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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
#Dao
Dao
i = 1024; while( i > 0 ) i = 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
#C.23
C#
for (int i = 10; i >= 0; i--) { Console.WriteLine(i); }
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.2B.2B
C++
for(int i = 10; i >= 0; --i) std::cout << i << "\n";
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.
#AutoHotkey
AutoHotkey
While mod(A_Index, 6) ;comment:everything but 0 is considered true output = %output%`n%A_Index% MsgBox % output
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.
#Arturo
Arturo
loop 0..5 'x [ loop 0..x 'y [ prints "*" ] print "" ]
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
#Befunge
Befunge
1 >:.55+,v @_^#`9:+2<
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.
#Rust
Rust
  const ARRAY_MAX: usize = 25_000; const LUDIC_MAX: usize = 2100;   /// Calculates and returns the first `LUDIC_MAX` Ludic numbers. /// /// Needs a sufficiently large `ARRAY_MAX`. fn ludic_numbers() -> Vec<usize> { // The first two Ludic numbers let mut numbers = vec![1, 2]; // We start the array with an immediate first removal to reduce memory usage by // collecting only odd numbers. numbers.extend((3..ARRAY_MAX).step_by(2));   // We keep the correct Ludic numbers in place, removing the incorrect ones. for ludic_idx in 2..LUDIC_MAX { let next_ludic = numbers[ludic_idx];   // We remove incorrect numbers by counting the indices after the correct numbers. // We start from zero and keep until we reach the potentially incorrect numbers. // Then we keep only those not divisible by the `next_ludic`. let mut idx = 0; numbers.retain(|_| { let keep = idx <= ludic_idx || (idx - ludic_idx) % next_ludic != 0; idx += 1; keep }); }   numbers }   fn main() { let ludic_numbers = ludic_numbers();   print!("First 25: "); print_n_ludics(&ludic_numbers, 25); println!(); print!("Number of Ludics below 1000: "); print_num_ludics_upto(&ludic_numbers, 1000); println!(); print!("Ludics from 2000 to 2005: "); print_ludics_from_to(&ludic_numbers, 2000, 2005); println!(); println!("Triplets below 250: "); print_triplets_until(&ludic_numbers, 250); }   /// Prints the first `n` Ludic numbers. fn print_n_ludics(x: &[usize], n: usize) { println!("{:?}", &x[..n]); }   /// Calculates how many Ludic numbers are below `max_num`. fn print_num_ludics_upto(x: &[usize], max_num: usize) { let num = x.iter().take_while(|&&i| i < max_num).count(); println!("{}", num); }   /// Prints Ludic numbers between two numbers. fn print_ludics_from_to(x: &[usize], from: usize, to: usize) { println!("{:?}", &x[from - 1..to - 1]); }   /// Calculates triplets until a certain Ludic number. fn triplets_below(ludics: &[usize], limit: usize) -> Vec<(usize, usize, usize)> { ludics .iter() .enumerate() .take_while(|&(_, &num)| num < limit) .filter_map(|(idx, &number)| { let triplet_2 = number + 2; let triplet_3 = number + 6;   // Search for the other two triplet numbers. We know they are larger than // `number` so we can give the searches lower bounds of `idx + 1` and // `idx + 2`. We also know that the `n + 2` number can only ever be two // numbers away from the previous and the `n + 6` number can only be four // away (because we removed some in between). Short circuiting and doing // the check more likely to fail first are also useful. let is_triplet = ludics[idx + 1..idx + 3].binary_search(&triplet_2).is_ok() && ludics[idx + 2..idx + 5].binary_search(&triplet_3).is_ok();   if is_triplet { Some((number, triplet_2, triplet_3)) } else { None } }) .collect() }   /// Prints triplets until a certain Ludic number. fn print_triplets_until(ludics: &[usize], limit: usize) { for (number, triplet_2, triplet_3) in triplets_below(ludics, limit) { println!("{} {} {}", number, triplet_2, triplet_3); } }  
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
#Euphoria
Euphoria
  for i = 1 to 10 do printf(1, "%g", {i}) if i < 10 then puts(1, ", ") end if end for  
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
#F.23
F#
  let rec print (lst : int list) = match lst with | hd :: [] -> printf "%i " hd | hd :: tl -> printf "%i, " hd print tl | [] -> printf "\n"   print [1..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
#Elixir
Elixir
defmodule Loops do def nested do list = Enum.shuffle(1..20) |> Enum.chunk(5) IO.inspect list, char_lists: :as_lists try do nested(list) catch  :find -> IO.puts "done" end end   def nested(list) do Enum.each(list, fn row -> Enum.each(row, fn x -> IO.write "#{x} " if x == 20, do: throw(:find) end) IO.puts "" end) end end   Loops.nested
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
#Erlang
Erlang
  -module( loops_nested ).   -export( [task/0] ).   task() -> Size = 20, Two_dimensional_array = [random_array(Size) || _X <- lists:seq(1, Size)], print_until_found( [], 20, Two_dimensional_array ).       print_until_found( [], N, [Row | T] ) -> print_until_found( print_until_found_row(N, Row), N, T ); print_until_found( _Found, _N, _Two_dimensional_array ) -> io:fwrite( "~n" ).   print_until_found_row( _N, [] ) -> []; print_until_found_row( N, [N | T] ) -> [N | T]; print_until_found_row( N, [H | T] ) -> io:fwrite( "~p ", [H] ), print_until_found_row( N, T ).   random_array( Size ) -> [random:uniform(Size) || _X <- lists:seq(1, Size)].  
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
#F.23
F#
for i in [1 .. 10] do printfn "%d" i   List.iter (fun i -> printfn "%d" i) [1 .. 10]
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
#Factor
Factor
{ 1 2 4 } [ . ] each
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
#CLU
CLU
luhn = proc (num: string) returns (bool) signals (bad_format) total: int := 0 even: bool := true for i: int in int$from_to_by(string$size(num), 1, -1) do digit: int := int$parse(string$c2s(num[i])) resignal bad_format even := ~even if even then digit := 2 * digit if digit >= 10 then digit := digit//10 + 1 end end total := total + digit end return(total // 10 = 0) end luhn   start_up = proc () po: stream := stream$primary_output() tests: sequence[string] := sequence[string]$ ["49927398716", "49927398717", "1234567812345678", "1234567812345670"] for test: string in sequence[string]$elements(tests) do stream$puts(po, test || ": ") if luhn(test) then stream$putl(po, "pass") else stream$putl(po, "fail") end end end start_up
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).
