressions are evaluated before the DO loop is executed, and those values are used
throughout the DO loop execution (even though, for instance, the value of Z may be
changed within the DO loop. This isn't the case here for this task.
A multiple-range DO loop can be constructed by using a comma (,) to separate additional ranges
(the use of multiple TO and/or BY keywords). This is the construct used in this task.
There are other forms of DO loops in PL/I involving the WHILE clause, but those won't be
needed here. DO loops without a TO clause might need a WHILE clause or some other
means of exiting the loop (such as LEAVE, RETURN, SIGNAL, GOTO, or STOP), or some other
(possible error) condition that causes transfer of control outside the DO loop.
Also, in PL/I, the check if the DO loop index value is outside the range is made at the
"head" (start) of the DO loop, so it's possible that the DO loop isn't executed, but
that isn't the case for any of the ranges used in this task.
In the example above, the clause: x to y by z
will cause the variable J to have to following values (in this order): 5 3 1 -1 -3 -5
In the example above, the clause: -seven to +seven by x
will cause the variable J to have to following values (in this order): -7 -2 3
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #QB64 | QB64 |
'Task
'Simulate/translate the above PL/I program snippet as best as possible
' in your language, with particular emphasis on the do loop
' construct.
'The do index must be incremented/decremented in the same order shown.
'If feasible, add commas to the two output numbers (being displayed).
'Show all output here.
'Unknown DO multiple conditions behaviour:
' this code implements a sequential/serial set of ranges mode for DO condition
Dim As Integer prod, sum, x, y, z, one, three, seven
Dim As _Integer64 Count(1 To 7)
Dim As Integer Index, IndexCondition
prod = 1
sum = 0
x = 5
y = -5
z = -2
one = 1
three = 3
seven = 7
Count(1) = -three
Count(2) = -seven
Count(3) = 555
Count(4) = 22
Count(5) = 1927
Count(6) = x
Count(7) = 11 ^ x
IndexCondition = 1
Do
If IndexCondition = 1 Then
If Count(1) + three < 3 ^ 3 Then Count(1) = Count(1) + three Else IndexCondition = 2
ElseIf IndexCondition = 2 Then
If Count(2) + x < seven Then Count(2) = Count(2) + x Else IndexCondition = 3
ElseIf IndexCondition = 3 Then
If Count(3) - 1 > 550 - y Then Count(3) = Count(3) - 1 Else IndexCondition = 4
ElseIf IndexCondition = 4 Then
If Count(4) - three > -28 Then Count(4) = Count(4) - three Else IndexCondition = 5
ElseIf IndexCondition = 5 Then
If Count(5) + 1 < 1939 Then Count(5) = Count(5) + 1 Else IndexCondition = 6
ElseIf IndexCondition = 6 Then
If Count(6) + z < y Then Count(6) = Count(6) + z Else IndexCondition = 7
ElseIf IndexCondition = 7 Then
If Count(7) + 1 < 11 ^ (x + one) Then Count(7) = Count(7) + 1 Else Exit Do
End If
sum = sum + Abs(Count(IndexCondition))
If Abs(prod) < 2 ^ 27 And (j <> 0) Then prod = prod * Count(IndexCondition)
Print sum
Print prod
Loop
|
http://rosettacode.org/wiki/Loops/With_multiple_ranges | Loops/With multiple ranges | Loops/With multiple ranges
You are encouraged to solve this task according to the task description, using any language you may know.
Some languages allow multiple loop ranges, such as the PL/I example (snippet) below.
/* all variables are DECLARED as integers. */
prod= 1; /*start with a product of unity. */
sum= 0; /* " " " sum " zero. */
x= +5;
y= -5;
z= -2;
one= 1;
three= 3;
seven= 7;
/*(below) ** is exponentiation: 4**3=64 */
do j= -three to 3**3 by three ,
-seven to +seven by x ,
555 to 550 - y ,
22 to -28 by -three ,
1927 to 1939 ,
x to y by z ,
11**x to 11**x + one;
/* ABS(n) = absolute value*/
sum= sum + abs(j); /*add absolute value of J.*/
if abs(prod)<2**27 & j¬=0 then prod=prod*j; /*PROD is small enough & J*/
end; /*not 0, then multiply it.*/
/*SUM and PROD are used for verification of J incrementation.*/
display (' sum= ' || sum); /*display strings to term.*/
display ('prod= ' || prod); /* " " " " */
Task
Simulate/translate the above PL/I program snippet as best as possible in your
language, with particular emphasis on the do loop construct.
The do index must be incremented/decremented in the same order shown.
If feasible, add commas to the two output numbers (being displayed).
Show all output here.
A simple PL/I DO loop (incrementing or decrementing) has the construct of:
DO variable = start_expression {TO ending_expression] {BY increment_expression} ;
---or---
DO variable = start_expression {BY increment_expression} {TO ending_expression] ;
where it is understood that all expressions will have a value. The variable is normally a
scaler variable, but need not be (but for this task, all variables and expressions are declared
to be scaler integers). If the BY expression is omitted, a BY value of unity is used.
All expressions are evaluated before the DO loop is executed, and those values are used
throughout the DO loop execution (even though, for instance, the value of Z may be
changed within the DO loop. This isn't the case here for this task.
A multiple-range DO loop can be constructed by using a comma (,) to separate additional ranges
(the use of multiple TO and/or BY keywords). This is the construct used in this task.
There are other forms of DO loops in PL/I involving the WHILE clause, but those won't be
needed here. DO loops without a TO clause might need a WHILE clause or some other
means of exiting the loop (such as LEAVE, RETURN, SIGNAL, GOTO, or STOP), or some other
(possible error) condition that causes transfer of control outside the DO loop.
Also, in PL/I, the check if the DO loop index value is outside the range is made at the
"head" (start) of the DO loop, so it's possible that the DO loop isn't executed, but
that isn't the case for any of the ranges used in this task.
In the example above, the clause: x to y by z
will cause the variable J to have to following values (in this order): 5 3 1 -1 -3 -5
In the example above, the clause: -seven to +seven by x
will cause the variable J to have to following values (in this order): -7 -2 3
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Raku | Raku | sub comma { ($^i < 0 ?? '-' !! '') ~ $i.abs.flip.comb(3).join(',').flip }
my \x = 5;
my \y = -5;
my \z = -2;
my \one = 1;
my \three = 3;
my \seven = 7;
my $j = flat
( -three, *+three … 3³ ),
( -seven, *+x …^ * > seven ),
( 555 .. 550 - y ),
( 22, *-three …^ * < -28 ),
( 1927 .. 1939 ),
( x, *+z …^ * < y ),
( 11**x .. 11**x + one );
put 'j sequence: ', $j;
put ' Sum: ', comma [+] $j».abs;
put ' Product: ', comma ([\*] $j.grep: so +*).first: *.abs > 2²⁷;
# Or, an alternate method for generating the 'j' sequence, employing user-defined
# operators to preserve the 'X to Y by Z' layout of the example code.
# Note that these operators will only work for monotonic sequences.
sub infix:<to> { $^a ... $^b }
sub infix:<by> { $^a[0, $^b.abs ... *] }
$j = cache flat
-three to 3**3 by three ,
-seven to seven by x ,
555 to (550 - y) ,
22 to -28 by -three ,
1927 to 1939 by one ,
x to y by z ,
11**x to (11**x + one) ;
put "\nLiteral minded variant:";
put ' Sum: ', comma [+] $j».abs;
put ' Product: ', comma ([\*] $j.grep: so +*).first: *.abs > 2²⁷; |
http://rosettacode.org/wiki/Loops/While | Loops/While | Task
Start an integer value at 1024.
Loop while it is greater than zero.
Print the value (with a newline) and divide it by two each time through the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreachbas
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #COBOL | COBOL | IDENTIFICATION DIVISION.
PROGRAM-ID. Loop-While.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 I PIC 9999 VALUE 1024.
PROCEDURE DIVISION.
PERFORM UNTIL NOT 0 < I
DISPLAY I
DIVIDE 2 INTO I
END-PERFORM
GOBACK
. |
http://rosettacode.org/wiki/Loops/While | Loops/While | Task
Start an integer value at 1024.
Loop while it is greater than zero.
Print the value (with a newline) and divide it by two each time through the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreachbas
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #ColdFusion | ColdFusion | <cfset i = 1024 /><cfloop condition="i GT 0"> #i#< br />
<cfset i /= 2 />
</cfloop> |
http://rosettacode.org/wiki/Loops/Downward_for | Loops/Downward for | Task
Write a for loop which writes a countdown from 10 to 0.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #bc | bc | for (i = 10; i >= 0; i--) i
quit |
http://rosettacode.org/wiki/Loops/Downward_for | Loops/Downward for | Task
Write a for loop which writes a countdown from 10 to 0.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Befunge | Befunge | 55+>:.:v
@ ^ -1_ |
http://rosettacode.org/wiki/Loops/Do-while | Loops/Do-while | Start with a value at 0. Loop while value mod 6 is not equal to 0.
Each time through the loop, add 1 to the value then print it.
The loop must execute at least once.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
Reference
Do while loop Wikipedia.
| #ARM_Assembly | ARM Assembly |
/* ARM assembly Raspberry PI */
/* program loopdowhile.s */
/* Constantes */
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessResult: .ascii "Counter = " @ message result
sMessValeur: .fill 12, 1, ' '
.asciz "\n"
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
push {fp,lr} @ saves 2 registers
mov r4,#0
1: @ begin loop
mov r0,r4
ldr r1,iAdrsMessValeur @ display value
bl conversion10 @ call function with 2 parameter (r0,r1)
ldr r0,iAdrszMessResult
bl affichageMess @ display message
add r4,#1 @ increment counter
mov r0,r4
mov r1,#6 @ division conuter by 6
bl division
cmp r3,#0 @ remainder = zéro ?
bne 1b @ no ->begin loop one
100: @ standard end of the program
mov r0, #0 @ return code
pop {fp,lr} @restaur 2 registers
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrsMessValeur: .int sMessValeur
iAdrszMessResult: .int szMessResult
/******************************************************************/
/* display text with size calculation */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {r0,r1,r2,r7,lr} @ save registres
mov r2,#0 @ counter length
1: @ loop length calculation
ldrb r1,[r0,r2] @ read octet start position + index
cmp r1,#0 @ if 0 its over
addne r2,r2,#1 @ else add 1 in the length
bne 1b @ and loop
@ so here r2 contains the length of the message
mov r1,r0 @ address message in r1
mov r0,#STDOUT @ code to write to the standard output Linux
mov r7, #WRITE @ code call system "write"
svc #0 @ call systeme
pop {r0,r1,r2,r7,lr} @ restaur des 2 registres */
bx lr @ return
/******************************************************************/
/* Converting a register to a decimal */
/******************************************************************/
/* r0 contains value and r1 address area */
conversion10:
push {r1-r4,lr} @ save registers
mov r3,r1
mov r2,#10
1: @ start loop
bl divisionpar10 @ r0 <- dividende. quotient ->r0 reste -> r1
add r1,#48 @ digit
strb r1,[r3,r2] @ store digit on area
sub r2,#1 @ previous position
cmp r0,#0 @ stop if quotient = 0 */
bne 1b @ else loop
@ and move spaces in first on area
mov r1,#' ' @ space
2:
strb r1,[r3,r2] @ store space in area
subs r2,#1 @ @ previous position
bge 2b @ loop if r2 >= zéro
100:
pop {r1-r4,lr} @ restaur registres
bx lr @return
/***************************************************/
/* division par 10 signé */
/* Thanks to http://thinkingeek.com/arm-assembler-raspberry-pi/*
/* and http://www.hackersdelight.org/ */
/***************************************************/
/* r0 dividende */
/* r0 quotient */
/* r1 remainder */
divisionpar10:
/* r0 contains the argument to be divided by 10 */
push {r2-r4} /* save registers */
mov r4,r0
mov r3,#0x6667 @ r3 <- magic_number lower
movt r3,#0x6666 @ r3 <- magic_number upper
smull r1, r2, r3, r0 @ r1 <- Lower32Bits(r1*r0). r2 <- Upper32Bits(r1*r0)
mov r2, r2, ASR #2 /* r2 <- r2 >> 2 */
mov r1, r0, LSR #31 /* r1 <- r0 >> 31 */
add r0, r2, r1 /* r0 <- r2 + r1 */
add r2,r0,r0, lsl #2 /* r2 <- r0 * 5 */
sub r1,r4,r2, lsl #1 /* r1 <- r4 - (r2 * 2) = r4 - (r0 * 10) */
pop {r2-r4}
bx lr /* leave function */
/***************************************************/
/* integer division unsigned */
/***************************************************/
division:
/* r0 contains dividend */
/* r1 contains divisor */
/* r2 returns quotient */
/* r3 returns remainder */
push {r4, lr}
mov r2, #0 @ init quotient
mov r3, #0 @ init remainder
mov r4, #32 @ init counter bits
b 2f
1: @ loop
movs r0, r0, LSL #1 @ r0 <- r0 << 1 updating cpsr (sets C if 31st bit of r0 was 1)
adc r3, r3, r3 @ r3 <- r3 + r3 + C. This is equivalent to r3 ? (r3 << 1) + C
cmp r3, r1 @ compute r3 - r1 and update cpsr
subhs r3, r3, r1 @ if r3 >= r1 (C=1) then r3 ? r3 - r1
adc r2, r2, r2 @ r2 <- r2 + r2 + C. This is equivalent to r2 <- (r2 << 1) + C
2:
subs r4, r4, #1 @ r4 <- r4 - 1
bpl 1b @ if r4 >= 0 (N=0) then loop
pop {r4, lr}
bx lr
|
http://rosettacode.org/wiki/Loops/For | Loops/For | “For” loops are used to make some block of code be iterated a number of times, setting a variable or parameter to a monotonically increasing integer value for each execution of the block of code.
Common extensions of this allow other counting patterns or iterating over abstract structures other than the integers.
Task
Show how two loops may be nested within each other, with the number of iterations performed by the inner for loop being controlled by the outer for loop.
Specifically print out the following pattern by using one for loop nested in another:
*
**
***
****
*****
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
Reference
For loop Wikipedia.
| #Apex | Apex | for (Integer i = 0; i < 5; i++) {
String line = '';
for (Integer j = 0; j < i; j++) {
line += '*';
}
System.debug(line);
}
List<String> lines = new List<String> {
'*',
'**',
'***',
'****',
'*****'
};
for (String line : lines) {
System.debug(line);
} |
http://rosettacode.org/wiki/Loops/For_with_a_specified_step | Loops/For with a specified step |
Task
Demonstrate a for-loop where the step-value is greater than one.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Axe | Axe | For(I,0,10)
Disp I▶Dec,i
I++
End |
http://rosettacode.org/wiki/Ludic_numbers | Ludic numbers | Ludic numbers are related to prime numbers as they are generated by a sieve quite like the Sieve of Eratosthenes is used to generate prime numbers.
The first ludic number is 1.
To generate succeeding ludic numbers create an array of increasing integers starting from 2.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...
(Loop)
Take the first member of the resultant array as the next ludic number 2.
Remove every 2nd indexed item from the array (including the first).
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...
(Unrolling a few loops...)
Take the first member of the resultant array as the next ludic number 3.
Remove every 3rd indexed item from the array (including the first).
3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 ...
Take the first member of the resultant array as the next ludic number 5.
Remove every 5th indexed item from the array (including the first).
5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 ...
Take the first member of the resultant array as the next ludic number 7.
Remove every 7th indexed item from the array (including the first).
7 11 13 17 23 25 29 31 37 41 43 47 53 55 59 61 67 71 73 77 83 85 89 91 97 ...
...
Take the first member of the current array as the next ludic number L.
Remove every Lth indexed item from the array (including the first).
...
Task
Generate and show here the first 25 ludic numbers.
How many ludic numbers are there less than or equal to 1000?
Show the 2000..2005th ludic numbers.
Stretch goal
Show all triplets of ludic numbers < 250.
A triplet is any three numbers
x
,
{\displaystyle x,}
x
+
2
,
{\displaystyle x+2,}
x
+
6
{\displaystyle x+6}
where all three numbers are also ludic numbers.
| #Raku | Raku | constant @ludic = gather {
my @taken = take 1;
my @rotor;
for 2..* -> $i {
loop (my $j = 0; $j < @rotor; $j++) {
--@rotor[$j] or last;
}
if $j < @rotor {
@rotor[$j] = @taken[$j+1];
}
else {
push @taken, take $i;
push @rotor, @taken[$j+1];
}
}
}
say @ludic[^25];
say "Number of Ludic numbers <= 1000: ", +(@ludic ...^ * > 1000);
say "Ludic numbers 2000..2005: ", @ludic[1999..2004];
my \l250 = set @ludic ...^ * > 250;
say "Ludic triples < 250: ", gather
for l250.keys.sort -> $a {
my $b = $a + 2;
my $c = $a + 6;
take "<$a $b $c>" if $b ∈ l250 and $c ∈ l250;
} |
http://rosettacode.org/wiki/Loops/N_plus_one_half | Loops/N plus one half | Quite often one needs loops which, in the last iteration, execute only part of the loop body.
Goal
Demonstrate the best way to do this.
Task
Write a loop which writes the comma-separated list
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
using separate output statements for the number
and the comma from within the body of the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #DWScript | DWScript | var i : Integer;
for i := 1 to 10 do begin
Print(i);
if i < 10 then
Print(', ');
end; |
http://rosettacode.org/wiki/Loops/N_plus_one_half | Loops/N plus one half | Quite often one needs loops which, in the last iteration, execute only part of the loop body.
Goal
Demonstrate the best way to do this.
Task
Write a loop which writes the comma-separated list
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
using separate output statements for the number
and the comma from within the body of the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #E | E | var i := 1
while (true) {
print(i)
if (i >= 10) { break }
print(", ")
i += 1
} |
http://rosettacode.org/wiki/Loops/Nested | Loops/Nested | Show a nested loop which searches a two-dimensional array filled with random numbers uniformly distributed over
[
1
,
…
,
20
]
{\displaystyle [1,\ldots ,20]}
.
The loops iterate rows and columns of the array printing the elements until the value
20
{\displaystyle 20}
is met.
Specifically, this task also shows how to break out of nested loops.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #D | D | import std.stdio, std.random;
void main() {
int[10][10] mat;
foreach (ref row; mat)
foreach (ref item; row)
item = uniform(1, 21);
outer:
foreach (row; mat)
foreach (item; row) {
write(item, ' ');
if (item == 20)
break outer;
}
writeln();
} |
http://rosettacode.org/wiki/Loops/Foreach | Loops/Foreach | Loop through and print each element in a collection in order.
Use your language's "for each" loop if it has one, otherwise iterate through the collection in order with some other loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Ela | Ela | open monad io
each [] = do return ()
each (x::xs) = do
putStrLn $ show x
each xs |
http://rosettacode.org/wiki/Loops/Foreach | Loops/Foreach | Loop through and print each element in a collection in order.