#Java
Java
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.
#Perl
Perl
# Compress a string to a list of output symbols. sub compress { my $uncompressed = shift;   # Build the dictionary. my $dict_size = 256; my %dictionary = map {chr $_ => chr $_} 0..$dict_size-1;   my $w = ""; my @result; foreach my $c (split '', $uncompressed) { my $wc = $w . $c; if (exists $dictionary{$wc}) { $w = $wc; } else { push @result, $dictionary{$w}; # Add wc to the dictionary. $dictionary{$wc} = $dict_size; $dict_size++; $w = $c; } }   # Output the code for w. if ($w) { push @result, $dictionary{$w}; } return @result; }   # Decompress a list of output ks to a string. sub decompress { my @compressed = @_;   # Build the dictionary. my $dict_size = 256; my %dictionary = map {chr $_ => chr $_} 0..$dict_size-1;   my $w = shift @compressed; my $result = $w; foreach my $k (@compressed) { my $entry; if (exists $dictionary{$k}) { $entry = $dictionary{$k}; } elsif ($k == $dict_size) { $entry = $w . substr($w,0,1); } else { die "Bad compressed k: $k"; } $result .= $entry;   # Add w+entry[0] to the dictionary. $dictionary{$dict_size} = $w . substr($entry,0,1); $dict_size++;   $w = $entry; } return $result; }   # How to use: my @compressed = compress('TOBEORNOTTOBEORTOBEORNOT'); print "@compressed\n"; my $decompressed = decompress(@compressed); print "$decompressed\n";
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
#Stata
Stata
mata : lud(a=(1,3,5\2,4,7\1,1,0),l=.,u=.,p=.)   : a 1 2 3 +-------------+ 1 | 1 3 5 | 2 | 2 4 7 | 3 | 1 1 0 | +-------------+   : l 1 2 3 +----------------+ 1 | 1 0 0 | 2 | .5 1 0 | 3 | .5 -1 1 | +----------------+   : u 1 2 3 +-------------------+ 1 | 2 4 7 | 2 | 0 1 1.5 | 3 | 0 0 -2 | +-------------------+   : p 1 +-----+ 1 | 2 | 2 | 1 | 3 | 3 | +-----+
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
#Ruby
Ruby
puts "Enter a story, terminated by an empty line:" story = "" until (line = gets).chomp.empty? story << line end   story.scan(/(?<=[<]).+?(?=[>])/).uniq.each do |var| print "Enter a value for '#{var}': " story.gsub!(/<#{var}>/, gets.chomp) end   puts puts story
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
#Phix
Phix
atom i=42, n=1 while n<=42 do if is_prime(i) then printf(1,"n = %-2d  %,19d\n", {n, i}) n += 1 i += i-1 end if i += 1 end while
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
#Python
Python
def isPrime(n): for x in 2, 3: if not n % x: return n == x d = 5 while d * d <= n: for x in 2, 4: if not n % d: return False d += x return True   i = 42 n = 0 while n < 42: if isPrime(i): n += 1 print('n = {:2} {:20,}'.format(n, i)) i += i - 1 i += 1
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
#Corescript
Corescript
  :top print Spam! goto top  
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
#Cowgol
Cowgol
include "cowgol.coh";   loop print("Spam\n"); end 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
#uBasic.2F4tH
uBasic/4tH
p = 1 ' product s = 0 ' sum   x = 5 y = -5 z = -2   o = 1 ' one t = 3 ' three v = 7 ' seVen   For j = -t To (3 ^ 3) Step t: Proc _Process(j) : Next For j = -v To v Step x: Proc _Process(j) : Next For j = 555 To 550 - y: Proc _Process(j) : Next For j = 22 To -28 Step -t: Proc _Process(j) : Next For j = 1927 To 1939: Proc _Process(j) : Next For j = x To y Step z: Proc _Process(j) : Next For j = (11 ^ x) To (11 ^ x) + o: Proc _Process(j) : Next   Print Using " sum= +###,###"; s Print Using "prod= +###,###,###"; p End   _Process Param (1)   s = s + Abs(a@) If (Abs(p) < (2 ^ 27)) * (a@ # 0) Then p = p * a@ Return
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
#Vala
Vala
const int CHARBIT = 8; long prod = 1; long sum = 0;   long labs(long n) { long mask = n >> ((long)sizeof(long) * CHARBIT - 1); return ((n + mask) ^ mask); }   long lpow(long base_num, long exp) { long result = 1; while (true) { if ((exp & 1) != 0) result *= base_num; exp >>= 1; if (exp == 0) break; base_num *= base_num; } return result; }   void process(long j) { sum += labs(j); if (labs(prod) < (1 << 27) && j != 0) prod *= j; }   void main() { const int x = 5; const int y = -5; const int z = -2; const int one = 1; const int three = 3; const int seven = 11; long p = lpow(11, x);   for (int j = -three; j <= lpow(3, 3); j += three ) process(j); for (int j = -seven; j <= seven; j += x) process(j); for (int j = 555; j <= 550 - y; ++j) process(j); for (int j = 22; j >= -28; j -= three) process(j); for (int j = 1928; j <= 1939; ++j) process(j); for (int j = x; j >= y; j -= -z) process(j); for (long j = p; j <= p + one; ++j) process(j); stdout.printf("sum = %10ld\n", sum); stdout.printf("prod = %10ld\n", 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
#Dc
Dc
[ q ] sQ [ d 0!<Q p 2 / lW x ] sW 1024 lW x
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
#DCL
DCL
$ i = 1024 $Loop: $ IF ( i .LE. 0 ) THEN GOTO LoopEnd $ WRITE sys$output F$FAO( " i = !4UL", i ) ! formatted ASCII output, fixed-width field $ ! Output alternatives: $ ! WRITE sys$output F$STRING( i )  ! explicit integer-to-string conversion $ ! WRITE sys$output i  ! implicit conversion to string/output $ i = i / 2 $ GOTO Loop $LoopEnd:
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
#Ceylon
Ceylon
for (i in 10..0) { print(i); }
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
#Chapel
Chapel
for i in 1..10 by -1 do writeln(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.
#AWK
AWK
BEGIN { val = 0 do { val++ print val } while( val % 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.
#Asymptote
Asymptote
for(int i = 0; i < 6; ++i) { for(int j = 0; j < i; ++j) { write("*", suffix=none); } write(""); }
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
#C
C
int i; for(i = 1; i < 10; i += 2) printf("%d\n", 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.
#Scala
Scala
object Ludic { def main(args: Array[String]): Unit = { println( s"""|First 25 Ludic Numbers: ${ludic.take(25).mkString(", ")} |Ludic Numbers <= 1000: ${ludic.takeWhile(_ <= 1000).size} |2000-2005th Ludic Numbers: ${ludic.slice(1999, 2005).mkString(", ")} |Triplets <= 250: ${triplets.takeWhile(_._3 <= 250).mkString(", ")}""".stripMargin) }   def dropByN[T](lst: LazyList[T], len: Int): LazyList[T] = lst.grouped(len).flatMap(_.init).to(LazyList) def ludic: LazyList[Int] = 1 #:: LazyList.unfold(LazyList.from(2)){case n +: ns => Some((n, dropByN(ns, n)))} def triplets: LazyList[(Int, Int, Int)] = LazyList.from(1).map(n => (n, n + 2, n + 6)).filter{case (a, b, c) => Seq(a, b, c).forall(ludic.takeWhile(_ <= c).contains)} }
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
#Factor
Factor
: print-comma-list ( n -- ) [ [1,b] ] keep '[ [ number>string write ] [ _ = [ ", " write ] unless ] bi ] each 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
#Falcon
Falcon
for value = 1 to 10 formiddle >> value >> ", " end forlast: > value end
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
#ERRE
ERRE
  DIM A%[10,10]  ! in declaration part ............. PRINT(CHR$(12);) !CLS FOR ROW=1 TO 10 DO FOR COL=1 TO 10 DO A%[ROW,COL]=INT(RND(1)*20)+1  ! INT and RND are ERRE predeclared functions  ! RND generates random numbers between 0 and 1 END FOR END FOR   FOR ROW=1 TO 10 DO FOR COL=1 TO 10 DO PRINT(A%[ROW,COL]) EXIT IF A%[ROW,COL]=20 END FOR EXIT IF A%[ROW,COL]=20  ! EXIT breaks the current loop only: you must repeat it,  ! use a boolean variable or a GOTO label statement 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
#Euphoria
Euphoria
sequence a a = rand(repeat(repeat(20, 10), 10))   integer wantExit wantExit = 0   for i = 1 to 10 do for j = 1 to 10 do printf(1, "%g ", {a[i][j]}) if a[i][j] = 20 then wantExit = 1 exit end if end for if wantExit then exit end if end for
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
#Fantom
Fantom
class Main { public static Void main () { Int[] collection := [1, 2, 3, 4, 5] collection.each |Int item| { echo (item) } } }
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
#Fennel
Fennel
(each [k v (ipairs [:apple :banana :orange])] (print k v))
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
#COBOL
COBOL
IDENTIFICATION DIVISION. PROGRAM-ID. LUHNTEST. ENVIRONMENT DIVISION. INPUT-OUTPUT SECTION. data division. WORKING-STORAGE SECTION. 01 inp-card. 03 inp-card-ch pic x(01) occurs 20 times. 01 ws-result pic 9(01). 88 pass-luhn-test value 0.   PROCEDURE DIVISION. move "49927398716" to inp-card perform test-card move "49927398717" to inp-card perform test-card move "1234567812345678" to inp-card perform test-card move "1234567812345670" to inp-card perform test-card stop run . test-card. call "LUHN" using inp-card, ws-result if pass-luhn-test display "input=" inp-card "pass" else display "input=" inp-card "fail" .   END PROGRAM LUHNTEST. IDENTIFICATION DIVISION. PROGRAM-ID. LUHN. ENVIRONMENT DIVISION. INPUT-OUTPUT SECTION. DATA DIVISION. WORKING-STORAGE SECTION. 01 maxlen pic 9(02) comp value 16. 01 inplen pic 9(02) comp value 0. 01 i pic 9(02) comp value 0. 01 j pic 9(02) comp value 0. 01 l pic 9(02) comp value 0. 01 dw pic 9(02) comp value 0. 01 ws-total pic 9(03) comp value 0. 01 ws-prod pic 99. 01 filler redefines ws-prod. 03 ws-prod-tens pic 9. 03 ws-prod-units pic 9. 01 ws-card. 03 filler occurs 16 times depending on maxlen. 05 ws-card-ch pic x(01). 05 ws-card-digit redefines ws-card-ch pic 9(01). LINKAGE SECTION. 01 inp-card. 03 inp-card-ch pic x(01) occurs 20 times. 01 ws-result pic 9(01). 88 pass-luhn-test value 0.   PROCEDURE DIVISION using inp-card, ws-result. perform varying i from 1 by +1 until i > maxlen or inp-card-ch (i) = space end-perform compute l = i - 1 compute inplen = l perform varying j from 1 by +1 until j > inplen if l < 1 move "0" to ws-card-ch (j) else move inp-card-ch (l) to ws-card-ch (j) compute l = l - 1 end-if end-perform move 0 to ws-total perform varying i from 1 by +1 until i > inplen compute dw = 2 - (i - 2 * function integer (i / 2)) compute ws-prod = ws-card-digit (i) * dw compute ws-total = ws-total + ws-prod-tens + ws-prod-units end-perform compute ws-result = ws-total - 10 * function integer (ws-total / 10) goback . END PROGRAM LUHN.
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).