Use your language's "for each" loop if it has one, otherwise iterate through the collection in order with some other loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Elena | Elena | import system'routines;
import extensions;
public program()
{
var things := new string[]{"Apple", "Banana", "Coconut"};
things.forEach:(thing)
{
console.printLine:thing
}
} |
http://rosettacode.org/wiki/Luhn_test_of_credit_card_numbers | Luhn test of credit card numbers | The Luhn test is used by some credit card companies to distinguish valid credit card numbers from what could be a random selection of digits.
Those companies using credit card numbers that can be validated by the Luhn test have numbers that pass the following test:
Reverse the order of the digits in the number.
Take the first, third, ... and every other odd digit in the reversed digits and sum them to form the partial sum s1
Taking the second, fourth ... and every other even digit in the reversed digits:
Multiply each digit by two and sum the digits if the answer is greater than nine to form partial sums for the even digits
Sum the partial sums of the even digits to form s2
If s1 + s2 ends in zero then the original number is in the form of a valid credit card number as verified by the Luhn test.
For example, if the trial number is 49927398716:
Reverse the digits:
61789372994
Sum the odd digits:
6 + 7 + 9 + 7 + 9 + 4 = 42 = s1
The even digits:
1, 8, 3, 2, 9
Two times each even digit:
2, 16, 6, 4, 18
Sum the digits of each multiplication:
2, 7, 6, 4, 9
Sum the last:
2 + 7 + 6 + 4 + 9 = 28 = s2
s1 + s2 = 70 which ends in zero which means that 49927398716 passes the Luhn test
Task
Write a function/method/procedure/subroutine that will validate a number with the Luhn test, and
use it to validate the following numbers:
49927398716
49927398717
1234567812345678
1234567812345670
Related tasks
SEDOL
ISIN
| #C.2B.2B | C++ | #include <iostream>
using namespace std;
int toInt(const char c)
{
return c-'0';
}
int confirm( const char *id)
{
bool is_odd_dgt = true;
int s = 0;
const char *cp;
for(cp=id; *cp; cp++);
while(cp > id) {
--cp;
int k = toInt(*cp);
if (is_odd_dgt) {
s += k;
}
else {
s += (k!=9)? (2*k)%9 : 9;
}
is_odd_dgt = !is_odd_dgt;
}
return 0 == s%10;
}
int main( )
{
const char * t_cases[] = {
"49927398716",
"49927398717",
"1234567812345678",
"1234567812345670",
NULL,
};
for ( const char **cp = t_cases; *cp; cp++) {
cout << *cp << ": " << confirm(*cp) << endl;
}
return 0;
} |
http://rosettacode.org/wiki/Lucas-Lehmer_test | Lucas-Lehmer test | Lucas-Lehmer Test:
for
p
{\displaystyle p}
an odd prime, the Mersenne number
2
p
−
1
{\displaystyle 2^{p}-1}
is prime if and only if
2
p
−
1
{\displaystyle 2^{p}-1}
divides
S
(
p
−
1
)
{\displaystyle S(p-1)}
where
S
(
n
+
1
)
=
(
S
(
n
)
)
2
−
2
{\displaystyle S(n+1)=(S(n))^{2}-2}
, and
S
(
1
)
=
4
{\displaystyle S(1)=4}
.
Task
Calculate all Mersenne primes up to the implementation's
maximum precision, or the 47th Mersenne prime (whichever comes first).
| #Go | Go | package main
import (
"fmt"
"math/big"
)
var primes = []uint{3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127}
var mersennes = []uint{521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689,
9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091,
756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917,
20996011, 24036583}
func main() {
llTest(primes)
fmt.Println()
llTest(mersennes)
}
func llTest(ps []uint) {
var s, m big.Int
one := big.NewInt(1)
two := big.NewInt(2)
for _, p := range ps {
m.Sub(m.Lsh(one, p), one)
s.SetInt64(4)
for i := uint(2); i < p; i++ {
s.Mod(s.Sub(s.Mul(&s, &s), two), &m)
}
if s.BitLen() == 0 {
fmt.Printf("M%d ", p)
}
}
} |
http://rosettacode.org/wiki/LZW_compression | LZW compression | The Lempel-Ziv-Welch (LZW) algorithm provides loss-less data compression.
You can read a complete description of it in the Wikipedia article on the subject. It was patented, but it entered the public domain in 2004.
| #Objeck | Objeck | use Collection;
class LZW {
function : Main(args : String[]) ~ Nil {
compressed := Compress("TOBEORNOTTOBEORTOBEORNOT");
Show(compressed);
decompressed := Decompress(compressed);
decompressed->PrintLine();
}
function : native : Compress(uncompressed : String) ~ IntVector {
# Build the dictionary.
dictSize := 256;
dictionary := StringMap->New();
for (i := 0; i < 256; i+=1;) {
key := "";
key->Append(i->As(Char));
dictionary->Insert(key, IntHolder->New(i));
};
w := "";
result := IntVector->New();
each (i : uncompressed) {
c := uncompressed->Get(i);
wc := String->New(w);
wc->Append(c);
if (dictionary->Has(wc)) {
w := wc;
}
else {
value := dictionary->Find(w)->As(IntHolder);
result->AddBack(value->Get());
# Add wc to the dictionary.
dictionary->Insert(wc, IntHolder->New(dictSize));
dictSize+=1;
w := "";
w->Append(c);
};
};
# Output the code for w.
if (w->Size() > 0) {
value := dictionary->Find(w)->As(IntHolder);
result->AddBack(value->Get());
};
return result;
}
function : Decompress(compressed : IntVector) ~ String {
# Build the dictionary.
dictSize := 256;
dictionary := IntMap->New();
for (i := 0; i < 256; i+=1;) {
value := "";
value->Append(i->As(Char));
dictionary->Insert(i, value);
};
w := "";
found := compressed->Remove(0);
w->Append(found->As(Char));
result := String->New(w);
each (i : compressed) {
k := compressed->Get(i);
entry : String;
if (dictionary->Has(k)) {
entry := dictionary->Find(k);
}
else if (k = dictSize) {
entry := String->New(w);
entry->Append(w->Get(0));
}
else {
return "";
};
result->Append(entry);
# Add w+entry[0] to the dictionary.
value := String->New(w);
value->Append(entry->Get(0));
dictionary->Insert(dictSize, value);
dictSize+=1;
w := entry;
};
return result;
}
function : Show(results : IntVector) ~ Nil {
"["->Print();
each(i : results) {
results->Get(i)->Print();
if(i + 1 < results->Size()) {
", "->Print();
};
};
"]"->PrintLine();
}
} |
http://rosettacode.org/wiki/LU_decomposition | LU decomposition | Every square matrix
A
{\displaystyle A}
can be decomposed into a product of a lower triangular matrix
L
{\displaystyle L}
and a upper triangular matrix
U
{\displaystyle U}
,
as described in LU decomposition.
A
=
L
U
{\displaystyle A=LU}
It is a modified form of Gaussian elimination.
While the Cholesky decomposition only works for symmetric,
positive definite matrices, the more general LU decomposition
works for any square matrix.
There are several algorithms for calculating L and U.
To derive Crout's algorithm for a 3x3 example,
we have to solve the following system:
A
=
(
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
)
=
(
l
11
0
0
l
21
l
22
0
l
31
l
32
l
33
)
(
u
11
u
12
u
13
0
u
22
u
23
0
0
u
33
)
=
L
U
{\displaystyle A={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\\end{pmatrix}}={\begin{pmatrix}l_{11}&0&0\\l_{21}&l_{22}&0\\l_{31}&l_{32}&l_{33}\\\end{pmatrix}}{\begin{pmatrix}u_{11}&u_{12}&u_{13}\\0&u_{22}&u_{23}\\0&0&u_{33}\end{pmatrix}}=LU}
We now would have to solve 9 equations with 12 unknowns. To make the system uniquely solvable, usually the diagonal elements of
L
{\displaystyle L}
are set to 1
l
11
=
1
{\displaystyle l_{11}=1}
l
22
=
1
{\displaystyle l_{22}=1}
l
33
=
1
{\displaystyle l_{33}=1}
so we get a solvable system of 9 unknowns and 9 equations.
A
=
(
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
)
=
(
1
0
0
l
21
1
0
l
31
l
32
1
)
(
u
11
u
12
u
13
0
u
22
u
23
0
0
u
33
)
=
(
u
11
u
12
u
13
u
11
l
21
u
12
l
21
+
u
22
u
13
l
21
+
u
23
u
11
l
31
u
12
l
31
+
u
22
l
32
u
13
l
31
+
u
23
l
32
+
u
33
)
=
L
U
{\displaystyle A={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\\end{pmatrix}}={\begin{pmatrix}1&0&0\\l_{21}&1&0\\l_{31}&l_{32}&1\\\end{pmatrix}}{\begin{pmatrix}u_{11}&u_{12}&u_{13}\\0&u_{22}&u_{23}\\0&0&u_{33}\end{pmatrix}}={\begin{pmatrix}u_{11}&u_{12}&u_{13}\\u_{11}l_{21}&u_{12}l_{21}+u_{22}&u_{13}l_{21}+u_{23}\\u_{11}l_{31}&u_{12}l_{31}+u_{22}l_{32}&u_{13}l_{31}+u_{23}l_{32}+u_{33}\end{pmatrix}}=LU}
Solving for the other
l
{\displaystyle l}
and
u
{\displaystyle u}
, we get the following equations:
u
11
=
a
11
{\displaystyle u_{11}=a_{11}}
u
12
=
a
12
{\displaystyle u_{12}=a_{12}}
u
13
=
a
13
{\displaystyle u_{13}=a_{13}}
u
22
=
a
22
−
u
12
l
21
{\displaystyle u_{22}=a_{22}-u_{12}l_{21}}
u
23
=
a
23
−
u
13
l
21
{\displaystyle u_{23}=a_{23}-u_{13}l_{21}}
u
33
=
a
33
−
(
u
13
l
31
+
u
23
l
32
)
{\displaystyle u_{33}=a_{33}-(u_{13}l_{31}+u_{23}l_{32})}
and for
l
{\displaystyle l}
:
l
21
=
1
u
11
a
21
{\displaystyle l_{21}={\frac {1}{u_{11}}}a_{21}}
l
31
=
1
u
11
a
31
{\displaystyle l_{31}={\frac {1}{u_{11}}}a_{31}}
l
32
=
1
u
22
(
a
32
−
u
12
l
31
)
{\displaystyle l_{32}={\frac {1}{u_{22}}}(a_{32}-u_{12}l_{31})}
We see that there is a calculation pattern, which can be expressed as the following formulas, first for
U
{\displaystyle U}
u
i
j
=
a
i
j
−
∑
k
=
1
i
−
1
u
k
j
l
i
k
{\displaystyle u_{ij}=a_{ij}-\sum _{k=1}^{i-1}u_{kj}l_{ik}}
and then for
L
{\displaystyle L}
l
i
j
=
1
u
j
j
(
a
i
j
−
∑
k
=
1
j
−
1
u
k
j
l
i
k
)
{\displaystyle l_{ij}={\frac {1}{u_{jj}}}(a_{ij}-\sum _{k=1}^{j-1}u_{kj}l_{ik})}
We see in the second formula that to get the
l
i
j
{\displaystyle l_{ij}}
below the diagonal, we have to divide by the diagonal element (pivot)
u
j
j
{\displaystyle u_{jj}}
, so we get problems when
u
j
j
{\displaystyle u_{jj}}
is either 0 or very small, which leads to numerical instability.
The solution to this problem is pivoting
A
{\displaystyle A}
, which means rearranging the rows of
A
{\displaystyle A}
, prior to the
L
U
{\displaystyle LU}
decomposition, in a way that the largest element of each column gets onto the diagonal of
A
{\displaystyle A}
. Rearranging the rows means to multiply
A
{\displaystyle A}
by a permutation matrix
P
{\displaystyle P}
:
P
A
⇒
A
′
{\displaystyle PA\Rightarrow A'}
Example:
(
0
1
1
0
)
(
1
4
2
3
)
⇒
(
2
3
1
4
)
{\displaystyle {\begin{pmatrix}0&1\\1&0\end{pmatrix}}{\begin{pmatrix}1&4\\2&3\end{pmatrix}}\Rightarrow {\begin{pmatrix}2&3\\1&4\end{pmatrix}}}
The decomposition algorithm is then applied on the rearranged matrix so that
P
A
=
L
U
{\displaystyle PA=LU}
Task description
The task is to implement a routine which will take a square nxn matrix
A
{\displaystyle A}
and return a lower triangular matrix
L
{\displaystyle L}
, a upper triangular matrix
U
{\displaystyle U}
and a permutation matrix
P
{\displaystyle P}
,
so that the above equation is fulfilled.
You should then test it on the following two examples and include your output.
Example 1
A
1 3 5
2 4 7
1 1 0
L
1.00000 0.00000 0.00000
0.50000 1.00000 0.00000
0.50000 -1.00000 1.00000
U
2.00000 4.00000 7.00000
0.00000 1.00000 1.50000
0.00000 0.00000 -2.00000
P
0 1 0
1 0 0
0 0 1
Example 2
A
11 9 24 2
1 5 2 6
3 17 18 1
2 5 7 1
L
1.00000 0.00000 0.00000 0.00000
0.27273 1.00000 0.00000 0.00000
0.09091 0.28750 1.00000 0.00000
0.18182 0.23125 0.00360 1.00000
U
11.00000 9.00000 24.00000 2.00000
0.00000 14.54545 11.45455 0.45455
0.00000 0.00000 -3.47500 5.68750
0.00000 0.00000 0.00000 0.51079
P
1 0 0 0
0 0 1 0
0 1 0 0
0 0 0 1
| #REXX | REXX | /*REXX program creates a matrix from console input, performs/shows LU decomposition.*/
#= 0; P.= 0; PA.= 0; L.= 0; U.= 0 /*initialize some variables to zero. */
parse arg x /*obtain matrix elements from the C.L. */
call bldAMat; call showMat 'A' /*build and display A matrix.*/
call bldPmat; call showMat 'P' /* " " " P " */
call multMat; call showMat 'PA' /* " " " PA " */
do y=1 for N; call bldUmat; call bldLmat /*build U and L " */
end /*y*/
call showMat 'L'; call showMat 'U' /*display L and U " */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
bldAMat: ?= words(x); do N=1 for ? until N**2>=? /*find matrix size. */
end /*N*/
if N**2\==? then do; say '***error*** wrong # of elements entered:' ?; exit 9
end
do r=1 for N /*build A matrix.*/
do c=1 for N; #= # + 1; _= word(x, #); A.r.c= _
if \datatype(_, 'N') then call er "element isn't numeric: " _
end /*c*/
end /*r*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
bldLmat: do r=1 for N /*build lower matrix.*/
do c=1 for N; if r==c then do; L.r.c= 1; iterate; end
if c\==y | r==c | c>r then iterate
_= PA.r.c
do k=1 for c-1; _= _ - U.k.c * L.r.k
end /*k*/
L.r.c= _ / U.c.c
end /*c*/
end /*r*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
bldPmat: c= N; do r=N by -1 for N; P.r.c= 1; c= c + 1 /*build perm. matrix.*/
if c>N then c= N%2; if c==N then c= 1
end /*r*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
bldUmat: do r=1 for N; if r\==y then iterate /*build upper matrix.*/
do c=1 for N; if c<r then iterate
_= PA.r.c
do k=1 for r-1; _= _ - U.k.c * L.r.k
end /*k*/
U.r.c= _ / 1
end /*c*/
end /*r*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
multMat: do i=1 for N /*multiply matrix P and A ──► PA */
do j=1 for N
do k=1 for N; pa.i.j= (pa.i.j + p.i.k * a.k.j) / 1
end /*k*/
end /*j*/ /*÷ by one does normalization [↑]. */
end /*i*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
showMat: parse arg mat,rows,cols; say; rows= word(rows N,1); cols= word(cols rows,1)
w= 0; do r=1 for rows
do c=1 for cols; w= max(w, length( value( mat'.'r"."c ) ) )
end /*c*/
end /*r*/
say center(mat 'matrix', cols * (w + 1) + 7, "─") /*display the header.*/
do r=1 for rows; _=
do c=1 for cols; _= _ right( value(mat'.'r"."c), w + 1)
end /*c*/
say _
end /*r*/; return |
http://rosettacode.org/wiki/Mad_Libs | Mad Libs |
This page uses content from Wikipedia. The original article was at Mad Libs. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Mad Libs is a phrasal template word game where one player prompts another for a list of words to substitute for blanks in a story, usually with funny results.
Task;
Write a program to create a Mad Libs like story.
The program should read an arbitrary multiline story from input.
The story will be terminated with a blank line.
Then, find each replacement to be made within the story, ask the user for a word to replace it with, and make all the replacements.
Stop when there are none left and print the final story.
The input should be an arbitrary story in the form:
<name> went for a walk in the park. <he or she>
found a <noun>. <name> decided to take it home.
Given this example, it should then ask for a name, a he or she and a noun (<name> gets replaced both times with the same value).
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
| #REBOL | REBOL |
t: {<name> went for a walk in the park. <he or she> found a <noun>. <name> decided to take it home.}
view layout [a: area wrap t btn "Done" [x: a/text unview]]
parse x [any [to "<" copy b thru ">" (append w: [] b)] to end]
foreach i unique w [replace/all x i ask join i ": "] alert x
|
http://rosettacode.org/wiki/Loops/Increment_loop_index_within_loop_body | Loops/Increment loop index within loop body | Sometimes, one may need (or want) a loop which
its iterator (the index
variable) is modified within the
loop body in addition to the normal incrementation by the (do) loop structure index.
Goal
Demonstrate the best way to accomplish this.
Task
Write a loop which:
starts the index (variable) at 42
(at iteration time) increments the index by unity
if the index is prime:
displays the count of primes found (so far) and the prime (to the terminal)
increments the index such that the new index is now the (old) index plus that prime
terminates the loop when 42 primes are shown
Extra credit: because of the primes get rather large, use commas
within the displayed primes to ease comprehension.
Show all output here.
Note
Not all programming languages allow the modification of a
loop's index. If that is the case, then use whatever method that
is appropriate or idiomatic for that language. Please add a note
if the loop's index isn't modifiable.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #M2000_Interpreter | M2000 Interpreter |
Module CheckIt {
Function IsPrime (x) {
if x<=5 OR frac(x) then {
if x = 2 OR x = 3 OR x = 5 then =true
Break
}
if x mod 2 else exit
if x mod 3 else exit
x1=sqrt(x): d=5@
{if x mod d else exit
d += 2@: if d>x1 then =true : exit
if x mod d else exit
d += 4@: if d<= x1 else =true: exit
loop
}
}
\\ For Next loops or For {} loops can't change iterator variable (variable has a copy of real iterator)
\\ In those loops we have to use Continue to skip lines and repeat the loop.