#JavaScript
JavaScript
  ////////// In JavaScript we don't have sqrt for BigInt - so here is implementation function newtonIteration(n, x0) { const x1 = ((n / x0) + x0) >> 1n; if (x0 === x1 || x0 === (x1 - 1n)) { return x0; } return newtonIteration(n, x1); }   function sqrt(value) { if (value < 0n) { throw 'square root of negative numbers is not supported' }   if (value < 2n) { return value; } return newtonIteration(value, 1n); } ////////// End of sqrt implementation   function isPrime(p) { if (p == 2n) { return true; } else if (p <= 1n || p % 2n === 0n) { return false; } else { var to = sqrt(p); for (var i = 3n; i <= to; i += 2n) if (p % i == 0n) { return false; } return true; } }   function isMersennePrime(p) { if (p == 2n) { return true; } else { var m_p = (1n << p) - 1n; var s = 4n; for (var i = 3n; i <= p; i++) { s = (s * s - 2n) % m_p; } return s === 0n; } }   var upb = 5000; var tm = Date.now(); console.log(`Finding Mersenne primes in M[2..${upb}]:`); console.log('M2'); for (var p = 3n; p <= upb; p += 2n){ if (isPrime(p) && isMersennePrime(p)) { console.log("M" + p); } } console.log(`... Took: ${Date.now()-tm} ms`);  
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.
#Phix
Phix
with javascript_semantics function compress(string uncompressed) integer dict = new_dict() sequence result = {} integer dictSize = 255, c string word = "" for i=0 to 255 do setd(""&i,i,dict) end for for i=1 to length(uncompressed) do c = uncompressed[i] if getd_index(word&c,dict) then word &= c else result &= getd(word,dict) dictSize += 1 setd(word&c,dictSize,dict) word = ""&c end if end for if word!="" then result &= getd(word,dict) end if destroy_dict(dict) return result end function function decompress(sequence compressed) integer dict = new_dict() integer dictSize = 255, k, ki string dent = "", result = "", word = "" for i=0 to 255 do setd(i,""&i,dict) end for for i=1 to length(compressed) do k = compressed[i] ki = getd_index(k,dict) if ki then dent = getd_by_index(ki,dict) elsif k=dictSize then dent = word&word[1] else return {NULL,i} end if result &= dent setd(dictSize,word&dent[1],dict) dictSize += 1 word = dent end for destroy_dict(dict) return result end function constant example = "TOBEORNOTTOBEORTOBEORNOT" sequence com = compress(example) pp(com,{pp_IntCh,true,pp_Maxlen,90}) ?decompress(com)
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
#Tcl
Tcl
package require Tcl 8.5 namespace eval matrix { namespace path {::tcl::mathfunc ::tcl::mathop}   # Construct an identity matrix of the given size proc identity {order} { set m [lrepeat $order [lrepeat $order 0]] for {set i 0} {$i < $order} {incr i} { lset m $i $i 1 } return $m }   # Produce the pivot matrix for a given matrix proc pivotize {matrix} { set n [llength $matrix] set p [identity $n] for {set j 0} {$j < $n} {incr j} { set max [lindex $matrix $j $j] set row $j for {set i $j} {$i < $n} {incr i} { if {[lindex $matrix $i $j] > $max} { set max [lindex $matrix $i $j] set row $i } } if {$j != $row} { # Row swap inlined; too trivial to have separate procedure set tmp [lindex $p $j] lset p $j [lindex $p $row] lset p $row $tmp } } return $p }   # Decompose a square matrix A by PA=LU and return L, U and P proc luDecompose {A} { set n [llength $A] set L [lrepeat $n [lrepeat $n 0]] set U $L set P [pivotize $A] set A [multiply $P $A]   for {set j 0} {$j < $n} {incr j} { lset L $j $j 1 for {set i 0} {$i <= $j} {incr i} { lset U $i $j [- [lindex $A $i $j] [SumMul $L $U $i $j $i]] } for {set i $j} {$i < $n} {incr i} { set sum [SumMul $L $U $i $j $j] lset L $i $j [/ [- [lindex $A $i $j] $sum] [lindex $U $j $j]] } }   return [list $L $U $P] }   # Helper that makes inner loop nicer; multiplies column and row, # possibly partially... proc SumMul {A B i j kmax} { set s 0.0 for {set k 0} {$k < $kmax} {incr k} { set s [+ $s [* [lindex $A $i $k] [lindex $B $k $j]]] } return $s } }
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
#Run_BASIC
Run BASIC
temp$="<name> went for a walk in the park. <he or she> found a <noun>. <name> decided to take it home." k = instr(temp$,"<") while k replace$ = mid$(temp$,k,instr(temp$,">")-k + 1) print "Replace:";replace$;" with:"; :input with$ while k temp$ = left$(temp$,k-1) + with$ + mid$(temp$,k + len(replace$)) k = instr(temp$,replace$,k) wend k = instr(temp$,"<") wend print temp$ wait
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
#R
R
i <- 42 primeCount <- 0 while(primeCount < 42) { if(gmp::isprime(i) == 2)#1 means "probably prime" and won't come up for numbers this small, 2 is what we want. { primeCount <- primeCount + 1 extraCredit <- format(i, big.mark=",", scientific = FALSE) cat("Prime count:", paste0(primeCount, ";"), "The prime just found was:", extraCredit, "\n") i <- i + i#This is missing the -1 from the Kotlin solution. There is no need to check i + i (it's even). } i <- i + 1 }
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
#Crystal
Crystal
loop do puts "SPAM" 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
#D
D
import std.stdio;   void main() { while (true) writeln("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
#VBA
VBA
Dim prod As Long, sum As Long Public Sub LoopsWithMultipleRanges() Dim x As Integer, y As Integer, z As Integer, one As Integer, three As Integer, seven As Integer, j As Long prod = 1 sum = 0 x = 5 y = -5 z = -2 one = 1 three = 3 seven = 7 For j = -three To pow(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 = pow(11, x) To pow(11, x) + one: Call process(j): Next j Debug.Print " sum= " & Format(sum, "#,##0") Debug.Print "prod= " & Format(prod, "#,##0") End Sub Private Function pow(x As Long, y As Integer) As Long pow = WorksheetFunction.Power(x, y) End Function Private Sub process(x As Long) sum = sum + Abs(x) If Abs(prod) < pow(2, 27) And x <> 0 Then prod = prod * x End Sub
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
#Delphi
Delphi
var i : Integer; begin i := 1024;   while i > 0 do begin Writeln(i); i := i div 2; end; 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
#Draco
Draco
proc nonrec main() void: word i; i := 1024; while i > 0 do writeln(i); i := i >> 1 od corp
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
#Clipper
Clipper
FOR i := 10 TO 0 STEP -1  ? i NEXT
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
#Clojure
Clojure
(doseq [x (range 10 -1 -1)] (println x))
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.
#Axe
Axe
0→A While 1 A++ Disp A▶Dec,i End!If A^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.
#AutoHotkey
AutoHotkey
Gui, Add, Edit, vOutput r5 w100 -VScroll ; Create an Edit-Control Gui, Show ; Show the window Loop, 5 ; loop 5 times { Loop, %A_Index% ; A_Index contains the Index of the current loop { output .= "*" ; append an "*" to the output var GuiControl, , Output, %Output% ; update the Edit-Control with the new content Sleep, 500 ; wait some(500ms) time, [just to show off] } Output .= (A_Index = 5) ? "" : "`n" ; append a new line to the output if A_Index is not "5" } Return ; End of auto-execution section
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
#C.23
C#
using System;   class Program { static void Main(string[] args) { for (int i = 2; i <= 8; i+= 2) { Console.Write("{0}, ", i); }   Console.WriteLine("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.
#Seed7
Seed7
$ include "seed7_05.s7i";   const func set of integer: ludicNumbers (in integer: n) is func result var set of integer: ludicNumbers is {1}; local var set of integer: sieve is EMPTY_SET; var integer: ludicNumber is 0; var integer: number is 0; var integer: count is 0; begin sieve := {2 .. n}; while sieve <> EMPTY_SET do ludicNumber := min(sieve); incl(ludicNumbers, ludicNumber); count := 0; for number range sieve do if count rem ludicNumber = 0 then excl(sieve, number); end if; incr(count); end for; end while; end func;   const integer: limit is 22000; const set of integer: ludicNumbers is ludicNumbers(limit);   const proc: main is func local var integer: number is 0; var integer: count is 0; begin write("First 25:"); for number range ludicNumbers until count = 25 do write(" " <& number); incr(count); end for; writeln; count := 0; for number range ludicNumbers until number > 1000 do incr(count); end for; writeln("Ludics below 1000: " <& count); write("Ludic 2000 to 2005:"); count := 0; for number range ludicNumbers until count >= 2005 do incr(count); if count >= 2000 then write(" " <& number); end if; end for; writeln; write("Triples below 250:"); for number range ludicNumbers until number > 250 do if number + 2 in ludicNumbers and number + 6 in ludicNumbers then write(" (" <& number <& ", " <& number + 2 <& ", " <& number + 6 <& ")"); end if; end for; writeln; end func;
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
#FALSE
FALSE
1[$9>~][$.", "1+]#.
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
#Fantom
Fantom
  class Main { public static Void main () { for (Int i := 1; i <= 10; i++) { Env.cur.out.writeObj (i) if (i == 10) break Env.cur.out.writeChars (", ") } Env.cur.out.printLine ("") } }  
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
#F.23
F#
  //Nigel Galloway: November 10th., 2017 let n = System.Random() let g = Array2D.init 8 8 (fun _ _ -> 1+n.Next()%20) Array2D.iter (fun n -> printf "%d " n) g; printfn "" g |> Seq.cast<int> |> Seq.takeWhile(fun n->n<20) |> Seq.iter (fun n -> printf "%d " n)  
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
#Forth
Forth
create a 3 , 2 , 1 , : .array ( a len -- ) cells bounds do i @ . cell +loop ; \ 3 2 1
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
#Fortran
Fortran
program main   implicit none   integer :: i character(len=5),dimension(5),parameter :: colors = ['Red ','Green','Blue ','Black','White']   !using a do loop: do i=1,size(colors) write(*,'(A)') colors(i) end do   !this will also print each element: write(*,'(A)') colors   end program main
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
#Comal
Comal
0010 FUNC luhn(s$) CLOSED 0020 total#:=0 0030 even#:=TRUE 0040 FOR i#:=LEN(s$) TO 1 STEP -1 DO 0050 digit#:=VAL(s$(i#)) 0060 even#:=NOT even# 0070 IF even# THEN digit#:=(2*digit#) DIV 10+(2*digit#) MOD 10 0080 total#:+digit# 0090 ENDFOR i# 0100 RETURN total# MOD 10=0 0110 ENDFUNC luhn 0120 // 0130 PROC test(s$) 0140 PRINT s$,": ", 0150 IF luhn(s$) THEN 0160 PRINT "pass" 0170 ELSE 0180 PRINT "fail" 0190 ENDIF 0200 ENDPROC test 0210 // 0220 test("49927398716") 0230 test("49927398717") 0240 test("1234567812345678") 0250 test("1234567812345670") 0260 END
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).
#jq
jq
# To take advantage of gojq's arbitrary-precision integer arithmetic: def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);   def is_prime: . as $n | if ($n < 2) then false elif ($n % 2 == 0) then $n == 2 elif ($n % 3 == 0) then $n == 3 elif ($n % 5 == 0) then $n == 5 elif ($n % 7 == 0) then $n == 7 elif ($n % 11 == 0) then $n == 11 elif ($n % 13 == 0) then $n == 13 elif ($n % 17 == 0) then $n == 17 elif ($n % 19 == 0) then $n == 19 else {i:23} | until( (.i * .i) > $n or ($n % .i == 0); .i += 2) | .i * .i > $n end;   # using the Lucac-Lehmer test for p>2, emit a stream of the form # Mp:l where p is a Mersenne_prime and l is (p|tostring|length). # 2^1 - 1 = 2 so we begin with M2:1. def mersenne_primes: "M2:1", (range(3;infinite;2) | . as $i | select(is_prime) | . as $p | ((2 | power($p)) - 1) as $mp | select(0 == (reduce range(3; $p + 1) as $_ (4; (power(2) -2) % $mp) ) ) | "M\($i):\($mp|tostring|length)" );   mersenne_primes
http://rosettacode.org/wiki/LZW_compression
LZW compression
The Lempel-Ziv-Welch (LZW) algorithm provides loss-less data compression. You can read a complete description of it in the   Wikipedia article   on the subject.   It was patented, but it entered the public domain in 2004.