\\ so we have to use Block iterator, using Loop which set a flag current block to repeat itself once.
def long Limit=42, n
def decimal i
i=Limit
{
if n<Limit Else exit
if isPrime(i) then n++ : Print format$("n={0::2}: {1:-20}", n, str$(i,"#,###")) : i+=i-1
i++
loop
}
}
CheckIt
|
http://rosettacode.org/wiki/Loops/Increment_loop_index_within_loop_body | Loops/Increment loop index within loop body | Sometimes, one may need (or want) a loop which
its iterator (the index
variable) is modified within the
loop body in addition to the normal incrementation by the (do) loop structure index.
Goal
Demonstrate the best way to accomplish this.
Task
Write a loop which:
starts the index (variable) at 42
(at iteration time) increments the index by unity
if the index is prime:
displays the count of primes found (so far) and the prime (to the terminal)
increments the index such that the new index is now the (old) index plus that prime
terminates the loop when 42 primes are shown
Extra credit: because of the primes get rather large, use commas
within the displayed primes to ease comprehension.
Show all output here.
Note
Not all programming languages allow the modification of a
loop's index. If that is the case, then use whatever method that
is appropriate or idiomatic for that language. Please add a note
if the loop's index isn't modifiable.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Maple | Maple | i := 42:
count := 0:
while(count < 42) do
i := i+1:
if type(i,prime) then
count := count + 1:
printf("n=%-2d %19d\n", count,i):
i := 2*i -1:
end if:
end do: |
http://rosettacode.org/wiki/Loops/Infinite | Loops/Infinite | Task
Print out SPAM followed by a newline in an infinite loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Chapel | Chapel | while true do writeln("SPAM"); |
http://rosettacode.org/wiki/Loops/Infinite | Loops/Infinite | Task
Print out SPAM followed by a newline in an infinite loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #ChucK | ChucK |
while(true) <<<"SPAM">>>;
|
http://rosettacode.org/wiki/Loops/With_multiple_ranges | Loops/With multiple ranges | Loops/With multiple ranges
You are encouraged to solve this task according to the task description, using any language you may know.
Some languages allow multiple loop ranges, such as the PL/I example (snippet) below.
/* all variables are DECLARED as integers. */
prod= 1; /*start with a product of unity. */
sum= 0; /* " " " sum " zero. */
x= +5;
y= -5;
z= -2;
one= 1;
three= 3;
seven= 7;
/*(below) ** is exponentiation: 4**3=64 */
do j= -three to 3**3 by three ,
-seven to +seven by x ,
555 to 550 - y ,
22 to -28 by -three ,
1927 to 1939 ,
x to y by z ,
11**x to 11**x + one;
/* ABS(n) = absolute value*/
sum= sum + abs(j); /*add absolute value of J.*/
if abs(prod)<2**27 & j¬=0 then prod=prod*j; /*PROD is small enough & J*/
end; /*not 0, then multiply it.*/
/*SUM and PROD are used for verification of J incrementation.*/
display (' sum= ' || sum); /*display strings to term.*/
display ('prod= ' || prod); /* " " " " */
Task
Simulate/translate the above PL/I program snippet as best as possible in your
language, with particular emphasis on the do loop construct.
The do index must be incremented/decremented in the same order shown.
If feasible, add commas to the two output numbers (being displayed).
Show all output here.
A simple PL/I DO loop (incrementing or decrementing) has the construct of:
DO variable = start_expression {TO ending_expression] {BY increment_expression} ;
---or---
DO variable = start_expression {BY increment_expression} {TO ending_expression] ;
where it is understood that all expressions will have a value. The variable is normally a
scaler variable, but need not be (but for this task, all variables and expressions are declared
to be scaler integers). If the BY expression is omitted, a BY value of unity is used.
All expressions are evaluated before the DO loop is executed, and those values are used
throughout the DO loop execution (even though, for instance, the value of Z may be
changed within the DO loop. This isn't the case here for this task.
A multiple-range DO loop can be constructed by using a comma (,) to separate additional ranges
(the use of multiple TO and/or BY keywords). This is the construct used in this task.
There are other forms of DO loops in PL/I involving the WHILE clause, but those won't be
needed here. DO loops without a TO clause might need a WHILE clause or some other
means of exiting the loop (such as LEAVE, RETURN, SIGNAL, GOTO, or STOP), or some other
(possible error) condition that causes transfer of control outside the DO loop.
Also, in PL/I, the check if the DO loop index value is outside the range is made at the
"head" (start) of the DO loop, so it's possible that the DO loop isn't executed, but
that isn't the case for any of the ranges used in this task.
In the example above, the clause: x to y by z
will cause the variable J to have to following values (in this order): 5 3 1 -1 -3 -5
In the example above, the clause: -seven to +seven by x
will cause the variable J to have to following values (in this order): -7 -2 3
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Red | Red | Red ["For loop with multiple ranges"]
->: make op! function [start end][
res: copy []
repeat n 1 + absolute to-integer end - start [
append res start + either start > end [1 - n][n - 1]
]
]
by: make op! function [s w] [extract s absolute w]
for: function ['word ranges body][
inp: copy []
foreach c reduce ranges [append inp c]
foreach i inp [set word i do body]
]
prod: 1
sum: 0
x: +5
y: -5
z: -2
one: 1
three: 3
seven: 7
for j [
0 - three -> (3 ** 3) by three
0 - seven -> seven by x
555 -> (550 - y)
22 -> -28 by (0 - three)
1927 -> 1939
x -> y by z
11 ** x -> (11 ** x + one)
] [
sum: sum + absolute j;
if all [(absolute prod) < power 2 27 j <> 0] [prod: prod * j]
]
print ["sum: " sum "^/prod:" prod] |
http://rosettacode.org/wiki/Loops/With_multiple_ranges | Loops/With multiple ranges | Loops/With multiple ranges
You are encouraged to solve this task according to the task description, using any language you may know.
Some languages allow multiple loop ranges, such as the PL/I example (snippet) below.
/* all variables are DECLARED as integers. */
prod= 1; /*start with a product of unity. */
sum= 0; /* " " " sum " zero. */
x= +5;
y= -5;
z= -2;
one= 1;
three= 3;
seven= 7;
/*(below) ** is exponentiation: 4**3=64 */
do j= -three to 3**3 by three ,
-seven to +seven by x ,
555 to 550 - y ,
22 to -28 by -three ,
1927 to 1939 ,
x to y by z ,
11**x to 11**x + one;
/* ABS(n) = absolute value*/
sum= sum + abs(j); /*add absolute value of J.*/
if abs(prod)<2**27 & j¬=0 then prod=prod*j; /*PROD is small enough & J*/
end; /*not 0, then multiply it.*/
/*SUM and PROD are used for verification of J incrementation.*/
display (' sum= ' || sum); /*display strings to term.*/
display ('prod= ' || prod); /* " " " " */
Task
Simulate/translate the above PL/I program snippet as best as possible in your
language, with particular emphasis on the do loop construct.
The do index must be incremented/decremented in the same order shown.
If feasible, add commas to the two output numbers (being displayed).
Show all output here.
A simple PL/I DO loop (incrementing or decrementing) has the construct of:
DO variable = start_expression {TO ending_expression] {BY increment_expression} ;
---or---
DO variable = start_expression {BY increment_expression} {TO ending_expression] ;
where it is understood that all expressions will have a value. The variable is normally a
scaler variable, but need not be (but for this task, all variables and expressions are declared
to be scaler integers). If the BY expression is omitted, a BY value of unity is used.
All expressions are evaluated before the DO loop is executed, and those values are used
throughout the DO loop execution (even though, for instance, the value of Z may be
changed within the DO loop. This isn't the case here for this task.
A multiple-range DO loop can be constructed by using a comma (,) to separate additional ranges
(the use of multiple TO and/or BY keywords). This is the construct used in this task.
There are other forms of DO loops in PL/I involving the WHILE clause, but those won't be
needed here. DO loops without a TO clause might need a WHILE clause or some other
means of exiting the loop (such as LEAVE, RETURN, SIGNAL, GOTO, or STOP), or some other
(possible error) condition that causes transfer of control outside the DO loop.
Also, in PL/I, the check if the DO loop index value is outside the range is made at the
"head" (start) of the DO loop, so it's possible that the DO loop isn't executed, but
that isn't the case for any of the ranges used in this task.
In the example above, the clause: x to y by z
will cause the variable J to have to following values (in this order): 5 3 1 -1 -3 -5
In the example above, the clause: -seven to +seven by x
will cause the variable J to have to following values (in this order): -7 -2 3
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #REXX | REXX | /*REXX program emulates a multiple─range DO loop (all variables can be any numbers). */
prod= 1;
sum= 0;
x= +5;
y= -5;
z= -2;
one= 1;
three= 3;
seven= 7;
do j= -three to 3**3 by three ; call meat; end;
do j= -seven to seven by x ; call meat; end;
do j= 555 to 550 - y ; call meat; end;
do j= 22 to -28 by -three ; call meat; end;
do j= 1927 to 1939 ; call meat; end;
do j= x to y by z ; call meat; end;
do j= 11**x to 11**x + one ; call meat; end;
say ' sum= ' || commas( sum); /*display SUM with commas. */
say 'prod= ' || commas(prod); /* " PROD " " */
exit; /*stick a fork in it, we're done.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: procedure; parse arg _; n= _'.9'; #= 123456789; b= verify(n, #, "M")
e= verify(n, #'0', , verify(n, #"0.", 'M') ) - 4
do j=e to b by -3; _= insert(',', _, j); end; return _
/*──────────────────────────────────────────────────────────────────────────────────────*/
meat: sum= sum + abs(j);
if abs(prod)<2**27 & j\==0 then prod= prod * j;
return; |
http://rosettacode.org/wiki/Loops/While | Loops/While | Task
Start an integer value at 1024.
Loop while it is greater than zero.
Print the value (with a newline) and divide it by two each time through the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreachbas
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Common_Lisp | Common Lisp | (let ((i 1024))
(loop while (plusp i) do
(print i)
(setf i (floor i 2))))
(loop with i = 1024
while (plusp i) do
(print i)
(setf i (floor i 2)))
(defparameter *i* 1024)
(loop while (plusp *i*) do
(print *i*)
(setf *i* (floor *i* 2)))
|
http://rosettacode.org/wiki/Loops/Downward_for | Loops/Downward for | Task
Write a for loop which writes a countdown from 10 to 0.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #BQN | BQN | •Show¨⌽↕11 |
http://rosettacode.org/wiki/Loops/Downward_for | Loops/Downward for | Task
Write a for loop which writes a countdown from 10 to 0.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Bracmat | Bracmat | 10:?i
& whl'(out$!i&!i+-1:~<0:?i) |
http://rosettacode.org/wiki/Loops/Do-while | Loops/Do-while | Start with a value at 0. Loop while value mod 6 is not equal to 0.
Each time through the loop, add 1 to the value then print it.
The loop must execute at least once.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
Reference
Do while loop Wikipedia.
| #AppleScript | AppleScript |
on printConsole(x)
return x as string
end printConsole
set {i, table} to {0, {return}}
repeat while (i mod 6 is not 0 or i is not 6)
set i to i + 1
set end of table to i & return
printConsole(table)
end repeat
|
http://rosettacode.org/wiki/Loops/For | Loops/For | “For” loops are used to make some block of code be iterated a number of times, setting a variable or parameter to a monotonically increasing integer value for each execution of the block of code.
Common extensions of this allow other counting patterns or iterating over abstract structures other than the integers.
Task
Show how two loops may be nested within each other, with the number of iterations performed by the inner for loop being controlled by the outer for loop.
Specifically print out the following pattern by using one for loop nested in another:
*
**
***
****
*****
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
Reference
For loop Wikipedia.
| #APL | APL | {⎕←⍵/'*'}¨⍳5 |
http://rosettacode.org/wiki/Loops/For_with_a_specified_step | Loops/For with a specified step |
Task
Demonstrate a for-loop where the step-value is greater than one.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #BASIC | BASIC | FOR I = 2 TO 8 STEP 2 : PRINT I; ", "; : NEXT I : PRINT "WHO DO WE APPRECIATE?" |
http://rosettacode.org/wiki/Ludic_numbers | Ludic numbers | Ludic numbers are related to prime numbers as they are generated by a sieve quite like the Sieve of Eratosthenes is used to generate prime numbers.
The first ludic number is 1.
To generate succeeding ludic numbers create an array of increasing integers starting from 2.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...
(Loop)
Take the first member of the resultant array as the next ludic number 2.
Remove every 2nd indexed item from the array (including the first).
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...
(Unrolling a few loops...)
Take the first member of the resultant array as the next ludic number 3.
Remove every 3rd indexed item from the array (including the first).
3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 ...
Take the first member of the resultant array as the next ludic number 5.
Remove every 5th indexed item from the array (including the first).
5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 ...
Take the first member of the resultant array as the next ludic number 7.
Remove every 7th indexed item from the array (including the first).
7 11 13 17 23 25 29 31 37 41 43 47 53 55 59 61 67 71 73 77 83 85 89 91 97 ...
...
Take the first member of the current array as the next ludic number L.
Remove every Lth indexed item from the array (including the first).
...
Task
Generate and show here the first 25 ludic numbers.
How many ludic numbers are there less than or equal to 1000?
Show the 2000..2005th ludic numbers.
Stretch goal
Show all triplets of ludic numbers < 250.
A triplet is any three numbers
x
,
{\displaystyle x,}
x
+
2
,
{\displaystyle x+2,}
x
+
6
{\displaystyle x+6}
where all three numbers are also ludic numbers.
| #REXX | REXX | /*REXX program gens/shows (a range of) ludic numbers, or a count when a range is used.*/
parse arg N count bot top triples . /*obtain optional arguments from the CL*/
if N=='' | N=="," then N= 25 /*Not specified? Then use the default.*/
if count=='' | count=="," then count= 1000 /* " " " " " " */
if bot=='' | bot=="," then bot= 2000 /* " " " " " " */
if top=='' | top=="," then top= 2005 /* " " " " " " */
if triples=='' | triples=="," then triples= 249 /* " " " " " " */
#= 0 /*the number of ludic numbers (so far).*/
$= ludic( max(N, count, bot, top, triples) ) /*generate enough ludic nums*/
say 'The first ' N " ludic numbers: " subword($,1,25) /*display 1st N ludic nums*/
do j=1 until word($, j) > count /*search up to a specific #.*/
end /*j*/
say
say "There are " j - 1 ' ludic numbers that are ≤ ' count
say
say "The " bot '───►' top ' (inclusive) ludic numbers are: ' subword($, bot)
@= /*list of ludic triples found (so far).*/
do j=1 for words($)
_= word($, j) /*it is known that ludic _ exists. */
if _>=triples then leave /*only process up to a specific number.*/
if wordpos(_+2, $)==0 | wordpos(_+6, $)==0 then iterate /*Not triple? Skip it.*/
#= # + 1 /*bump the triple counter. */
@= @ '◄'_ _+2 _+6"► " /*append the newly found triple ──► @ */
end /*j*/
say
if @=='' then say 'From 1──►'triples", no triples found."
else say 'From 1──►'triples", " # ' triples found:' @
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
ludic: procedure; parse arg m,,@; $= 1 2 /*$≡ludic numbers superset; @≡sequence*/
do j=3 by 2 to m*15; @= @ j /*construct an initial list of numbers.*/
end /*j*/
@= @' '; n= words(@) /*append a blank to the number sequence*/
do while n\==0; f= word(@, 1) /*examine the first word in the @ list.*/
$= $ f /*add the word to the $ list. */
do d=1 by f while d<=n; n= n-1 /*use 1st number, elide all occurrences*/
@= changestr(' 'word(@, d)" ", @, ' . ') /*cross─out a number in @ */
end /*d*/ /* [↑] done eliding the "1st" number. */
@= translate(@, , .) /*change dots to blanks; count numbers.*/
end /*while*/ /* [↑] done eliding ludic numbers. */
return subword($, 1, m) /*return a range of ludic numbers. */ |
http://rosettacode.org/wiki/Loops/N_plus_one_half | Loops/N plus one half | Quite often one needs loops which, in the last iteration, execute only part of the loop body.
Goal
Demonstrate the best way to do this.
Task
Write a loop which writes the comma-separated list
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
using separate output statements for the number
and the comma from within the body of the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #EchoLisp | EchoLisp |
(string-delimiter "")
(for ((i (in-range 1 11))) (write i) #:break (= i 10) (write ","))
→ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10
;; or
(string-join (range 1 11) ",")
→ 1,2,3,4,5,6,7,8,9,10
|
http://rosettacode.org/wiki/Loops/Nested | Loops/Nested | Show a nested loop which searches a two-dimensional array filled with random numbers uniformly distributed over
[
1
,
…
,
20
]
{\displaystyle [1,\ldots ,20]}
.
The loops iterate rows and columns of the array printing the elements until the value
20
{\displaystyle 20}
is met.
Specifically, this task also shows how to break out of nested loops.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #dc | dc | 1 ss [Seed of the random number generator.]sz
[*
* lrx -- (number)
* Push a random number from 1 to 20.
*]sz
[
[ [If preventing modulo bias:]sz
sz [Drop this random number.]sz
lLx [Loop.]sz
]SI
[ [Loop:]sz
[*
* Formula (from POSIX) for random numbers of low quality.
* Push a random number from 0 to 32767.
*]sz
ls 1103515245 * 12345 + 4294967296 % ss
ls 65536 / 32768 %
d 32768 20 % >I [Prevent modulo bias.]sz
]d SL x
20 % 1 + [Be from 1 to 20.]sz
LLsz LIsz [Restore L, I.]sz
]sr
5 sb [b = Total rows]sz
5 sc [c = Total columns]sz
[Fill array a[] with random numbers from 1 to 20.]sz
[ [Inner loop for j:]sz
lrx [Push random number.]sz
li lc * lj + [Push index of a[i, j].]sz
:a [Put in a[].]sz
lj 1 + d sj [j += 1]sz
lc >I [Loop while c > j.]sz
]sI
[ [Outer loop for i:]sz
0 d sj [j = 0]sz
lc >I [Enter inner loop.]sz
li 1 + d si [i += 1]sz
lb >L [Loop while b > i.]sz
]sL
0 d si [i = 0]sz
lb >L [Enter outer loop.]sz
[Find a 20.]sz
[ [If detecting a 20:]sz
li lj + 3 + Q [Break outer loop.]sz
]sD
[ [Inner loop for j:]sz
li lc * lj + [Push index of a[i,j].]sz
;a [Push value from a[].]sz
p [Print value and a newline.]sz
20 =D [Detect a 20.]sz
lj 1 + d sj [j += 1]sz
lc >I [Loop while c > j.]sz
]sI
[ [Outer loop for i:]sz
0 d sj [j = 0]sz
lc >I [Enter inner loop.]sz
[==
]P [Print "==" and a newline.]sz
li 1 + d si [i += 1]sz
lb >L [Loop while b > i.]sz
]sL
0 d si [i = 0]sz
lb >L [Enter outer loop.]sz |
http://rosettacode.org/wiki/Loops/Nested | Loops/Nested | Show a nested loop which searches a two-dimensional array filled with random numbers uniformly distributed over
[
1
,
…
,
20
]
{\displaystyle [1,\ldots ,20]}
.
The loops iterate rows and columns of the array printing the elements until the value
20
{\displaystyle 20}
is met.
Specifically, this task also shows how to break out of nested loops.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Delphi.2FPascal | Delphi/Pascal | var
matrix: array[1..10,1..10] of Integer;
row, col: Integer;
broken: Boolean;
begin
// Launch random number generator
randomize;
// Filling matrix with random numbers
for row := 1 to 10 do
for col := 1 to 10 do
matrix[row, col] := Succ(Random(20));
// Displaying values one by one, until at the end or reached number 20
Broken := False;
for row := 1 to 10 do
begin
for col := 1 to 10 do
begin
ShowMessage(IntToStr(matrix[row, col]));
if matrix[row, col] = 20 then
begin
Broken := True;
break;
end;
end;
if Broken then break;
end;
end; |
http://rosettacode.org/wiki/Loops/Foreach | Loops/Foreach | Loop through and print each element in a collection in order.
Use your language's "for each" loop if it has one, otherwise iterate through the collection in order with some other loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Elixir | Elixir | iex(1)> list = [1,3.14,"abc",[3],{0,5}]
[1, 3.14, "abc", [3], {0, 5}]
iex(2)> Enum.each(list, fn x -> IO.inspect x end)
1
3.14
"abc"
[3]
{0, 5}
:ok |
http://rosettacode.org/wiki/Luhn_test_of_credit_card_numbers | Luhn test of credit card numbers | The Luhn test is used by some credit card companies to distinguish valid credit card numbers from what could be a random selection of digits.
Those companies using credit card numbers that can be validated by the Luhn test have numbers that pass the following test:
Reverse the order of the digits in the number.
Take the first, third, ... and every other odd digit in the reversed digits and sum them to form the partial sum s1
Taking the second, fourth ... and every other even digit in the reversed digits:
Multiply each digit by two and sum the digits if the answer is greater than nine to form partial sums for the even digits
Sum the partial sums of the even digits to form s2
If s1 + s2 ends in zero then the original number is in the form of a valid credit card number as verified by the Luhn test.
For example, if the trial number is 49927398716:
Reverse the digits:
61789372994
Sum the odd digits:
6 + 7 + 9 + 7 + 9 + 4 = 42 = s1
The even digits:
1, 8, 3, 2, 9
Two times each even digit:
2, 16, 6, 4, 18
Sum the digits of each multiplication:
2, 7, 6, 4, 9
Sum the last:
2 + 7 + 6 + 4 + 9 = 28 = s2
s1 + s2 = 70 which ends in zero which means that 49927398716 passes the Luhn test
Task
Write a function/method/procedure/subroutine that will validate a number with the Luhn test, and
use it to validate the following numbers:
49927398716
49927398717
1234567812345678
1234567812345670
Related tasks
SEDOL
ISIN
| #Cach.C3.A9_ObjectScript | Caché ObjectScript | Class Utils.Check [ Abstract ]
{
ClassMethod Luhn(x As %String) As %Boolean
{
// https://www.simple-talk.com/sql/t-sql-programming/calculating-and-verifying-check-digits-in-t-sql/
SET x=$TRANSLATE(x," "), cd=$EXTRACT(x,*)
SET x=$REVERSE($EXTRACT(x,1,*-1)), t=0
FOR i=1:1:$LENGTH(x) {
SET n=$EXTRACT(x,i)
IF i#2 SET n=n*2 IF $LENGTH(n)>1 SET n=$EXTRACT(n,1)+$EXTRACT(n,2)
SET t=t+n
}
QUIT cd=((t*9)#10)
}
} |
http://rosettacode.org/wiki/Lucas-Lehmer_test | Lucas-Lehmer test | Lucas-Lehmer Test:
for
p
{\displaystyle p}
an odd prime, the Mersenne number
2
p
−
1
{\displaystyle 2^{p}-1}
is prime if and only if
2
p
−
1
{\displaystyle 2^{p}-1}
divides
S
(
p
−
1
)
{\displaystyle S(p-1)}
where
S
(
n
+
1
)
=
(
S
(
n
)
)
2
−
2
{\displaystyle S(n+1)=(S(n))^{2}-2}
, and
S
(
1
)
=
4
{\displaystyle S(1)=4}
.
Task
Calculate all Mersenne primes up to the implementation's
maximum precision, or the 47th Mersenne prime (whichever comes first).
| #Haskell | Haskell | module Main
where
main = printMersennes $ take 45 $ filter lucasLehmer $ sieve [2..]
s mp 1 = 4 `mod` mp
s mp n = ((s mp $ n-1)^2-2) `mod` mp
lucasLehmer 2 = True
lucasLehmer p = s (2^p-1) (p-1) == 0
printMersennes = mapM_ (\x -> putStrLn $ "M" ++ show x) |
http://rosettacode.org/wiki/LZW_compression | LZW compression | The Lempel-Ziv-Welch (LZW) algorithm provides loss-less data compression.
You can read a complete description of it in the Wikipedia article on the subject. It was patented, but it entered the public domain in 2004.
| #Objective-C | Objective-C | #import <Foundation/Foundation.h>
#import <stdio.h>
@interface LZWCompressor : NSObject
{
@private
NSMutableArray *iostream;
NSMutableDictionary *dict;
NSUInteger codemark;
}
-(instancetype) init;
-(instancetype) initWithArray: (NSMutableArray *) stream;
-(BOOL) compressData: (NSData *) string;
-(void) setArray: (NSMutableArray *) stream;
-(NSArray *) getArray;
@end
@implementation LZWCompressor : NSObject
-(instancetype) init
{
self = [super init];
if ( self )
{
iostream = nil;
codemark = 256;
dict = [[NSMutableDictionary alloc] initWithCapacity: 512];
}
return self;
}
-(instancetype) initWithArray: (NSMutableArray *) stream
{
self = [self init];
if ( self )
{
[self setArray: stream];
}
return self;
}
-(void) setArray: (NSMutableArray *) stream
{
iostream = stream;
}
-(BOOL) compressData: (NSData *) string;
{
// prepare dict
for(NSUInteger i=0; i < 256; i++)
{
unsigned char j = i;
NSData *s = [NSData dataWithBytes: &j length: 1];
dict[s] = @(i);
}
NSData *w = [NSData data];
for(NSUInteger i=0; i < [string length]; i++)
{
NSMutableData *wc = [NSMutableData dataWithData: w];
[wc appendData: [string subdataWithRange: NSMakeRange(i, 1)]];
if ( dict[wc] != nil )
{
w = wc;
} else {
[iostream addObject: dict[w]];
dict[wc] = @(codemark);
codemark++;
w = [string subdataWithRange: NSMakeRange(i, 1)];
}
}
if ( [w length] != 0 )
{
[iostream addObject: dict[w]];
}
return YES;
}
-(NSArray *) getArray
{
return iostream;
}
@end |
http://rosettacode.org/wiki/LU_decomposition | LU decomposition | Every square matrix
A
{\displaystyle A}
can be decomposed into a product of a lower triangular matrix
L
{\displaystyle L}
and a upper triangular matrix
U
{\displaystyle U}
,
as described in LU decomposition.
A
=
L
U
{\displaystyle A=LU}
It is a modified form of Gaussian elimination.
While the Cholesky decomposition only works for symmetric,
positive definite matrices, the more general LU decomposition
works for any square matrix.
There are several algorithms for calculating L and U.
To derive Crout's algorithm for a 3x3 example,
we have to solve the following system:
A
=
(
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
)
=
(
l
11
0
0
l
21
l
22
0
l
31
l
32
l
33
)
(
u
11
u
12
u
13
0
u
22
u
23
0
0
u
33
)
=
L
U
{\displaystyle A={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\\end{pmatrix}}={\begin{pmatrix}l_{11}&0&0\\l_{21}&l_{22}&0\\l_{31}&l_{32}&l_{33}\\\end{pmatrix}}{\begin{pmatrix}u_{11}&u_{12}&u_{13}\\0&u_{22}&u_{23}\\0&0&u_{33}\end{pmatrix}}=LU}
We now would have to solve 9 equations with 12 unknowns. To make the system uniquely solvable, usually the diagonal elements of
L
{\displaystyle L}
are set to 1
l
11
=
1
{\displaystyle l_{11}=1}
l
22
=
1
{\displaystyle l_{22}=1}
l
33
=
1
{\displaystyle l_{33}=1}
so we get a solvable system of 9 unknowns and 9 equations.
A
=
(
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
)
=
(
1
0
0
l
21
1
0
l
31
l
32
1
)
(
u
11
u
12
u
13
0
u
22
u
23
0
0
u
33
)
=
(
u
11
u
12
u
13
u
11
l
21
u
12
l
21
+
u
22
u
13
l
21
+
u
23
u
11
l
31
u
12
l
31
+
u
22
l
32
u
13
l
31
+
u
23
l
32
+
u
33
)
=
L
U
{\displaystyle A={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\\end{pmatrix}}={\begin{pmatrix}1&0&0\\l_{21}&1&0\\l_{31}&l_{32}&1\\\end{pmatrix}}{\begin{pmatrix}u_{11}&u_{12}&u_{13}\\0&u_{22}&u_{23}\\0&0&u_{33}\end{pmatrix}}={\begin{pmatrix}u_{11}&u_{12}&u_{13}\\u_{11}l_{21}&u_{12}l_{21}+u_{22}&u_{13}l_{21}+u_{23}\\u_{11}l_{31}&u_{12}l_{31}+u_{22}l_{32}&u_{13}l_{31}+u_{23}l_{32}+u_{33}\end{pmatrix}}=LU}
Solving for the other
l
{\displaystyle l}
and
u
{\displaystyle u}
, we get the following equations:
u
11
=
a
11
{\displaystyle u_{11}=a_{11}}
u
12
=
a
12
{\displaystyle u_{12}=a_{12}}
u
13
=
a
13
{\displaystyle u_{13}=a_{13}}
u
22
=
a
22
−
u
12
l
21
{\displaystyle u_{22}=a_{22}-u_{12}l_{21}}
u
23
=
a
23
−
u
13
l
21
{\displaystyle u_{23}=a_{23}-u_{13}l_{21}}
u
33
=
a
33
−
(
u
13
l
31
+
u
23
l
32
)
{\displaystyle u_{33}=a_{33}-(u_{13}l_{31}+u_{23}l_{32})}
and for
l
{\displaystyle l}
:
l
21
=
1
u
11
a
21
{\displaystyle l_{21}={\frac {1}{u_{11}}}a_{21}}
l
31
=
1
u
11
a
31
{\displaystyle l_{31}={\frac {1}{u_{11}}}a_{31}}
l
32
=
1
u
22
(
a
32
−
u
12
l
31
)
{\displaystyle l_{32}={\frac {1}{u_{22}}}(a_{32}-u_{12}l_{31})}
We see that there is a calculation pattern, which can be expressed as the following formulas, first for
U
{\displaystyle U}
u
i
j
=
a
i
j
−
∑
k
=
1
i
−
1
u
k
j
l
i
k
{\displaystyle u_{ij}=a_{ij}-\sum _{k=1}^{i-1}u_{kj}l_{ik}}
and then for
L
{\displaystyle L}
l
i
j
=
1
u
j
j
(
a
i
j
−
∑
k
=
1
j
−
1
u
k
j
l
i
k
)
{\displaystyle l_{ij}={\frac {1}{u_{jj}}}(a_{ij}-\sum _{k=1}^{j-1}u_{kj}l_{ik})}
We see in the second formula that to get the
l
i
j
{\displaystyle l_{ij}}
below the diagonal, we have to divide by the diagonal element (pivot)
u
j
j
{\displaystyle u_{jj}}
, so we get problems when
u
j
j
{\displaystyle u_{jj}}
is either 0 or very small, which leads to numerical instability.
The solution to this problem is pivoting
A
{\displaystyle A}
, which means rearranging the rows of
A
{\displaystyle A}
, prior to the
L
U
{\displaystyle LU}
decomposition, in a way that the largest element of each column gets onto the diagonal of
A
{\displaystyle A}
. Rearranging the rows means to multiply
A
{\displaystyle A}
by a permutation matrix
P
{\displaystyle P}
:
P
A
⇒
A
′
{\displaystyle PA\Rightarrow A'}
Example:
(
0
1
1
0
)
(
1
4
2
3
)
⇒
(
2
3
1
4
)
{\displaystyle {\begin{pmatrix}0&1\\1&0\end{pmatrix}}{\begin{pmatrix}1&4\\2&3\end{pmatrix}}\Rightarrow {\begin{pmatrix}2&3\\1&4\end{pmatrix}}}
The decomposition algorithm is then applied on the rearranged matrix so that
P
A
=
L
U
{\displaystyle PA=LU}
Task description
The task is to implement a routine which will take a square nxn matrix
A
{\displaystyle A}
and return a lower triangular matrix
L
{\displaystyle L}
, a upper triangular matrix
U
{\displaystyle U}
and a permutation matrix
P
{\displaystyle P}
,
so that the above equation is fulfilled.
You should then test it on the following two examples and include your output.
Example 1
A
1 3 5
2 4 7
1 1 0
L
1.00000 0.00000 0.00000
0.50000 1.00000 0.00000
0.50000 -1.00000 1.00000
U
2.00000 4.00000 7.00000
0.00000 1.00000 1.50000
0.00000 0.00000 -2.00000
P
0 1 0
1 0 0
0 0 1
Example 2
A
11 9 24 2
1 5 2 6
3 17 18 1
2 5 7 1
L
1.00000 0.00000 0.00000 0.00000
0.27273 1.00000 0.00000 0.00000
0.09091 0.28750 1.00000 0.00000
0.18182 0.23125 0.00360 1.00000
U
11.00000 9.00000 24.00000 2.00000
0.00000 14.54545 11.45455 0.45455
0.00000 0.00000 -3.47500 5.68750
0.00000 0.00000 0.00000 0.51079
P
1 0 0 0
0 0 1 0
0 1 0 0
0 0 0 1
| #Ruby | Ruby | require 'matrix'
class Matrix
def lu_decomposition
p = get_pivot
tmp = p * self
u = Matrix.zero(row_size).to_a
l = Matrix.identity(row_size).to_a
(0 ... row_size).each do |i|
(0 ... row_size).each do |j|
if j >= i
# upper
u[i][j] = tmp[i,j] - (0 ... i).inject(0.0) {|sum, k| sum + u[k][j] * l[i][k]}
else
# lower
l[i][j] = (tmp[i,j] - (0 ... j).inject(0.0) {|sum, k| sum + u[k][j] * l[i][k]}) / u[j][j]
end
end
end
[ Matrix[*l], Matrix[*u], p ]
end
def get_pivot
raise ArgumentError, "must be square" unless square?
id = Matrix.identity(row_size).to_a
(0 ... row_size).each do |i|
max = self[i,i]
row = i
(i ... row_size).each do |j|
if self[j,i] > max
max = self[j,i]
row = j
end
end
id[i], id[row] = id[row], id[i]
end
Matrix[*id]
end
def pretty_print(format, head=nil)
puts head if head
puts each_slice(column_size).map{|row| format*row_size % row}
end
end
puts "Example 1:"
a = Matrix[[1, 3, 5],
[2, 4, 7],
[1, 1, 0]]
a.pretty_print(" %2d", "A")
l, u, p = a.lu_decomposition
l.pretty_print(" %8.5f", "L")
u.pretty_print(" %8.5f", "U")
p.pretty_print(" %d", "P")
puts "\nExample 2:"
a = Matrix[[11, 9,24,2],
[ 1, 5, 2,6],
[ 3,17,18,1],
[ 2, 5, 7,1]]
a.pretty_print(" %2d", "A")
l, u, p = a.lu_decomposition
l.pretty_print(" %8.5f", "L")
u.pretty_print(" %8.5f", "U")
p.pretty_print(" %d", "P") |
http://rosettacode.org/wiki/Mad_Libs | Mad Libs |
This page uses content from Wikipedia. The original article was at Mad Libs. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Mad Libs is a phrasal template word game where one player prompts another for a list of words to substitute for blanks in a story, usually with funny results.
Task;
Write a program to create a Mad Libs like story.
The program should read an arbitrary multiline story from input.
The story will be terminated with a blank line.
Then, find each replacement to be made within the story, ask the user for a word to replace it with, and make all the replacements.
Stop when there are none left and print the final story.
The input should be an arbitrary story in the form:
<name> went for a walk in the park. <he or she>
found a <noun>. <name> decided to take it home.
Given this example, it should then ask for a name, a he or she and a noun (<name> gets replaced both times with the same value).
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
| #Red | Red | phrase: ask "Enter phrase, leave line empty to terminate:^/"
while [not empty? line: input] [append phrase rejoin ["^/" line]]
words: parse phrase [collect [any [to "<" copy b thru ">" keep (b)]]]
foreach w unique words [replace/all phrase w ask rejoin [w ": "]]
print phrase |
http://rosettacode.org/wiki/Loops/Increment_loop_index_within_loop_body | Loops/Increment loop index within loop body | Sometimes, one may need (or want) a loop which
its iterator (the index
variable) is modified within the
loop body in addition to the normal incrementation by the (do) loop structure index.
Goal
Demonstrate the best way to accomplish this.
Task
Write a loop which:
starts the index (variable) at 42
(at iteration time) increments the index by unity
if the index is prime:
displays the count of primes found (so far) and the prime (to the terminal)
increments the index such that the new index is now the (old) index plus that prime
terminates the loop when 42 primes are shown
Extra credit: because of the primes get rather large, use commas
within the displayed primes to ease comprehension.
Show all output here.
Note
Not all programming languages allow the modification of a
loop's index. If that is the case, then use whatever method that
is appropriate or idiomatic for that language. Please add a note
if the loop's index isn't modifiable.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Mathematica_.2F_Wolfram_Language | Mathematica / Wolfram Language | {i, n} = {42, 0};
While[n < 42,
If[PrimeQ[i],
Print["n=", n++, "\t", i];
i += i - 1;
];
i++;
] |
http://rosettacode.org/wiki/Loops/Increment_loop_index_within_loop_body | Loops/Increment loop index within loop body | Sometimes, one may need (or want) a loop which
its iterator (the index
variable) is modified within the
loop body in addition to the normal incrementation by the (do) loop structure index.
Goal
Demonstrate the best way to accomplish this.
Task
Write a loop which:
starts the index (variable) at 42
(at iteration time) increments the index by unity
if the index is prime:
displays the count of primes found (so far) and the prime (to the terminal)
increments the index such that the new index is now the (old) index plus that prime
terminates the loop when 42 primes are shown
Extra credit: because of the primes get rather large, use commas
within the displayed primes to ease comprehension.
Show all output here.