#PHP
PHP
class LZW { function compress($unc) { $i;$c;$wc; $w = ""; $dictionary = array(); $result = array(); $dictSize = 256; for ($i = 0; $i < 256; $i += 1) { $dictionary[chr($i)] = $i; } for ($i = 0; $i < strlen($unc); $i++) { $c = $unc[$i]; $wc = $w.$c; if (array_key_exists($w.$c, $dictionary)) { $w = $w.$c; } else { array_push($result,$dictionary[$w]); $dictionary[$wc] = $dictSize++; $w = (string)$c; } } if ($w !== "") { array_push($result,$dictionary[$w]); } return implode(",",$result); }   function decompress($com) { $com = explode(",",$com); $i;$w;$k;$result; $dictionary = array(); $entry = ""; $dictSize = 256; for ($i = 0; $i < 256; $i++) { $dictionary[$i] = chr($i); } $w = chr($com[0]); $result = $w; for ($i = 1; $i < count($com);$i++) { $k = $com[$i]; if ($dictionary[$k]) { $entry = $dictionary[$k]; } else { if ($k === $dictSize) { $entry = $w.$w[0]; } else { return null; } } $result .= $entry; $dictionary[$dictSize++] = $w . $entry[0]; $w = $entry; } return $result; } }   //How to use $str = 'TOBEORNOTTOBEORTOBEORNOT'; $lzw = new LZW(); $com = $lzw->compress($str); $dec = $lzw->decompress($com); echo $com . "<br>" . $dec;  
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
#VBA
VBA
Option Base 1 Private Function pivotize(m As Variant) As Variant Dim n As Integer: n = UBound(m) Dim im() As Double ReDim im(n, n) For i = 1 To n For j = 1 To n im(i, j) = 0 Next j im(i, i) = 1 Next i For i = 1 To n mx = Abs(m(i, i)) row_ = i For j = i To n If Abs(m(j, i)) > mx Then mx = Abs(m(j, i)) row_ = j End If Next j If i <> Row Then For j = 1 To n tmp = im(i, j) im(i, j) = im(row_, j) im(row_, j) = tmp Next j End If Next i pivotize = im End Function   Private Function lu(a As Variant) As Variant Dim n As Integer: n = UBound(a) Dim l() As Double ReDim l(n, n) For i = 1 To n For j = 1 To n l(i, j) = 0 Next j Next i u = l p = pivotize(a) a2 = WorksheetFunction.MMult(p, a) For j = 1 To n l(j, j) = 1# For i = 1 To j sum1 = 0# For k = 1 To i sum1 = sum1 + u(k, j) * l(i, k) Next k u(i, j) = a2(i, j) - sum1 Next i For i = j + 1 To n sum2 = 0# For k = 1 To j sum2 = sum2 + u(k, j) * l(i, k) Next k l(i, j) = (a2(i, j) - sum2) / u(j, j) Next i Next j Dim res(4) As Variant res(1) = a res(2) = l res(3) = u res(4) = p lu = res End Function   Public Sub main()   a = [{1, 3, 5; 2, 4, 7; 1, 1, 0}] Debug.Print "== a,l,u,p: ==" result = lu(a) For i = 1 To 4 For j = 1 To UBound(result(1)) For k = 1 To UBound(result(1), 2) Debug.Print result(i)(j, k), Next k Debug.Print Next j Debug.Print Next i a = [{11, 9,24, 2; 1, 5, 2, 6; 3,17,18, 1; 2, 5, 7, 1}] Debug.Print "== a,l,u,p: ==" result = lu(a) For i = 1 To 4 For j = 1 To UBound(result(1)) For k = 1 To UBound(result(1), 2) Debug.Print Format(result(i)(j, k), "0.#####"), Next k Debug.Print Next j Debug.Print Next i End Sub
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
#Rust
Rust
extern crate regex;   use regex::Regex; use std::collections::HashMap; use std::io;   fn main() { let mut input_line = String::new(); let mut template = String::new();   println!("Please enter a multi-line story template with <parts> to replace, terminated by a blank line.\n"); loop { io::stdin() .read_line(&mut input_line) .expect("The read line failed."); if input_line.trim().is_empty() { break; } template.push_str(&input_line); input_line.clear(); }   let re = Regex::new(r"<[^>]+>").unwrap(); let mut parts: HashMap<_, _> = re .captures_iter(&template) .map(|x| (x.get(0).unwrap().as_str().to_string(), "".to_string())) .collect(); if parts.is_empty() { println!("No <parts> to replace.\n"); } else { for (k, v) in parts.iter_mut() { println!("Please provide a replacement for {}: ", k); io::stdin() .read_line(&mut input_line) .expect("The read line failed."); *v = input_line.trim().to_string(); println!(); template = template.replace(k, v); input_line.clear(); } } println!("Resulting story:\n\n{}", template); }
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
#Racket
Racket
#lang racket   (require math/number-theory)   (define (comma x) (string-join (reverse (for/list ([digit (in-list (reverse (string->list (~a x))))] [i (in-naturals)]) (cond [(and (= 0 (modulo i 3)) (> i 0)) (string digit #\,)] [else (string digit)]))) ""))   (let loop ([x 42] [cnt 0]) (cond [(= cnt 42) (void)] [(prime? x) (printf "~a: ~a\n" (add1 cnt) (comma x)) (loop (* 2 x) (add1 cnt))] [else (loop (add1 x) cnt)]))
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
#Raku
Raku
# the actual sequence logic my @seq = grep *.is-prime, (42, { .is-prime ?? $_+<1 !! $_+1 } … *);   # display code say (1+$_).fmt("%-4s"), @seq[$_].flip.comb(3).join(',').flip.fmt("%20s") for ^42;
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
#Dart
Dart
  main() { while(true) { print("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
#dc
dc
[[SPAM ]P dx]dx
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
#Visual_Basic_.NET
Visual Basic .NET
Partial Module Program ' Stop and Step are language keywords and must be escaped with brackets. Iterator Function Range(start As Integer, [stop] As Integer, Optional [step] As Integer = 1) As IEnumerable(Of Integer) For i = start To [stop] Step [step] Yield i Next End Function End Module
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
#Dragon
Dragon
i = 1024 while(i > 0){ showln i i >>= 1 //also acceptable: 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
#COBOL
COBOL
identification division. program-id. countdown. environment division. data division. working-storage section. 01 counter pic 99. 88 counter-done value 0. 01 counter-disp pic Z9. procedure division. perform with test after varying counter from 10 by -1 until counter-done move counter to counter-disp display counter-disp end-perform stop run.