Note
Not all programming languages allow the modification of a
loop's index. If that is the case, then use whatever method that
is appropriate or idiomatic for that language. Please add a note
if the loop's index isn't modifiable.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Microsoft_Small_Basic | Microsoft Small Basic | 'Loops Increment loop index within loop body - 16/07/2018
imax=42
i=0
n=42
While i<imax
isprime_n()
If ret_isprime_n Then
i=i+1
format_i()
format_n()
TextWindow.WriteLine("i="+ret_format_i+" : "+ret_format_n)
n=n+n-1
EndIf
n=n+1
EndWhile
Sub isprime_n
If n=2 Or n=3 Then
ret_isprime_n="True"
ElseIf Math.Remainder(n,2)=0 Or Math.Remainder(n,3)=0 Then
ret_isprime_n="False"
Else
j=5
While j*j<=n
If Math.Remainder(n,j)=0 Or Math.Remainder(n,j+2)=0 Then
ret_isprime_n="False"
Goto exitsub
EndIf
j=j+6
EndWhile
ret_isprime_n="True"
EndIf
exitsub:
EndSub 'isprime_n
Sub format_i
ret_format_i=Text.GetSubText(" ",1,3-Text.GetLength(i))+i
EndSub 'format_i
Sub format_n
nn=""
l=-1
For k=Text.GetLength(n) To 1 Step -1
l=l+1
cc=Text.GetSubText(n,k,1)
If l=3 Then
cv=","
l=0
Else
cv=""
EndIf
nn=Text.Append(cc,Text.Append(cv,nn))
EndFor
space=" "
nn=Text.GetSubText(space,1,Text.GetLength(space)-Text.GetLength(nn))+nn
ret_format_n=nn
EndSub 'format_n |
http://rosettacode.org/wiki/Loops/Infinite | Loops/Infinite | Task
Print out SPAM followed by a newline in an infinite loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Clojure | Clojure | (loop [] (println "SPAM") (recur)) |
http://rosettacode.org/wiki/Loops/Infinite | Loops/Infinite | Task
Print out SPAM followed by a newline in an infinite loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #COBOL | COBOL | IDENTIFICATION DIVISION.
PROGRAM-ID. Spam.
PROCEDURE DIVISION.
PERFORM UNTIL 1 <> 1
DISPLAY "SPAM"
END-PERFORM
GOBACK
. |
http://rosettacode.org/wiki/Loops/With_multiple_ranges | Loops/With multiple ranges | Loops/With multiple ranges
You are encouraged to solve this task according to the task description, using any language you may know.
Some languages allow multiple loop ranges, such as the PL/I example (snippet) below.
/* all variables are DECLARED as integers. */
prod= 1; /*start with a product of unity. */
sum= 0; /* " " " sum " zero. */
x= +5;
y= -5;
z= -2;
one= 1;
three= 3;
seven= 7;
/*(below) ** is exponentiation: 4**3=64 */
do j= -three to 3**3 by three ,
-seven to +seven by x ,
555 to 550 - y ,
22 to -28 by -three ,
1927 to 1939 ,
x to y by z ,
11**x to 11**x + one;
/* ABS(n) = absolute value*/
sum= sum + abs(j); /*add absolute value of J.*/
if abs(prod)<2**27 & j¬=0 then prod=prod*j; /*PROD is small enough & J*/
end; /*not 0, then multiply it.*/
/*SUM and PROD are used for verification of J incrementation.*/
display (' sum= ' || sum); /*display strings to term.*/
display ('prod= ' || prod); /* " " " " */
Task
Simulate/translate the above PL/I program snippet as best as possible in your
language, with particular emphasis on the do loop construct.
The do index must be incremented/decremented in the same order shown.
If feasible, add commas to the two output numbers (being displayed).
Show all output here.
A simple PL/I DO loop (incrementing or decrementing) has the construct of:
DO variable = start_expression {TO ending_expression] {BY increment_expression} ;
---or---
DO variable = start_expression {BY increment_expression} {TO ending_expression] ;
where it is understood that all expressions will have a value. The variable is normally a
scaler variable, but need not be (but for this task, all variables and expressions are declared
to be scaler integers). If the BY expression is omitted, a BY value of unity is used.
All expressions are evaluated before the DO loop is executed, and those values are used
throughout the DO loop execution (even though, for instance, the value of Z may be
changed within the DO loop. This isn't the case here for this task.
A multiple-range DO loop can be constructed by using a comma (,) to separate additional ranges
(the use of multiple TO and/or BY keywords). This is the construct used in this task.
There are other forms of DO loops in PL/I involving the WHILE clause, but those won't be
needed here. DO loops without a TO clause might need a WHILE clause or some other
means of exiting the loop (such as LEAVE, RETURN, SIGNAL, GOTO, or STOP), or some other
(possible error) condition that causes transfer of control outside the DO loop.
Also, in PL/I, the check if the DO loop index value is outside the range is made at the
"head" (start) of the DO loop, so it's possible that the DO loop isn't executed, but
that isn't the case for any of the ranges used in this task.
In the example above, the clause: x to y by z
will cause the variable J to have to following values (in this order): 5 3 1 -1 -3 -5
In the example above, the clause: -seven to +seven by x
will cause the variable J to have to following values (in this order): -7 -2 3
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Ring | Ring |
prod = 1
total = 0
x = 5
y = -5
z = -2
one = 1
three = 3
seven = 7
loopset = [[-three,pow(3,3),three],
[-seven,seven,x],
[555,550 - y,1],
[22,-28,-three],
[1927,1939,1],
[x,y,z],
[pow(11,x),pow(11,x) + one,1]]
for i=1 to len(loopset)
f = loopset[i][1]
t = loopset[i][2]
s = loopset[i][3]
for j=f to t step s
total += fabs(j)
if fabs(prod)<pow(2,27) and j!=0
prod *= j
ok
next
next
see "total = " + total + nl
see "product = " + prod + nl
|
http://rosettacode.org/wiki/Loops/With_multiple_ranges | Loops/With multiple ranges | Loops/With multiple ranges
You are encouraged to solve this task according to the task description, using any language you may know.
Some languages allow multiple loop ranges, such as the PL/I example (snippet) below.
/* all variables are DECLARED as integers. */
prod= 1; /*start with a product of unity. */
sum= 0; /* " " " sum " zero. */
x= +5;
y= -5;
z= -2;
one= 1;
three= 3;
seven= 7;
/*(below) ** is exponentiation: 4**3=64 */
do j= -three to 3**3 by three ,
-seven to +seven by x ,
555 to 550 - y ,
22 to -28 by -three ,
1927 to 1939 ,
x to y by z ,
11**x to 11**x + one;
/* ABS(n) = absolute value*/
sum= sum + abs(j); /*add absolute value of J.*/
if abs(prod)<2**27 & j¬=0 then prod=prod*j; /*PROD is small enough & J*/
end; /*not 0, then multiply it.*/
/*SUM and PROD are used for verification of J incrementation.*/
display (' sum= ' || sum); /*display strings to term.*/
display ('prod= ' || prod); /* " " " " */
Task
Simulate/translate the above PL/I program snippet as best as possible in your
language, with particular emphasis on the do loop construct.
The do index must be incremented/decremented in the same order shown.
If feasible, add commas to the two output numbers (being displayed).
Show all output here.
A simple PL/I DO loop (incrementing or decrementing) has the construct of:
DO variable = start_expression {TO ending_expression] {BY increment_expression} ;
---or---
DO variable = start_expression {BY increment_expression} {TO ending_expression] ;
where it is understood that all expressions will have a value. The variable is normally a
scaler variable, but need not be (but for this task, all variables and expressions are declared
to be scaler integers). If the BY expression is omitted, a BY value of unity is used.
All expressions are evaluated before the DO loop is executed, and those values are used
throughout the DO loop execution (even though, for instance, the value of Z may be
changed within the DO loop. This isn't the case here for this task.
A multiple-range DO loop can be constructed by using a comma (,) to separate additional ranges
(the use of multiple TO and/or BY keywords). This is the construct used in this task.
There are other forms of DO loops in PL/I involving the WHILE clause, but those won't be
needed here. DO loops without a TO clause might need a WHILE clause or some other
means of exiting the loop (such as LEAVE, RETURN, SIGNAL, GOTO, or STOP), or some other
(possible error) condition that causes transfer of control outside the DO loop.
Also, in PL/I, the check if the DO loop index value is outside the range is made at the
"head" (start) of the DO loop, so it's possible that the DO loop isn't executed, but
that isn't the case for any of the ranges used in this task.
In the example above, the clause: x to y by z
will cause the variable J to have to following values (in this order): 5 3 1 -1 -3 -5
In the example above, the clause: -seven to +seven by x
will cause the variable J to have to following values (in this order): -7 -2 3
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Ruby | Ruby | x, y, z, one, three, seven = 5, -5, -2, 1, 3, 7
enums = (-three).step(3**3, three) +
(-seven).step(seven, x) +
555 .step(550-y, -1) +
22 .step(-28, -three) +
(1927..1939) + # just toying, 1927.step(1939) is fine too
x .step(y, z) +
(11**x) .step(11**x + one)
# enums is an enumerator, consisting of a bunch of chained enumerators,
# none of which has actually produced a value.
puts "Sum of absolute numbers: #{enums.sum(&:abs)}"
prod = enums.inject(1){|prod, j| ((prod.abs < 2**27) && j!=0) ? prod*j : prod}
puts "Product (but not really): #{prod}"
|
http://rosettacode.org/wiki/Loops/While | Loops/While | Task
Start an integer value at 1024.
Loop while it is greater than zero.
Print the value (with a newline) and divide it by two each time through the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreachbas
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Cowgol | Cowgol | include "cowgol.coh";
var n: uint16 := 1024;
while n > 0 loop
print_i16(n);
print_nl();
n := n/2;
end loop; |
http://rosettacode.org/wiki/Loops/Downward_for | Loops/Downward for | Task
Write a for loop which writes a countdown from 10 to 0.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Brainf.2A.2A.2A | Brainf*** | >++++++++[-<++++++>] //cell 0 now contains 48 the ASCII code for "0"
<+.-. //print the digits 1 and 0
>++++++++++. //cell 1 now contains the carriage return; print it!
>+++++++++ //cell 2 now contains the number 9; this is our counter
<<+++++++++>> //cell 0 now contains 57 the ASCII code for "9"
[<<.->.>-] //print and decrement the display digit; print a newline; decrement the loop variable
<<.>. //print the final 0 and a final newline |
http://rosettacode.org/wiki/Loops/Do-while | Loops/Do-while | Start with a value at 0. Loop while value mod 6 is not equal to 0.
Each time through the loop, add 1 to the value then print it.
The loop must execute at least once.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
Reference
Do while loop Wikipedia.
| #Arturo | Arturo | value: 0
until [
value: value + 1
print value
] [ 0 = value%6 ] |
http://rosettacode.org/wiki/Loops/For | Loops/For | “For” loops are used to make some block of code be iterated a number of times, setting a variable or parameter to a monotonically increasing integer value for each execution of the block of code.
Common extensions of this allow other counting patterns or iterating over abstract structures other than the integers.
Task
Show how two loops may be nested within each other, with the number of iterations performed by the inner for loop being controlled by the outer for loop.
Specifically print out the following pattern by using one for loop nested in another:
*
**
***
****
*****
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
Reference
For loop Wikipedia.
| #AppleScript | AppleScript | set x to linefeed
repeat with i from 1 to 5
repeat with j from 1 to i
set x to x & "*"
end repeat
set x to x & linefeed
end repeat
return x |
http://rosettacode.org/wiki/Loops/For_with_a_specified_step | Loops/For with a specified step |
Task
Demonstrate a for-loop where the step-value is greater than one.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Batch_File | Batch File | @echo off
for /l %%A in (1,2,10) do (
echo %%A
) |
http://rosettacode.org/wiki/Ludic_numbers | Ludic numbers | Ludic numbers are related to prime numbers as they are generated by a sieve quite like the Sieve of Eratosthenes is used to generate prime numbers.
The first ludic number is 1.
To generate succeeding ludic numbers create an array of increasing integers starting from 2.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...
(Loop)
Take the first member of the resultant array as the next ludic number 2.
Remove every 2nd indexed item from the array (including the first).
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...
(Unrolling a few loops...)
Take the first member of the resultant array as the next ludic number 3.
Remove every 3rd indexed item from the array (including the first).
3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 ...
Take the first member of the resultant array as the next ludic number 5.
Remove every 5th indexed item from the array (including the first).
5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 ...
Take the first member of the resultant array as the next ludic number 7.
Remove every 7th indexed item from the array (including the first).
7 11 13 17 23 25 29 31 37 41 43 47 53 55 59 61 67 71 73 77 83 85 89 91 97 ...
...
Take the first member of the current array as the next ludic number L.
Remove every Lth indexed item from the array (including the first).
...
Task
Generate and show here the first 25 ludic numbers.
How many ludic numbers are there less than or equal to 1000?
Show the 2000..2005th ludic numbers.
Stretch goal
Show all triplets of ludic numbers < 250.
A triplet is any three numbers
x
,
{\displaystyle x,}
x
+
2
,
{\displaystyle x+2,}
x
+
6
{\displaystyle x+6}
where all three numbers are also ludic numbers.
| #Ring | Ring |
# Project : Ludic numbers
ludic = list(300)
resludic = []
nr = 1
for n = 1 to len(ludic)
ludic[n] = n+1
next
see "the first 25 Ludic numbers are:" + nl
ludicnumbers(ludic)
showarray(resludic)
see nl
see "Ludic numbers below 1000: "
ludic = list(3000)
resludic = []
for n = 1 to len(ludic)
ludic[n] = n+1
next
ludicnumbers(ludic)
showarray2(resludic)
see nr
see nl + nl
see "the 2000..2005th Ludic numbers are:" + nl
ludic = list(60000)
resludic = []
for n = 1 to len(ludic)
ludic[n] = n+1
next
ludicnumbers(ludic)
showarray3(resludic)
func ludicnumbers(ludic)
for n = 1 to len(ludic)
delludic = []
for m = 1 to len(ludic) step ludic[1]
add(delludic, m)
next
add(resludic, ludic[1])
for p = len(delludic) to 1 step -1
del(ludic, delludic[p])
next
next
func showarray(vect)
see "[1, "
svect = ""
for n = 1 to 24
svect = svect + vect[n] + ", "
next
svect = left(svect, len(svect) - 2)
see svect
see "]" + nl
func showarray2(vect)
for n = 1 to len(vect)
if vect[n] <= 1000
nr = nr + 1
ok
next
return nr
func showarray3(vect)
see "["
svect = ""
for n = 1999 to 2004
svect = svect + vect[n] + ", "
next
svect = left(svect, len(svect) - 2)
see svect
see "]" + nl
|
http://rosettacode.org/wiki/Loops/N_plus_one_half | Loops/N plus one half | Quite often one needs loops which, in the last iteration, execute only part of the loop body.
Goal
Demonstrate the best way to do this.
Task
Write a loop which writes the comma-separated list
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
using separate output statements for the number
and the comma from within the body of the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #EDSAC_order_code | EDSAC order code | [ N and a half times loop
=======================
A program for the EDSAC
Works with Initial Orders 2 ]
T56K
GK
O16@
[ 1 ] T24@
A25@
A18@
U25@
S23@
E11@
O25@
O19@
O20@
G1@
[ 11 ] O18@
O17@
O21@
O22@
ZF
[ 16 ] #F
[ 17 ] PF
[ 18 ] QF
[ 19 ] NF
[ 20 ] !F
[ 21 ] @F
[ 22 ] &F
[ 23 ] JF
[ 24 ] PF
[ 25 ] PF
EZPF |
http://rosettacode.org/wiki/Loops/N_plus_one_half | Loops/N plus one half | Quite often one needs loops which, in the last iteration, execute only part of the loop body.
Goal
Demonstrate the best way to do this.
Task
Write a loop which writes the comma-separated list
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
using separate output statements for the number
and the comma from within the body of the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Elixir | Elixir | defmodule Loops do
def n_plus_one_half([]), do: IO.puts ""
def n_plus_one_half([x]), do: IO.puts x
def n_plus_one_half([h|t]) do
IO.write "#{h}, "
n_plus_one_half(t)
end
end
Enum.to_list(1..10) |> Loops.n_plus_one_half |
http://rosettacode.org/wiki/Loops/Nested | Loops/Nested | Show a nested loop which searches a two-dimensional array filled with random numbers uniformly distributed over
[
1
,
…
,
20
]
{\displaystyle [1,\ldots ,20]}
.
The loops iterate rows and columns of the array printing the elements until the value
20
{\displaystyle 20}
is met.
Specifically, this task also shows how to break out of nested loops.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Dyalect | Dyalect | let array = [[2, 12, 10, 4], [18, 11, 20, 2]]
for row in array {
break when {
for element in row {
print("\(element)")
if element == 20 {
break true
}
}
}
}
print("*Done") |
http://rosettacode.org/wiki/Loops/Nested | Loops/Nested | Show a nested loop which searches a two-dimensional array filled with random numbers uniformly distributed over
[
1
,
…
,
20
]
{\displaystyle [1,\ldots ,20]}
.
The loops iterate rows and columns of the array printing the elements until the value
20
{\displaystyle 20}
is met.
Specifically, this task also shows how to break out of nested loops.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #E | E | def array := accum [] for i in 1..5 { _.with(accum [] for i in 1..5 { _.with(entropy.nextInt(20) + 1) }) }
escape done {
for row in array {
for x in row {
print(`$x$\t`)
if (x == 20) {
done()
}
}
println()
}
}
println("done.") |
http://rosettacode.org/wiki/Loops/Foreach | Loops/Foreach | Loop through and print each element in a collection in order.
Use your language's "for each" loop if it has one, otherwise iterate through the collection in order with some other loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Emacs_Lisp | Emacs Lisp | (dolist (x '(1 2 3 4))
(message "x=%d" x)) |
http://rosettacode.org/wiki/Loops/Foreach | Loops/Foreach | Loop through and print each element in a collection in order.
Use your language's "for each" loop if it has one, otherwise iterate through the collection in order with some other loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Erlang | Erlang | io:format("~p~n",[Collection]). |
http://rosettacode.org/wiki/Luhn_test_of_credit_card_numbers | Luhn test of credit card numbers | The Luhn test is used by some credit card companies to distinguish valid credit card numbers from what could be a random selection of digits.
Those companies using credit card numbers that can be validated by the Luhn test have numbers that pass the following test:
Reverse the order of the digits in the number.
Take the first, third, ... and every other odd digit in the reversed digits and sum them to form the partial sum s1
Taking the second, fourth ... and every other even digit in the reversed digits:
Multiply each digit by two and sum the digits if the answer is greater than nine to form partial sums for the even digits
Sum the partial sums of the even digits to form s2
If s1 + s2 ends in zero then the original number is in the form of a valid credit card number as verified by the Luhn test.