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
#CoffeeScript
CoffeeScript
# The more compact "array comprehension" style console.log i for i in [10..0]   # The "regular" for loop style. for i in [10..0] console.log i   # More compact version of the above for i in [10..0] then console.log 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.
#BASIC
BASIC
a = 0 DO a = a + 1 PRINT a LOOP WHILE a MOD 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.
#Avail
Avail
For each row from 1 to 5 do [ For each length from 1 to row do [Print: "*";]; Print: "\n"; ];
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
#C.2B.2B
C++
for (int i = 1; i < 10; i += 2) std::cout << i << std::endl;
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.
#SequenceL
SequenceL
  import <Utilities/Set.sl>;   ludic(v(1), result(1)) := let n := head(v); filtered[i] := v[i] when (i-1) mod n /= 0; in result when size(v) < 1 else ludic(filtered, result ++ [n]);   count : int(1) * int * int -> int; count(v(1), top, index) := index-1 when v[index] > top else count(v, top, index + 1);   main() := let ludics := ludic(2...100000, [1]); ludics250 := ludics[1 ... count(ludics, 250, 1)]; triplets[i] := [i, i+2, i+6] when elementOf(i+2, ludics250) and elementOf(i+6, ludics250) foreach i within ludics250; in "First 25:\n" ++ toString(ludics[1...25]) ++ "\n\nLudics below 1000:\n" ++ toString(count(ludics, 1000, 1)) ++ "\n\nLudic 2000 to 2005:\n" ++ toString(ludics[2000...2005]) ++ "\n\nTriples below 250:\n" ++ toString(triplets) ;  
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
#FBSL
FBSL
  #APPTYPE CONSOLE FOR DIM i = 1 TO 10 PRINT i; IF i < 10 THEN PRINT ", "; NEXT PAUSE
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
#Forth
Forth
: comma-list ( n -- ) dup 1 ?do i 1 .r ." , " loop . ;
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
#Factor
Factor
USING: io kernel math.ranges prettyprint random sequences ;   10 [ 20 [ 20 [1,b] random ] replicate ] replicate  ! make a table of random values [ [ dup pprint bl 20 = ] find nl drop ] find 2drop  ! print values until 20 is found
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
#Fantom
Fantom
class Main { public static Void main () { rows := 10 cols := 10 // create and fill an array of given size with random numbers Int[][] array := [,] rows.times { row := [,] cols.times { row.add(Int.random(1..20)) } array.add (row) } // now do the search try { for (i := 0; i < rows; i++) { for (j := 0; j < cols; j++) { echo ("now at ($i, $j) which is ${array[i][j]}") if (array[i][j] == 20) throw (Err("found it")) } } } catch (Err e) { echo (e.msg) return // and finish } echo ("No 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
#friendly_interactive_shell
friendly interactive shell
for path in $PATH echo You have $path in PATH. 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
#Frink
Frink
  array = [1, 2, 3, 5, 7] for n = array println[n]  
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
#Common_Lisp
Common Lisp
(defun luhn (n) (labels ((sum-digits (n) (if (> n 9) (- n 9) n))) (let ((n* (reverse n)) (l (length n))) (let ((s1 (loop for i from 0 below l by 2 summing (digit-char-p (aref n* i)))) (s2 (loop for i from 1 below l by 2 summing (sum-digits (* 2 (digit-char-p (aref n* i))))))) (zerop (mod (+ s1 s2) 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).
#Julia
Julia
  using Primes   function getmersenneprimes(n) t1 = time() count = 0 i = 2 while(n > count) if(isprime(i) && ismersenneprime(2^BigInt(i) - 1)) println("M$i, cumulative time elapsed: $(time() - t1) seconds") count += 1 end i += 1 end end   getmersenneprimes(50)  
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.
#Picat
Picat
go => S = "TOBEORNOTTOBEORTOBEORNOT", println(s=S), println(len=S.length),   Compressed = compress(S), println(compressed=Compressed), println(len=Compressed.length),   Uncompressed = uncompress(Compressed), println(uncompressed=Uncompressed),   printf("compressed to %3.3f%%\n", 100*(Compressed.length / S.length)),   if S = Uncompressed then println("Same!") else println("Error: S != Uncompressed!"), printf("S.length: %d Uncompressed.length: %d\n", S.length, Uncompressed.length), edit(S,Uncompressed,Distance,Diffs), println(distance=Distance), println(diffs=Diffs) end, nl.   compress(Uncompressed) = Compressed => DictSize = 256, Dict = new_map([C=C : I in 1..DictSize-1, C=chr(I).to_string()]), W = "", Result = [], foreach(C in Uncompressed) C := C.to_string(), WC = W ++ C, if Dict.has_key(WC) then W := WC else Result := Result ++ [Dict.get(W)], Dict.put(WC, DictSize), DictSize := DictSize + 1, W := C end end, if W.length > 0 then Result := Result ++ [Dict.get(W)] end, Compressed = Result.   uncompress(Compressed) = Uncompressed => DictSize = 256, Dict = new_map([ C=C : I in 1..DictSize-1, C=chr(I).to_string()]), W = Compressed.first(), Compressed := Compressed.tail(), Result = W,   Entry = "", foreach(K in Compressed) if Dict.has_key(K) then Entry := Dict.get(K) elseif K == DictSize then Entry := W ++ W[1].to_string() else printf("Bad compressed K: %w\n", K) end, Result := Result ++ Entry, Dict.put(DictSize,(W ++ Entry[1].to_string())), DictSize := DictSize + 1, W := Entry end, Uncompressed = Result.flatten().   % % Computing the minimal editing distance of two given lists % table(+,+,min,-) edit([],[],D,Diffs) => D=0, Diffs=[]. edit([X|Xs],[X|Ys],D,Diffs) =>  % copy edit(Xs,Ys,D,Diffs). edit(Xs,[Y|Ys],D,Diffs) ?=>  % insert edit(Xs,Ys,D1,Diffs1), D=D1+1, Diffs = [insert=Y,xPos=Xs.length,yPos=Ys.length|Diffs1]. edit([X|Xs],Ys,D,Diffs) =>  % delete edit(Xs,Ys,D1,Diffs1), D=D1+1, Diffs = [[delete=X,xPos=Xs.length,yPos=Ys.length]|Diffs1].