For example, if the trial number is 49927398716:
Reverse the digits:
61789372994
Sum the odd digits:
6 + 7 + 9 + 7 + 9 + 4 = 42 = s1
The even digits:
1, 8, 3, 2, 9
Two times each even digit:
2, 16, 6, 4, 18
Sum the digits of each multiplication:
2, 7, 6, 4, 9
Sum the last:
2 + 7 + 6 + 4 + 9 = 28 = s2
s1 + s2 = 70 which ends in zero which means that 49927398716 passes the Luhn test
Task
Write a function/method/procedure/subroutine that will validate a number with the Luhn test, and
use it to validate the following numbers:
49927398716
49927398717
1234567812345678
1234567812345670
Related tasks
SEDOL
ISIN
| #Ceylon | Ceylon | shared void run() {
value numbers = "49927398716
49927398717
1234567812345678
1234567812345670";
for(number in numbers.lines) {
print("``number`` passes? ``luhn(number)``");
}
}
shared Boolean luhn(String number) {
value digits = number
.reversed
.map(Character.string)
.map(Integer.parse)
.narrow<Integer>();
value s1 = sum { 0, *digits.by(2) };
value s2 = sum {
0,
*digits
.skip(1)
.by(2)
.map(curry(times<Integer>)(2))
.map((Integer element) => element / 10 + element % 10)
};
return (s1 + s2) % 10 == 0;
} |
http://rosettacode.org/wiki/Lucas-Lehmer_test | Lucas-Lehmer test | Lucas-Lehmer Test:
for
p
{\displaystyle p}
an odd prime, the Mersenne number
2
p
−
1
{\displaystyle 2^{p}-1}
is prime if and only if
2
p
−
1
{\displaystyle 2^{p}-1}
divides
S
(
p
−
1
)
{\displaystyle S(p-1)}
where
S
(
n
+
1
)
=
(
S
(
n
)
)
2
−
2
{\displaystyle S(n+1)=(S(n))^{2}-2}
, and
S
(
1
)
=
4
{\displaystyle S(1)=4}
.
Task
Calculate all Mersenne primes up to the implementation's
maximum precision, or the 47th Mersenne prime (whichever comes first).
| #HicEst | HicEst | s = 0
DO exponent = 2, 31
IF(exponent > 2) s = 4
n = 2^exponent - 1
DO i = 1, exponent-2
s = MOD(s*s - 2, n)
ENDDO
IF(s == 0) WRITE(Messagebox) 'M', exponent, ' is prime;', n
ENDDO
END |
http://rosettacode.org/wiki/LZW_compression | LZW compression | The Lempel-Ziv-Welch (LZW) algorithm provides loss-less data compression.
You can read a complete description of it in the Wikipedia article on the subject. It was patented, but it entered the public domain in 2004.
| #OCaml | OCaml | #directory "+extlib" (* or maybe "+site-lib/extlib/" *)
#load "extLib.cma"
open ExtString
(** compress a string to a list of output symbols *)
let compress ~uncompressed =
(* build the dictionary *)
let dict_size = 256 in
let dictionary = Hashtbl.create 397 in
for i=0 to 255 do
let str = String.make 1 (char_of_int i) in
Hashtbl.add dictionary str i
done;
let f = (fun (w, dict_size, result) c ->
let c = String.make 1 c in
let wc = w ^ c in
if Hashtbl.mem dictionary wc then
(wc, dict_size, result)
else
begin
(* add wc to the dictionary *)
Hashtbl.add dictionary wc dict_size;
let this = Hashtbl.find dictionary w in
(c, dict_size + 1, this::result)
end
) in
let w, _, result =
String.fold_left f ("", dict_size, []) uncompressed
in
(* output the code for w *)
let result =
if w = ""
then result
else (Hashtbl.find dictionary w) :: result
in
(List.rev result)
;;
exception ValueError of string
(** decompress a list of output symbols to a string *)
let decompress ~compressed =
(* build the dictionary *)
let dict_size = 256 in
let dictionary = Hashtbl.create 397 in
for i=0 to pred dict_size do
let str = String.make 1 (char_of_int i) in
Hashtbl.add dictionary i str
done;
let w, compressed =
match compressed with
| hd::tl -> (String.make 1 (char_of_int hd)), tl
| [] -> failwith "empty input"
in
let result = [w] in
let result, _, _ =
List.fold_left (fun (result, w, dict_size) k ->
let entry =
if Hashtbl.mem dictionary k then
Hashtbl.find dictionary k
else if k = Hashtbl.length dictionary then
w ^ (String.make 1 w.[0])
else
raise(ValueError(Printf.sprintf "Bad compressed k: %d" k))
in
let result = entry :: result in
(* add (w ^ entry.[0]) to the dictionary *)
Hashtbl.add dictionary dict_size (w ^ (String.make 1 entry.[0]));
(result, entry, dict_size + 1)
) (result, w, dict_size) compressed
in
(List.rev result)
;; |
http://rosettacode.org/wiki/LU_decomposition | LU decomposition | Every square matrix
A
{\displaystyle A}
can be decomposed into a product of a lower triangular matrix
L
{\displaystyle L}
and a upper triangular matrix
U
{\displaystyle U}
,
as described in LU decomposition.
A
=
L
U
{\displaystyle A=LU}
It is a modified form of Gaussian elimination.
While the Cholesky decomposition only works for symmetric,
positive definite matrices, the more general LU decomposition
works for any square matrix.
There are several algorithms for calculating L and U.
To derive Crout's algorithm for a 3x3 example,
we have to solve the following system:
A
=
(
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
)
=
(
l
11
0
0
l
21
l
22
0
l
31
l
32
l
33
)
(
u
11
u
12
u
13
0
u
22
u
23
0
0
u
33
)
=
L
U
{\displaystyle A={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\\end{pmatrix}}={\begin{pmatrix}l_{11}&0&0\\l_{21}&l_{22}&0\\l_{31}&l_{32}&l_{33}\\\end{pmatrix}}{\begin{pmatrix}u_{11}&u_{12}&u_{13}\\0&u_{22}&u_{23}\\0&0&u_{33}\end{pmatrix}}=LU}
We now would have to solve 9 equations with 12 unknowns. To make the system uniquely solvable, usually the diagonal elements of
L
{\displaystyle L}
are set to 1
l
11
=
1
{\displaystyle l_{11}=1}
l
22
=
1
{\displaystyle l_{22}=1}
l
33
=
1
{\displaystyle l_{33}=1}
so we get a solvable system of 9 unknowns and 9 equations.
A
=
(
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
)
=
(
1
0
0
l
21
1
0
l
31
l
32
1
)
(
u
11
u
12
u
13
0
u
22
u
23
0
0
u
33
)
=
(
u
11
u
12
u
13
u
11
l
21
u
12
l
21
+
u
22
u
13
l
21
+
u
23
u
11
l
31
u
12
l
31
+
u
22
l
32
u
13
l
31
+
u
23
l
32
+
u
33
)
=
L
U
{\displaystyle A={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\\end{pmatrix}}={\begin{pmatrix}1&0&0\\l_{21}&1&0\\l_{31}&l_{32}&1\\\end{pmatrix}}{\begin{pmatrix}u_{11}&u_{12}&u_{13}\\0&u_{22}&u_{23}\\0&0&u_{33}\end{pmatrix}}={\begin{pmatrix}u_{11}&u_{12}&u_{13}\\u_{11}l_{21}&u_{12}l_{21}+u_{22}&u_{13}l_{21}+u_{23}\\u_{11}l_{31}&u_{12}l_{31}+u_{22}l_{32}&u_{13}l_{31}+u_{23}l_{32}+u_{33}\end{pmatrix}}=LU}
Solving for the other
l
{\displaystyle l}
and
u
{\displaystyle u}
, we get the following equations:
u
11
=
a
11
{\displaystyle u_{11}=a_{11}}
u
12
=
a
12
{\displaystyle u_{12}=a_{12}}
u
13
=
a
13
{\displaystyle u_{13}=a_{13}}
u
22
=
a
22
−
u
12
l
21
{\displaystyle u_{22}=a_{22}-u_{12}l_{21}}
u
23
=
a
23
−
u
13
l
21
{\displaystyle u_{23}=a_{23}-u_{13}l_{21}}
u
33
=
a
33
−
(
u
13
l
31
+
u
23
l
32
)
{\displaystyle u_{33}=a_{33}-(u_{13}l_{31}+u_{23}l_{32})}
and for
l
{\displaystyle l}
:
l
21
=
1
u
11
a
21
{\displaystyle l_{21}={\frac {1}{u_{11}}}a_{21}}
l
31
=
1
u
11
a
31
{\displaystyle l_{31}={\frac {1}{u_{11}}}a_{31}}
l
32
=
1
u
22
(
a
32
−
u
12
l
31
)
{\displaystyle l_{32}={\frac {1}{u_{22}}}(a_{32}-u_{12}l_{31})}
We see that there is a calculation pattern, which can be expressed as the following formulas, first for
U
{\displaystyle U}
u
i
j
=
a
i
j
−
∑
k
=
1
i
−
1
u
k
j
l
i
k
{\displaystyle u_{ij}=a_{ij}-\sum _{k=1}^{i-1}u_{kj}l_{ik}}
and then for
L
{\displaystyle L}
l
i
j
=
1
u
j
j
(
a
i
j
−
∑
k
=
1
j
−
1
u
k
j
l
i
k
)
{\displaystyle l_{ij}={\frac {1}{u_{jj}}}(a_{ij}-\sum _{k=1}^{j-1}u_{kj}l_{ik})}
We see in the second formula that to get the
l
i
j
{\displaystyle l_{ij}}
below the diagonal, we have to divide by the diagonal element (pivot)
u
j
j
{\displaystyle u_{jj}}
, so we get problems when
u
j
j
{\displaystyle u_{jj}}
is either 0 or very small, which leads to numerical instability.
The solution to this problem is pivoting
A
{\displaystyle A}
, which means rearranging the rows of
A
{\displaystyle A}
, prior to the
L
U
{\displaystyle LU}
decomposition, in a way that the largest element of each column gets onto the diagonal of
A
{\displaystyle A}
. Rearranging the rows means to multiply
A
{\displaystyle A}
by a permutation matrix
P
{\displaystyle P}
:
P
A
⇒
A
′
{\displaystyle PA\Rightarrow A'}
Example:
(
0
1
1
0
)
(
1
4
2
3
)
⇒
(
2
3
1
4
)
{\displaystyle {\begin{pmatrix}0&1\\1&0\end{pmatrix}}{\begin{pmatrix}1&4\\2&3\end{pmatrix}}\Rightarrow {\begin{pmatrix}2&3\\1&4\end{pmatrix}}}
The decomposition algorithm is then applied on the rearranged matrix so that
P
A
=
L
U
{\displaystyle PA=LU}
Task description
The task is to implement a routine which will take a square nxn matrix
A
{\displaystyle A}
and return a lower triangular matrix
L
{\displaystyle L}
, a upper triangular matrix
U
{\displaystyle U}
and a permutation matrix
P
{\displaystyle P}
,
so that the above equation is fulfilled.
You should then test it on the following two examples and include your output.
Example 1
A
1 3 5
2 4 7
1 1 0
L
1.00000 0.00000 0.00000
0.50000 1.00000 0.00000
0.50000 -1.00000 1.00000
U
2.00000 4.00000 7.00000
0.00000 1.00000 1.50000
0.00000 0.00000 -2.00000
P
0 1 0
1 0 0
0 0 1
Example 2
A
11 9 24 2
1 5 2 6
3 17 18 1
2 5 7 1
L
1.00000 0.00000 0.00000 0.00000
0.27273 1.00000 0.00000 0.00000
0.09091 0.28750 1.00000 0.00000
0.18182 0.23125 0.00360 1.00000
U
11.00000 9.00000 24.00000 2.00000
0.00000 14.54545 11.45455 0.45455
0.00000 0.00000 -3.47500 5.68750
0.00000 0.00000 0.00000 0.51079
P
1 0 0 0
0 0 1 0
0 1 0 0
0 0 0 1
| #Rust | Rust |
#![allow(non_snake_case)]
use ndarray::{Array, Axis, Array2, arr2, Zip, NdFloat, s};
fn main() {
println!("Example 1:");
let A: Array2<f64> = arr2(&[
[1.0, 3.0, 5.0],
[2.0, 4.0, 7.0],
[1.0, 1.0, 0.0],
]);
println!("A \n {}", A);
let (L, U, P) = lu_decomp(A);
println!("L \n {}", L);
println!("U \n {}", U);
println!("P \n {}", P);
println!("\nExample 2:");
let A: Array2<f64> = arr2(&[
[11.0, 9.0, 24.0, 2.0],
[1.0, 5.0, 2.0, 6.0],
[3.0, 17.0, 18.0, 1.0],
[2.0, 5.0, 7.0, 1.0],
]);
println!("A \n {}", A);
let (L, U, P) = lu_decomp(A);
println!("L \n {}", L);
println!("U \n {}", U);
println!("P \n {}", P);
}
fn pivot<T>(A: &Array2<T>) -> Array2<T>
where T: NdFloat {
let matrix_dimension = A.rows();
let mut P: Array2<T> = Array::eye(matrix_dimension);
for (i, column) in A.axis_iter(Axis(1)).enumerate() {
// find idx of maximum value in column i
let mut max_pos = i;
for j in i..matrix_dimension {
if column[max_pos].abs() < column[j].abs() {
max_pos = j;
}
}
// swap rows of P if necessary
if max_pos != i {
swap_rows(&mut P, i, max_pos);
}
}
P
}
fn swap_rows<T>(A: &mut Array2<T>, idx_row1: usize, idx_row2: usize)
where T: NdFloat {
// to swap rows, get two ArrayViewMuts for the corresponding rows
// and apply swap elementwise using ndarray::Zip
let (.., mut matrix_rest) = A.view_mut().split_at(Axis(0), idx_row1);
let (row0, mut matrix_rest) = matrix_rest.view_mut().split_at(Axis(0), 1);
let (_matrix_helper, mut matrix_rest) = matrix_rest.view_mut().split_at(Axis(0), idx_row2 - idx_row1 - 1);
let (row1, ..) = matrix_rest.view_mut().split_at(Axis(0), 1);
Zip::from(row0).and(row1).apply(std::mem::swap);
}
fn lu_decomp<T>(A: Array2<T>) -> (Array2<T>, Array2<T>, Array2<T>)
where T: NdFloat {
let matrix_dimension = A.rows();
assert_eq!(matrix_dimension, A.cols(), "Tried LU decomposition with a non-square matrix.");
let P = pivot(&A);
let pivotized_A = P.dot(&A);
let mut L: Array2<T> = Array::eye(matrix_dimension);
let mut U: Array2<T> = Array::zeros((matrix_dimension, matrix_dimension));
for idx_col in 0..matrix_dimension {
// fill U
for idx_row in 0..idx_col+1 {
U[[idx_row, idx_col]] = pivotized_A[[idx_row, idx_col]] -
U.slice(s![0..idx_row,idx_col]).dot(&L.slice(s![idx_row,0..idx_row]));
}
// fill L
for idx_row in idx_col+1..matrix_dimension {
L[[idx_row, idx_col]] = (pivotized_A[[idx_row, idx_col]] -
U.slice(s![0..idx_col,idx_col]).dot(&L.slice(s![idx_row,0..idx_col]))) /
U[[idx_col, idx_col]];
}
}
(L, U, P)
}
|
http://rosettacode.org/wiki/Mad_Libs | Mad Libs |
This page uses content from Wikipedia. The original article was at Mad Libs. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Mad Libs is a phrasal template word game where one player prompts another for a list of words to substitute for blanks in a story, usually with funny results.
Task;
Write a program to create a Mad Libs like story.
The program should read an arbitrary multiline story from input.
The story will be terminated with a blank line.
Then, find each replacement to be made within the story, ask the user for a word to replace it with, and make all the replacements.
Stop when there are none left and print the final story.
The input should be an arbitrary story in the form:
<name> went for a walk in the park. <he or she>
found a <noun>. <name> decided to take it home.
Given this example, it should then ask for a name, a he or she and a noun (<name> gets replaced both times with the same value).
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 program prompts the user for a template substitutions within a story (MAD LIBS).*/
parse arg iFID . /*allow user to specify the input file.*/
if iFID=='' | iFID=="," then iFID="MAD_LIBS.TXT" /*Not specified? Then use the default.*/
@.= /*assign defaults to some variables. */
$=; do recs=1 while lines(iFID)\==0 /*read the input file until it's done. */
@.recs=linein(iFID); $=$ @.recs /*read a record; and append it to @ */
if @.recs='' then leave /*Read a blank line? Then we're done.*/
end /*recs*/
recs=recs-1 /*adjust for a E─O─F or a blank line.*/
pm= 'please enter a word or phrase to replace: ' /*this is part of the Prompt Message. */
!.=0 /*placeholder for phrases in MAD LIBS.*/
#=0; do forever /*look for templates within the text. */
parse var $ '<' ? ">" $ /*scan for <ααα> stuff in the text.*/
if ?='' then leave /*No ααα ? Then we're all finished.*/
if !.? then iterate /*Already asked? Then keep scanning. */
!.?=1 /*mark this ααα as being "found". */
do until ans\='' /*prompt user for a replacement. */
say '───────────' pm ? /*prompt the user with a prompt message*/
parse pull ans /*PULL obtains the text from console. */
end /*forever*/
#=#+1 /*bump the template counter. */
old.# = '<'?">"; new.# = ans /*assign the "old" name and "new" name.*/
end /*forever*/
say /*display a blank line for a separator.*/
say; say copies('═', 79) /*display a blank line and a fence. */
do m=1 for recs /*display the text, line for line. */
do n=1 for # /*perform substitutions in the text. */
@.m=changestr(old.n, @.m, new.n) /*maybe replace text in @.m haystack.*/
end /*n*/
say @.m /*display the (new) substituted text. */
end /*m*/
say copies('═', 79) /*display a final (output) fence. */
say /*stick a fork in it, we're all done. */ |
http://rosettacode.org/wiki/Loops/Increment_loop_index_within_loop_body | Loops/Increment loop index within loop body | Sometimes, one may need (or want) a loop which
its iterator (the index
variable) is modified within the
loop body in addition to the normal incrementation by the (do) loop structure index.
Goal
Demonstrate the best way to accomplish this.
Task
Write a loop which:
starts the index (variable) at 42
(at iteration time) increments the index by unity
if the index is prime:
displays the count of primes found (so far) and the prime (to the terminal)
increments the index such that the new index is now the (old) index plus that prime
terminates the loop when 42 primes are shown
Extra credit: because of the primes get rather large, use commas
within the displayed primes to ease comprehension.
Show all output here.
Note
Not all programming languages allow the modification of a
loop's index. If that is the case, then use whatever method that
is appropriate or idiomatic for that language. Please add a note
if the loop's index isn't modifiable.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Nanoquery | Nanoquery | limit = 42
def isPrime(n)
if ((n % 2) = 0) or ((n % 3) = 0)
return false
end
d = 5
while (d * d) <= n
if (n % d) = 0
return false
end
d += 2
if (n % d) = 0
return false
end
d += 4
end
return true
end
i = limit
for (n = 0) (n < limit) (i += 1)
if isPrime(i)
n += 1
print format("n = %-2d %,19d\n", n, i)
i += i - 1
end
end |
http://rosettacode.org/wiki/Loops/Increment_loop_index_within_loop_body | Loops/Increment loop index within loop body | Sometimes, one may need (or want) a loop which
its iterator (the index
variable) is modified within the
loop body in addition to the normal incrementation by the (do) loop structure index.
Goal
Demonstrate the best way to accomplish this.
Task
Write a loop which:
starts the index (variable) at 42
(at iteration time) increments the index by unity
if the index is prime:
displays the count of primes found (so far) and the prime (to the terminal)
increments the index such that the new index is now the (old) index plus that prime
terminates the loop when 42 primes are shown
Extra credit: because of the primes get rather large, use commas
within the displayed primes to ease comprehension.
Show all output here.
Note
Not all programming languages allow the modification of a
loop's index. If that is the case, then use whatever method that
is appropriate or idiomatic for that language. Please add a note
if the loop's index isn't modifiable.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #NewLISP | NewLISP |
#! /usr/local/bin/newlisp
(define (prime? n)
(and
(set 'lst (factor n))
(= (length lst) 1)))
(define (thousands_separator i)
(setq i (string i))
(setq len (length i))
(setq i (reverse (explode i)))
(setq o "")
(setq count3 0)
(dolist (x i)
(setq o (string o x))
(inc count3)
(if (and (= 3 count3) (< (+ $idx 1) len))
(begin
(setq o (string o "_"))
(setq count3 0))))
(reverse o))
;- - - Main begins here
(setq i 42)
(setq n 0)
(while (< n 42)
(if (prime? i)
(begin
(inc n)
(println (string "n = " n " -> " (thousands_separator i)))
(setq i (+ i i -1))))
(inc i)
)
(exit)
|
http://rosettacode.org/wiki/Loops/Infinite | Loops/Infinite | Task
Print out SPAM followed by a newline in an infinite loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #CoffeeScript | CoffeeScript | loop
console.log 'SPAM'
|
http://rosettacode.org/wiki/Loops/Infinite | Loops/Infinite | Task
Print out SPAM followed by a newline in an infinite loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #ColdFusion | ColdFusion | <cfloop condition = "true NEQ false">
SPAM
</cfloop> |
http://rosettacode.org/wiki/Loops/With_multiple_ranges | Loops/With multiple ranges | Loops/With multiple ranges
You are encouraged to solve this task according to the task description, using any language you may know.
Some languages allow multiple loop ranges, such as the PL/I example (snippet) below.
/* all variables are DECLARED as integers. */
prod= 1; /*start with a product of unity. */
sum= 0; /* " " " sum " zero. */
x= +5;
y= -5;
z= -2;
one= 1;
three= 3;
seven= 7;
/*(below) ** is exponentiation: 4**3=64 */
do j= -three to 3**3 by three ,
-seven to +seven by x ,
555 to 550 - y ,
22 to -28 by -three ,
1927 to 1939 ,
x to y by z ,
11**x to 11**x + one;
/* ABS(n) = absolute value*/
sum= sum + abs(j); /*add absolute value of J.*/
if abs(prod)<2**27 & j¬=0 then prod=prod*j; /*PROD is small enough & J*/
end; /*not 0, then multiply it.*/
/*SUM and PROD are used for verification of J incrementation.*/
display (' sum= ' || sum); /*display strings to term.*/
display ('prod= ' || prod); /* " " " " */
Task
Simulate/translate the above PL/I program snippet as best as possible in your
language, with particular emphasis on the do loop construct.
The do index must be incremented/decremented in the same order shown.
If feasible, add commas to the two output numbers (being displayed).
Show all output here.
A simple PL/I DO loop (incrementing or decrementing) has the construct of:
DO variable = start_expression {TO ending_expression] {BY increment_expression} ;
---or---
DO variable = start_expression {BY increment_expression} {TO ending_expression] ;
where it is understood that all expressions will have a value. The variable is normally a
scaler variable, but need not be (but for this task, all variables and expressions are declared
to be scaler integers). If the BY expression is omitted, a BY value of unity is used.
All expressions are evaluated before the DO loop is executed, and those values are used
throughout the DO loop execution (even though, for instance, the value of Z may be
changed within the DO loop. This isn't the case here for this task.
A multiple-range DO loop can be constructed by using a comma (,) to separate additional ranges
(the use of multiple TO and/or BY keywords). This is the construct used in this task.
There are other forms of DO loops in PL/I involving the WHILE clause, but those won't be
needed here. DO loops without a TO clause might need a WHILE clause or some other
means of exiting the loop (such as LEAVE, RETURN, SIGNAL, GOTO, or STOP), or some other
(possible error) condition that causes transfer of control outside the DO loop.
Also, in PL/I, the check if the DO loop index value is outside the range is made at the
"head" (start) of the DO loop, so it's possible that the DO loop isn't executed, but
that isn't the case for any of the ranges used in this task.
In the example above, the clause: x to y by z
will cause the variable J to have to following values (in this order): 5 3 1 -1 -3 -5
In the example above, the clause: -seven to +seven by x
will cause the variable J to have to following values (in this order): -7 -2 3
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Smalltalk | Smalltalk | prod := 1.
sum := 0.
x := 5.
y := -5.
z := -2.
one := 1.
three := 3.
seven := 7.
(three negated to: 3**3 by: three ) ,
(seven negated to: seven by: x ) ,
(555 to: 550-y ) ,
(22 to: -28 by: three negated) ,
(1927 to: 1939 ) ,
(x to: y by:z ) ,
(11**x to: 11**x + one )
do:[:j |
sum := sum + j abs.
((prod abs < (2**27)) and:[ j ~= 0 ]) ifTrue:[
prod := prod*j
].
].
Transcript show:' sum = '; showCR:sum.
Transcript show:'prod = '; showCR:prod |
http://rosettacode.org/wiki/Loops/While | Loops/While | Task
Start an integer value at 1024.
Loop while it is greater than zero.
Print the value (with a newline) and divide it by two each time through the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreachbas
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Crack | Crack | i = 1024;
while( i > 0 ) {
cout ` $i\n`;
i = i/2;
} |
http://rosettacode.org/wiki/Loops/While | Loops/While | Task
Start an integer value at 1024.
Loop while it is greater than zero.
Print the value (with a newline) and divide it by two each time through the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreachbas
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Crystal | Crystal | i = 1024
while i > 0
puts i
i //= 2
end |
http://rosettacode.org/wiki/Loops/Downward_for | Loops/Downward for | Task
Write a for loop which writes a countdown from 10 to 0.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Brat | Brat | 10.to 0 { n | p n } |
http://rosettacode.org/wiki/Loops/Downward_for | Loops/Downward for | Task
Write a for loop which writes a countdown from 10 to 0.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #C | C | int i;
for(i = 10; i >= 0; --i)
printf("%d\n",i); |
http://rosettacode.org/wiki/Loops/Do-while | Loops/Do-while | Start with a value at 0. Loop while value mod 6 is not equal to 0.
Each time through the loop, add 1 to the value then print it.
The loop must execute at least once.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
Reference
Do while loop Wikipedia.
| #Asymptote | Asymptote | int i = 0;
do {
++i;
write(" ", i, suffix=none);
} while (i % 6 != 0); |
http://rosettacode.org/wiki/Loops/For | Loops/For | “For” loops are used to make some block of code be iterated a number of times, setting a variable or parameter to a monotonically increasing integer value for each execution of the block of code.
Common extensions of this allow other counting patterns or iterating over abstract structures other than the integers.
Task
Show how two loops may be nested within each other, with the number of iterations performed by the inner for loop being controlled by the outer for loop.
Specifically print out the following pattern by using one for loop nested in another:
*
**
***
****
*****
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
Reference
For loop Wikipedia.
| #ARM_Assembly | ARM Assembly |
/* ARM assembly Raspberry PI */
/* program loop1.s */
/* Constantes */
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
/* Initialized data */
.data
szMessX: .asciz "X"
szCarriageReturn: .asciz "\n"
/* UnInitialized data */
.bss
/* code section */
.text
.global main
main: /* entry of program */
push {fp,lr} /* saves 2 registers */
mov r2,#0 @ counter loop 1
1: @ loop start 1
mov r1,#0 @ counter loop 2
2: @ loop start 2
ldr r0,iAdrszMessX
bl affichageMess
add r1,#1 @ r1 + 1
cmp r1,r2 @ compare r1 r2
ble 2b @ loop label 2 before
ldr r0,iAdrszCarriageReturn
bl affichageMess
add r2,#1 @ r2 + 1
cmp r2,#5 @ for five loop
blt 1b @ loop label 1 before
100: /* standard end of the program */
mov r0, #0 @ return code
pop {fp,lr} @restaur 2 registers
mov r7, #EXIT @ request to exit program
swi 0 @ perform the system call
iAdrszMessX: .int szMessX
iAdrszCarriageReturn: .int szCarriageReturn
/******************************************************************/
/* display text with size calculation */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {fp,lr} /* save registres */
push {r0,r1,r2,r7} /* save others registers */
mov r2,#0 /* counter length */
1: /* loop length calculation */
ldrb r1,[r0,r2] /* read octet start position + index */
cmp r1,#0 /* if 0 its over */
addne r2,r2,#1 /* else add 1 in the length */
bne 1b /* and loop */
/* so here r2 contains the length of the message */
mov r1,r0 /* address message in r1 */
mov r0,#STDOUT /* code to write to the standard output Linux */
mov r7, #WRITE /* code call system "write" */
swi #0 /* call systeme */
pop {r0,r1,r2,r7} /* restaur others registers */
pop {fp,lr} /* restaur des 2 registres */
bx lr /* return */
|
http://rosettacode.org/wiki/Loops/For_with_a_specified_step | Loops/For with a specified step |
Task
Demonstrate a for-loop where the step-value is greater than one.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #bc | bc | for (i = 2; i <= 10; i += 2) {
i
} |
http://rosettacode.org/wiki/Ludic_numbers | Ludic numbers | Ludic numbers are related to prime numbers as they are generated by a sieve quite like the Sieve of Eratosthenes is used to generate prime numbers.
The first ludic number is 1.
To generate succeeding ludic numbers create an array of increasing integers starting from 2.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...
(Loop)
Take the first member of the resultant array as the next ludic number 2.
Remove every 2nd indexed item from the array (including the first).
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...
(Unrolling a few loops...)
Take the first member of the resultant array as the next ludic number 3.
Remove every 3rd indexed item from the array (including the first).
3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 ...
Take the first member of the resultant array as the next ludic number 5.
Remove every 5th indexed item from the array (including the first).
5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 ...
Take the first member of the resultant array as the next ludic number 7.
Remove every 7th indexed item from the array (including the first).
7 11 13 17 23 25 29 31 37 41 43 47 53 55 59 61 67 71 73 77 83 85 89 91 97 ...
...
Take the first member of the current array as the next ludic number L.
Remove every Lth indexed item from the array (including the first).
...
Task
Generate and show here the first 25 ludic numbers.
How many ludic numbers are there less than or equal to 1000?
Show the 2000..2005th ludic numbers.
Stretch goal
Show all triplets of ludic numbers < 250.
A triplet is any three numbers
x
,
{\displaystyle x,}
x
+
2
,
{\displaystyle x+2,}
x
+
6
{\displaystyle x+6}
where all three numbers are also ludic numbers.
| #Ruby | Ruby | def ludic(nmax=100000)
Enumerator.new do |y|
y << 1
ary = *2..nmax
until ary.empty?
y << (n = ary.first)
(0...ary.size).step(n){|i| ary[i] = nil}
ary.compact!
end
end
end
puts "First 25 Ludic numbers:", ludic.first(25).to_s
puts "Ludics below 1000:", ludic(1000).count
puts "Ludic numbers 2000 to 2005:", ludic.first(2005).last(6).to_s
ludics = ludic(250).to_a
puts "Ludic triples below 250:",
ludics.select{|x| ludics.include?(x+2) and ludics.include?(x+6)}.map{|x| [x, x+2, x+6]}.to_s |
http://rosettacode.org/wiki/Loops/N_plus_one_half | Loops/N plus one half | Quite often one needs loops which, in the last iteration, execute only part of the loop body.
Goal
Demonstrate the best way to do this.
Task
Write a loop which writes the comma-separated list
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
using separate output statements for the number
and the comma from within the body of the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Erlang | Erlang | %% Implemented by Arjun Sunel
-module(loop).
-export([main/0]).
main() ->
for_loop(1).
for_loop(N) ->
if N < 10 ->
io:format("~p, ",[N] ),
for_loop(N+1);
true ->
io:format("~p\n",[N])
end.
|
http://rosettacode.org/wiki/Loops/N_plus_one_half | Loops/N plus one half | Quite often one needs loops which, in the last iteration, execute only part of the loop body.
Goal
Demonstrate the best way to do this.
Task
Write a loop which writes the comma-separated list
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
using separate output statements for the number
and the comma from within the body of the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #ERRE | ERRE |
FOR I=1 TO 10 DO
PRINT(I;)
EXIT IF I=10
PRINT(", ";)
END FOR
|
http://rosettacode.org/wiki/Loops/Nested | Loops/Nested | Show a nested loop which searches a two-dimensional array filled with random numbers uniformly distributed over
[
1
,
…
,
20
]
{\displaystyle [1,\ldots ,20]}
.
The loops iterate rows and columns of the array printing the elements until the value
20
{\displaystyle 20}
is met.
Specifically, this task also shows how to break out of nested loops.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #EchoLisp | EchoLisp |
(lib 'math) ;; for 2D-arrays
(define array (build-array 42 42 (lambda(i j) (1+ (random 20)))))
→ array
;;
(for* ((row array) (aij row)) (write aij) #:break (= aij 20))
→ 9 8 11 1 14 11 1 9 16 1 10 5 5 6 5 4 13 17 14 13 6 10 16 4 8 5 1 17 16 19 4 6 18 1 15 3 4 13 19
6 12 5 5 17 19 16 3 7 2 15 16 14 16 16 19 18 14 16 6 18 14 17 20
|
http://rosettacode.org/wiki/Loops/Foreach | Loops/Foreach | Loop through and print each element in a collection in order.
Use your language's "for each" loop if it has one, otherwise iterate through the collection in order with some other loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #ERRE | ERRE |
FOR INDEX$=("The","quick","brown","fox","jumps","over","the","lazy","dog.") DO
PRINT(INDEX$;" ";)
END FOR
PRINT
|
http://rosettacode.org/wiki/Loops/Foreach | Loops/Foreach | Loop through and print each element in a collection in order.
Use your language's "for each" loop if it has one, otherwise iterate through the collection in order with some other loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Euphoria | Euphoria |
include std/console.e
sequence s = {-2,-1,0,1,2} --print elements of a numerical list
for i = 1 to length(s) do
? s[i]
end for
puts(1,'\n')
s = {"Name","Date","Field1","Field2"} -- print elements of a list of 'strings'
for i = 1 to length(s) do
printf(1,"%s\n",{s[i]})
end for
puts(1,'\n')
for i = 1 to length(s) do -- print subelements of elements of a list of 'strings'
for j = 1 to length(s[i]) do
printf(1,"%s\n",s[i][j])
end for
puts(1,'\n')
end for
if getc(0) then end if
|
http://rosettacode.org/wiki/Luhn_test_of_credit_card_numbers | Luhn test of credit card numbers | The Luhn test is used by some credit card companies to distinguish valid credit card numbers from what could be a random selection of digits.
Those companies using credit card numbers that can be validated by the Luhn test have numbers that pass the following test:
Reverse the order of the digits in the number.
Take the first, third, ... and every other odd digit in the reversed digits and sum them to form the partial sum s1
Taking the second, fourth ... and every other even digit in the reversed digits:
Multiply each digit by two and sum the digits if the answer is greater than nine to form partial sums for the even digits
Sum the partial sums of the even digits to form s2
If s1 + s2 ends in zero then the original number is in the form of a valid credit card number as verified by the Luhn test.
For example, if the trial number is 49927398716:
Reverse the digits:
61789372994
Sum the odd digits:
6 + 7 + 9 + 7 + 9 + 4 = 42 = s1
The even digits:
1, 8, 3, 2, 9
Two times each even digit:
2, 16, 6, 4, 18
Sum the digits of each multiplication:
2, 7, 6, 4, 9
Sum the last:
2 + 7 + 6 + 4 + 9 = 28 = s2
s1 + s2 = 70 which ends in zero which means that 49927398716 passes the Luhn test
Task
Write a function/method/procedure/subroutine that will validate a number with the Luhn test, and
use it to validate the following numbers:
49927398716
49927398717
1234567812345678
1234567812345670
Related tasks
SEDOL
ISIN
| #Clojure | Clojure | (defn luhn? [cc]
(let [factors (cycle [1 2])
numbers (map #(Character/digit % 10) cc)
sum (reduce + (map #(+ (quot % 10) (mod % 10))
(map * (reverse numbers) factors)))]
(zero? (mod sum 10))))
(doseq [n ["49927398716" "49927398717" "1234567812345678" "1234567812345670"]]
(println (luhn? n))) |
http://rosettacode.org/wiki/Lucas-Lehmer_test | Lucas-Lehmer test | Lucas-Lehmer Test:
for
p
{\displaystyle p}
an odd prime, the Mersenne number
2
p
−
1
{\displaystyle 2^{p}-1}
is prime if and only if
2
p
−
1
{\displaystyle 2^{p}-1}
divides
S
(
p
−
1
)
{\displaystyle S(p-1)}
where
S
(
n
+
1
)
=
(
S
(
n
)
)
2
−
2
{\displaystyle S(n+1)=(S(n))^{2}-2}
, and
S
(
1
)
=
4
{\displaystyle S(1)=4}
.
Task
Calculate all Mersenne primes up to the implementation's
maximum precision, or the 47th Mersenne prime (whichever comes first).
| #J | J | import java.math.BigInteger;
public class Mersenne
{
public static boolean isPrime(int p) {
if (p == 2)
return true;
else if (p <= 1 || p % 2 == 0)
return false;
else {
int to = (int)Math.sqrt(p);
for (int i = 3; i <= to; i += 2)
if (p % i == 0)
return false;
return true;
}
}
public static boolean isMersennePrime(int p) {
if (p == 2)
return true;
else {
BigInteger m_p = BigInteger.ONE.shiftLeft(p).subtract(BigInteger.ONE);
BigInteger s = BigInteger.valueOf(4);
for (int i = 3; i <= p; i++)
s = s.multiply(s).subtract(BigInteger.valueOf(2)).mod(m_p);
return s.equals(BigInteger.ZERO);
}
}
// an arbitrary upper bound can be given as an argument
public static void main(String[] args) {
int upb;
if (args.length == 0)
upb = 500;
else
upb = Integer.parseInt(args[0]);
System.out.print(" Finding Mersenne primes in M[2.." + upb + "]:\nM2 ");
for (int p = 3; p <= upb; p += 2)
if (isPrime(p) && isMersennePrime(p))
System.out.print(" M" + p);
System.out.println();
}
} |
http://rosettacode.org/wiki/LZW_compression | LZW compression | The Lempel-Ziv-Welch (LZW) algorithm provides loss-less data compression.