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
#Wren
Wren
import "/matrix" for Matrix import "/fmt" for Fmt   var arrays = [ [ [1, 3, 5], [2, 4, 7], [1, 1, 0] ],   [ [11, 9, 24, 2], [ 1, 5, 2, 6], [ 3, 17, 18, 1], [ 2, 5, 7, 1] ] ]   for (array in arrays) { var m = Matrix.new(array) System.print("A\n") Fmt.mprint(m, 2, 0) System.print("\nL\n") var lup = m.lup Fmt.mprint(lup[0], 8, 5) System.print("\nU\n") Fmt.mprint(lup[1], 8, 5) System.print("\nP\n") Fmt.mprint(lup[2], 2, 0) System.print() }
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
#Scala
Scala
object MadLibs extends App{ val input = "<name> went for a walk in the park. <he or she>\nfound a <noun>. <name> decided to take it home." println(input) println   val todo = "(<[^>]+>)".r val replacements = todo.findAllIn(input).toSet.map{found: String => found -> readLine(s"Enter a $found ") }.toMap   val output = todo.replaceAllIn(input, found => replacements(found.matched)) println println(output) }
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
#REXX
REXX
/*REXX pgm displays primes found: starting Z at 42, if Z is a prime, add Z, else add 1.*/ numeric digits 20; d=digits() /*ensure enough decimal digits for Z. */ parse arg limit . /*obtain optional arguments from the CL*/ if limit=='' | limit=="," then limit=42 /*Not specified? Then use the default.*/ n=0 /*the count of number of primes found. */ do z=42 until n==limit /* ◄──this DO loop's index is modified.*/ if isPrime(z) then do; n=n + 1 /*Z a prime? Them bump prime counter.*/ say right('n='n, 9) right(commas(z), d) z=z + z - 1 /*also, bump the DO loop index Z. */ end end /*z*/ /* [↑] a small tribute to Douglas Adams*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg _; do j=length(_)-3 to 1 by -3; _=insert(',', _, j); end; return _ /*──────────────────────────────────────────────────────────────────────────────────────*/ isPrime: procedure; parse arg #; if wordpos(#, '2 3 5 7')\==0 then return 1 if # // 2==0 | # // 3 ==0 then return 0 do j=5 by 6 until j*j>#; if # // j==0 | # // (J+2)==0 then return 0 end /*j*/ /* ___ */ return 1 /*Exceeded √ #  ? Then # is prime. */
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
#DCL
DCL
$ loop: $ write sys$output "SPAM" $ goto loop
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
#Delphi
Delphi
proc nonrec main() void: while true do writeln("SPAM") od corp
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
#Wren
Wren
import "/fmt" for Fmt   var prod = 1 var sum = 0 var x = 5 var y = -5 var z = -2 var one = 1 var three = 3 var seven = 7 var p = 11.pow(x) var j = 0   var process = Fn.new { sum = sum + j.abs if (prod.abs < (1 << 27) && j != 0) prod = prod * j }   j = -three while (j <= 3.pow(3)) { process.call() j = j + three }   j = -seven while (j <= seven) { process.call() j = j + x }   j = 555 while (j <= 550 - y) { process.call() j = j + 1 }   j = 22 while (j >= -28) { process.call() j = j - three }   j = 1927 while (j <= 1939) { process.call() j = j + 1 }   j = x while (j >= y) { process.call() j = j - (-z) }   j = p while (j <= p + one) { process.call() j = j + 1 }   System.print("sum =  %(Fmt.dc(sum))") System.print("prod = %(Fmt.dc(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
#DUP
DUP
1024[$][$.10,2/\%]# {Short form}
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
#DWScript
DWScript
var i := 1024;   while i > 0 do begin PrintLn(i); i := i div 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
#ColdFusion
ColdFusion
<cfloop index = "i" from = "10" to = "0" step = "-1"> #i# </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
#Common_Lisp
Common Lisp
(loop for i from 10 downto 1 do (print 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.
#bc
bc
i = 0 for (;;) { ++i /* increments then prints i */ if (i % 6 == 0) break } quit
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.
#AWK
AWK
BEGIN { for(i=1; i < 6; i++) { for(j=1; j <= i; j++ ) { printf "*" } print } }
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
#Ceylon
Ceylon
shared void run() {   for(i in (2..8).by(2)) { process.write("``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.
#Sidef
Sidef
func ludics_upto(nmax=100000) { Enumerator({ |collect| collect(1) var arr = @(2..nmax) while (arr) { collect(var n = arr[0]) arr.range.by(n).each {|i| arr[i] = nil} arr.compact! } }) }   func ludics_first(n) { ludics_upto(n * n.log2).first(n) }   say("First 25 Ludic numbers: ", ludics_first(25).join(' ')) say("Ludics below 1000: ", ludics_upto(1000).len) say("Ludic numbers 2000 to 2005: ", ludics_first(2005).last(6).join(' '))   var a = ludics_upto(250).to_a say("Ludic triples below 250: ", a.grep{|x| a.contains_all([x+2, x+6]) } \ .map {|x| '(' + [x, x+2, x+6].join(' ') + ')' } \ .join(' '))