You can read a complete description of it in the Wikipedia article on the subject. It was patented, but it entered the public domain in 2004.
| #Ol | Ol |
(define (compress str)
(let loop ((dc (fold (lambda (f x) ; dictionary (simplest, not optimized), with reversed codes
(cons (list x) (cons x f)))
'() (iota 256)))
(w '()) ; output sequence (reversed)
(s 256) ; maximal dictionary code value + 1
(x '()) ; current sequence
(r (str-iter str))); input stream
(cond
((null? r)
(reverse (cons (cadr (member x dc)) w)))
((pair? r)
(let ((xy (cons (car r) x)))
(if (member xy dc)
(loop dc w s xy (cdr r))
(loop (cons xy (cons s dc)) ; update dictionary with xy . s
(cons (cadr (member x dc)) w) ; add code to output stream
(+ s 1) ; increase code
(list (car r)) ; new current sequence
(cdr r))))) ; next input
(else
(loop dc w s x (r)))))
)
(print (compress "TOBEORNOTTOBEORTOBEORNOT")) ; => (84 79 66 69 79 82 78 79 84 256 258 260 265 259 261 263)
|
http://rosettacode.org/wiki/LU_decomposition | LU decomposition | Every square matrix
A
{\displaystyle A}
can be decomposed into a product of a lower triangular matrix
L
{\displaystyle L}
and a upper triangular matrix
U
{\displaystyle U}
,
as described in LU decomposition.
A
=
L
U
{\displaystyle A=LU}
It is a modified form of Gaussian elimination.
While the Cholesky decomposition only works for symmetric,
positive definite matrices, the more general LU decomposition
works for any square matrix.
There are several algorithms for calculating L and U.
To derive Crout's algorithm for a 3x3 example,
we have to solve the following system:
A
=
(
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
)
=
(
l
11
0
0
l
21
l
22
0
l
31
l
32
l
33
)
(
u
11
u
12
u
13
0
u
22
u
23
0
0
u
33
)
=
L
U
{\displaystyle A={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\\end{pmatrix}}={\begin{pmatrix}l_{11}&0&0\\l_{21}&l_{22}&0\\l_{31}&l_{32}&l_{33}\\\end{pmatrix}}{\begin{pmatrix}u_{11}&u_{12}&u_{13}\\0&u_{22}&u_{23}\\0&0&u_{33}\end{pmatrix}}=LU}
We now would have to solve 9 equations with 12 unknowns. To make the system uniquely solvable, usually the diagonal elements of
L
{\displaystyle L}
are set to 1
l
11
=
1
{\displaystyle l_{11}=1}
l
22
=
1
{\displaystyle l_{22}=1}
l
33
=
1
{\displaystyle l_{33}=1}
so we get a solvable system of 9 unknowns and 9 equations.
A
=
(
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
)
=
(
1
0
0
l
21
1
0
l
31
l
32
1
)
(
u
11
u
12
u
13
0
u
22
u
23
0
0
u
33
)
=
(
u
11
u
12
u
13
u
11
l
21
u
12
l
21
+
u
22
u
13
l
21
+
u
23
u
11
l
31
u
12
l
31
+
u
22
l
32
u
13
l
31
+
u
23
l
32
+
u
33
)
=
L
U
{\displaystyle A={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\\end{pmatrix}}={\begin{pmatrix}1&0&0\\l_{21}&1&0\\l_{31}&l_{32}&1\\\end{pmatrix}}{\begin{pmatrix}u_{11}&u_{12}&u_{13}\\0&u_{22}&u_{23}\\0&0&u_{33}\end{pmatrix}}={\begin{pmatrix}u_{11}&u_{12}&u_{13}\\u_{11}l_{21}&u_{12}l_{21}+u_{22}&u_{13}l_{21}+u_{23}\\u_{11}l_{31}&u_{12}l_{31}+u_{22}l_{32}&u_{13}l_{31}+u_{23}l_{32}+u_{33}\end{pmatrix}}=LU}
Solving for the other
l
{\displaystyle l}
and
u
{\displaystyle u}
, we get the following equations:
u
11
=
a
11
{\displaystyle u_{11}=a_{11}}
u
12
=
a
12
{\displaystyle u_{12}=a_{12}}
u
13
=
a
13
{\displaystyle u_{13}=a_{13}}
u
22
=
a
22
−
u
12
l
21
{\displaystyle u_{22}=a_{22}-u_{12}l_{21}}
u
23
=
a
23
−
u
13
l
21
{\displaystyle u_{23}=a_{23}-u_{13}l_{21}}
u
33
=
a
33
−
(
u
13
l
31
+
u
23
l
32
)
{\displaystyle u_{33}=a_{33}-(u_{13}l_{31}+u_{23}l_{32})}
and for
l
{\displaystyle l}
:
l
21
=
1
u
11
a
21
{\displaystyle l_{21}={\frac {1}{u_{11}}}a_{21}}
l
31
=
1
u
11
a
31
{\displaystyle l_{31}={\frac {1}{u_{11}}}a_{31}}
l
32
=
1
u
22
(
a
32
−
u
12
l
31
)
{\displaystyle l_{32}={\frac {1}{u_{22}}}(a_{32}-u_{12}l_{31})}
We see that there is a calculation pattern, which can be expressed as the following formulas, first for
U
{\displaystyle U}
u
i
j
=
a
i
j
−
∑
k
=
1
i
−
1
u
k
j
l
i
k
{\displaystyle u_{ij}=a_{ij}-\sum _{k=1}^{i-1}u_{kj}l_{ik}}
and then for
L
{\displaystyle L}
l
i
j
=
1
u
j
j
(
a
i
j
−
∑
k
=
1
j
−
1
u
k
j
l
i
k
)
{\displaystyle l_{ij}={\frac {1}{u_{jj}}}(a_{ij}-\sum _{k=1}^{j-1}u_{kj}l_{ik})}
We see in the second formula that to get the
l
i
j
{\displaystyle l_{ij}}
below the diagonal, we have to divide by the diagonal element (pivot)
u
j
j
{\displaystyle u_{jj}}
, so we get problems when
u
j
j
{\displaystyle u_{jj}}
is either 0 or very small, which leads to numerical instability.
The solution to this problem is pivoting
A
{\displaystyle A}
, which means rearranging the rows of
A
{\displaystyle A}
, prior to the
L
U
{\displaystyle LU}
decomposition, in a way that the largest element of each column gets onto the diagonal of
A
{\displaystyle A}
. Rearranging the rows means to multiply
A
{\displaystyle A}
by a permutation matrix
P
{\displaystyle P}
:
P
A
⇒
A
′
{\displaystyle PA\Rightarrow A'}
Example:
(
0
1
1
0
)
(
1
4
2
3
)
⇒
(
2
3
1
4
)
{\displaystyle {\begin{pmatrix}0&1\\1&0\end{pmatrix}}{\begin{pmatrix}1&4\\2&3\end{pmatrix}}\Rightarrow {\begin{pmatrix}2&3\\1&4\end{pmatrix}}}
The decomposition algorithm is then applied on the rearranged matrix so that
P
A
=
L
U
{\displaystyle PA=LU}
Task description
The task is to implement a routine which will take a square nxn matrix
A
{\displaystyle A}
and return a lower triangular matrix
L
{\displaystyle L}
, a upper triangular matrix
U
{\displaystyle U}
and a permutation matrix
P
{\displaystyle P}
,
so that the above equation is fulfilled.
You should then test it on the following two examples and include your output.
Example 1
A
1 3 5
2 4 7
1 1 0
L
1.00000 0.00000 0.00000
0.50000 1.00000 0.00000
0.50000 -1.00000 1.00000
U
2.00000 4.00000 7.00000
0.00000 1.00000 1.50000
0.00000 0.00000 -2.00000
P
0 1 0
1 0 0
0 0 1
Example 2
A
11 9 24 2
1 5 2 6
3 17 18 1
2 5 7 1
L
1.00000 0.00000 0.00000 0.00000
0.27273 1.00000 0.00000 0.00000
0.09091 0.28750 1.00000 0.00000
0.18182 0.23125 0.00360 1.00000
U
11.00000 9.00000 24.00000 2.00000
0.00000 14.54545 11.45455 0.45455
0.00000 0.00000 -3.47500 5.68750
0.00000 0.00000 0.00000 0.51079
P
1 0 0 0
0 0 1 0
0 1 0 0
0 0 0 1
| #Sidef | Sidef | func is_square(m) { m.all { .len == m.len } }
func matrix_zero(n, m=n) { m.of { n.of(0) } }
func matrix_ident(n) { n.of {|i| n.of {|j| i==j ? 1 : 0 } } }
func pivotize(m) {
var size = m.len
var id = matrix_ident(size)
for i (^size) {
var max = m[i][i]
var row = i
for j (i .. size-1) {
if (m[j][i] > max) {
max = m[j][i]
row = j
}
}
if (row != i) {
id.swap(row, i)
}
}
return id
}
func mmult(a, b) {
var p = []
for r,c (^a ~X ^b[0]) {
for i (^b) {
p[r][c] := 0 += (a[r][i] * b[i][c])
}
}
return p
}
func lu(a) {
is_square(a) || die "Defined only for square matrices!";
var n = a.len
var P = pivotize(a)
var Aʼ = mmult(P, a)
var L = matrix_ident(n)
var U = matrix_zero(n)
for i,j (^n ~X ^n) {
if (j >= i) {
U[i][j] = (Aʼ[i][j] - ({ U[_][j] * L[i][_] }.map(^i).sum))
} else {
L[i][j] = (Aʼ[i][j] - ({ U[_][j] * L[i][_] }.map(^j).sum))/U[j][j]
}
}
return [P, Aʼ, L, U]
}
func say_it(message, array) {
say "\n#{message}"
array.each { |row|
say row.map{"%7s" % .as_rat}.join(' ')
}
}
var t = [[
%n(1 3 5),
%n(2 4 7),
%n(1 1 0),
],[
%n(11 9 24 2),
%n( 1 5 2 6),
%n( 3 17 18 1),
%n( 2 5 7 1),
]]
for test (t) {
say_it('A Matrix', test);
for a,b (['P Matrix', 'Aʼ Matrix', 'L Matrix', 'U Matrix'] ~Z lu(test)) {
say_it(a, b)
}
} |
http://rosettacode.org/wiki/Mad_Libs | Mad Libs |
This page uses content from Wikipedia. The original article was at Mad Libs. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Mad Libs is a phrasal template word game where one player prompts another for a list of words to substitute for blanks in a story, usually with funny results.
Task;
Write a program to create a Mad Libs like story.
The program should read an arbitrary multiline story from input.
The story will be terminated with a blank line.
Then, find each replacement to be made within the story, ask the user for a word to replace it with, and make all the replacements.
Stop when there are none left and print the final story.
The input should be an arbitrary story in the form:
<name> went for a walk in the park. <he or she>
found a <noun>. <name> decided to take it home.
Given this example, it should then ask for a name, a he or she and a noun (<name> gets replaced both times with the same value).
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 |
temp="<name> went for a walk in the park. <he or she> found a <noun>. <name> decided to take it home."
k = substr(temp,"<")
while k
replace = substr(temp,k,substr(temp,">")-k + 1)
see "replace:" + replace + " with: "
give with
while k
temp = left(temp,k-1) + with + substr(temp,k + len(replace))
k = substr(temp,replace)
end
k = substr(temp,"<")
end
see temp + nl
|
http://rosettacode.org/wiki/Loops/Increment_loop_index_within_loop_body | Loops/Increment loop index within loop body | Sometimes, one may need (or want) a loop which
its iterator (the index
variable) is modified within the
loop body in addition to the normal incrementation by the (do) loop structure index.
Goal
Demonstrate the best way to accomplish this.
Task
Write a loop which:
starts the index (variable) at 42
(at iteration time) increments the index by unity
if the index is prime:
displays the count of primes found (so far) and the prime (to the terminal)
increments the index such that the new index is now the (old) index plus that prime
terminates the loop when 42 primes are shown
Extra credit: because of the primes get rather large, use commas
within the displayed primes to ease comprehension.
Show all output here.
Note
Not all programming languages allow the modification of a
loop's index. If that is the case, then use whatever method that
is appropriate or idiomatic for that language. Please add a note
if the loop's index isn't modifiable.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Nim | Nim |
import strformat
from strutils import insertSep
func isPrime(i: int): bool =
if i == 2 or i == 3: return true
elif i mod 2 == 0 or i mod 3 == 0: return false
var idx = 5
while idx*idx <= i:
if i mod idx == 0: return false
idx.inc 2
if i mod idx == 0: return false
idx.inc 4
result = true
const limit = 42
proc main =
var
i = 42
n = 0
while n < limit:
if i.isPrime:
inc n
echo &"""n {n:>2} = {($i).insertSep(sep=','):>19}"""
i.inc i
continue
inc i
main()
|
http://rosettacode.org/wiki/Loops/Increment_loop_index_within_loop_body | Loops/Increment loop index within loop body | Sometimes, one may need (or want) a loop which
its iterator (the index
variable) is modified within the
loop body in addition to the normal incrementation by the (do) loop structure index.
Goal
Demonstrate the best way to accomplish this.
Task
Write a loop which:
starts the index (variable) at 42
(at iteration time) increments the index by unity
if the index is prime:
displays the count of primes found (so far) and the prime (to the terminal)
increments the index such that the new index is now the (old) index plus that prime
terminates the loop when 42 primes are shown
Extra credit: because of the primes get rather large, use commas
within the displayed primes to ease comprehension.
Show all output here.
Note
Not all programming languages allow the modification of a
loop's index. If that is the case, then use whatever method that
is appropriate or idiomatic for that language. Please add a note
if the loop's index isn't modifiable.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Perl | Perl | use ntheory qw(is_prime);
$i = 42;
while ($n < 42) {
if (is_prime($i)) {
$n++;
printf "%2d %21s\n", $n, commatize($i);
$i += $i - 1;
}
$i++;
}
sub commatize {
(my $s = reverse shift) =~ s/(.{3})/$1,/g;
$s =~ s/,$//;
$s = reverse $s;
} |
http://rosettacode.org/wiki/Loops/Infinite | Loops/Infinite | Task
Print out SPAM followed by a newline in an infinite loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Comal | Comal | LOOP
PRINT "SPAM"
ENDLOOP |
http://rosettacode.org/wiki/Loops/Infinite | Loops/Infinite | Task
Print out SPAM followed by a newline in an infinite loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #Common_Lisp | Common Lisp | (loop (write-line "SPAM")) |
http://rosettacode.org/wiki/Loops/With_multiple_ranges | Loops/With multiple ranges | Loops/With multiple ranges
You are encouraged to solve this task according to the task description, using any language you may know.
Some languages allow multiple loop ranges, such as the PL/I example (snippet) below.
/* all variables are DECLARED as integers. */
prod= 1; /*start with a product of unity. */
sum= 0; /* " " " sum " zero. */
x= +5;
y= -5;
z= -2;
one= 1;
three= 3;
seven= 7;
/*(below) ** is exponentiation: 4**3=64 */
do j= -three to 3**3 by three ,
-seven to +seven by x ,
555 to 550 - y ,
22 to -28 by -three ,
1927 to 1939 ,
x to y by z ,
11**x to 11**x + one;
/* ABS(n) = absolute value*/
sum= sum + abs(j); /*add absolute value of J.*/
if abs(prod)<2**27 & j¬=0 then prod=prod*j; /*PROD is small enough & J*/
end; /*not 0, then multiply it.*/
/*SUM and PROD are used for verification of J incrementation.*/
display (' sum= ' || sum); /*display strings to term.*/
display ('prod= ' || prod); /* " " " " */
Task
Simulate/translate the above PL/I program snippet as best as possible in your
language, with particular emphasis on the do loop construct.
The do index must be incremented/decremented in the same order shown.
If feasible, add commas to the two output numbers (being displayed).
Show all output here.
A simple PL/I DO loop (incrementing or decrementing) has the construct of:
DO variable = start_expression {TO ending_expression] {BY increment_expression} ;
---or---
DO variable = start_expression {BY increment_expression} {TO ending_expression] ;
where it is understood that all expressions will have a value. The variable is normally a
scaler variable, but need not be (but for this task, all variables and expressions are declared
to be scaler integers). If the BY expression is omitted, a BY value of unity is used.
All expressions are evaluated before the DO loop is executed, and those values are used
throughout the DO loop execution (even though, for instance, the value of Z may be
changed within the DO loop. This isn't the case here for this task.
A multiple-range DO loop can be constructed by using a comma (,) to separate additional ranges
(the use of multiple TO and/or BY keywords). This is the construct used in this task.
There are other forms of DO loops in PL/I involving the WHILE clause, but those won't be
needed here. DO loops without a TO clause might need a WHILE clause or some other
means of exiting the loop (such as LEAVE, RETURN, SIGNAL, GOTO, or STOP), or some other
(possible error) condition that causes transfer of control outside the DO loop.
Also, in PL/I, the check if the DO loop index value is outside the range is made at the
"head" (start) of the DO loop, so it's possible that the DO loop isn't executed, but
that isn't the case for any of the ranges used in this task.
In the example above, the clause: x to y by z
will cause the variable J to have to following values (in this order): 5 3 1 -1 -3 -5
In the example above, the clause: -seven to +seven by x
will cause the variable J to have to following values (in this order): -7 -2 3
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreach
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #True_BASIC | True BASIC |
SUB process(x)
LET sum = sum + ABS(x)
IF ABS(prod) < (2 ^ 27) AND x <> 0 THEN LET prod = prod * x
END SUB
LET prod = 1
LET sum = 0
LET x = 5
LET y = -5
LET z = -2
LET one = 1
LET three = 3
LET seven = 7
FOR j = -three TO (3 ^ 3) STEP three
CALL process(j)
NEXT j
FOR j = -seven TO seven STEP x
CALL process(j)
NEXT j
FOR j = 555 TO 550 - y
CALL process(j)
NEXT j
FOR j = 22 TO -28 STEP -three
CALL process(j)
NEXT j
FOR j = 1927 TO 1939
CALL process(j)
NEXT j
FOR j = x TO y STEP z
CALL process(j)
NEXT j
FOR j = (11 ^ x) TO (11 ^ x) + one
CALL process(j)
NEXT j
PRINT " sum= "; sum
PRINT "prod= "; prod
END
|
http://rosettacode.org/wiki/Loops/While | Loops/While | Task
Start an integer value at 1024.
Loop while it is greater than zero.
Print the value (with a newline) and divide it by two each time through the loop.
Related tasks
Loop over multiple arrays simultaneously
Loops/Break
Loops/Continue
Loops/Do-while
Loops/Downward for
Loops/For
Loops/For with a specified step
Loops/Foreachbas
Loops/Increment loop index within loop body
Loops/Infinite
Loops/N plus one half
Loops/Nested
Loops/While
Loops/with multiple ranges
Loops/Wrong ranges
| #D | D | import std.stdio;
void main() {
int i = 1024;
while (i > 0) {
writeln(i);
i >>= 1;
}
} |
Subsets and Splits
Select Specific Languages Codes
Retrieves specific programming language names and codes from training data, providing basic filtering but limited analytical value beyond identifying these particular languages.