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http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Kotlin
Kotlin
// version 1.1.3   typealias Func = () -> Int   fun a(k: Int, x1: Func, x2: Func, x3: Func, x4: Func, x5: Func): Int { var kk = k fun b(): Int = a(--kk, ::b, x1, x2, x3, x4) return if (kk <= 0) x4() + x5() else b() }   fun main(args: Array<String>) { println(" k a") for (k in 0..12) { println("${"%2d".format(k)}: ${a(k, { 1 }, { -1 }, { -1 }, { 1 }, { 0 })}") } }  
http://rosettacode.org/wiki/Matrix_transposition
Matrix transposition
Transpose an arbitrarily sized rectangular Matrix.
#Euphoria
Euphoria
function transpose(sequence in) sequence out out = repeat(repeat(0,length(in)),length(in[1])) for n = 1 to length(in) do for m = 1 to length(in[1]) do out[m][n] = in[n][m] end for end for return out end function   sequence m m = { {1,2,3,4}, {5,6,7,8}, {9,10,11,12} }   ? transpose(m)
http://rosettacode.org/wiki/Maze_generation
Maze generation
This page uses content from Wikipedia. The original article was at Maze generation algorithm. 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) Task Generate and show a maze, using the simple Depth-first search algorithm. Start at a random cell. Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor: If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell. Related tasks Maze solving.
#Lua
Lua
  math.randomseed( os.time() )   -- Fisher-Yates shuffle from http://santos.nfshost.com/shuffling.html function shuffle(t) for i = 1, #t - 1 do local r = math.random(i, #t) t[i], t[r] = t[r], t[i] end end   -- builds a width-by-height grid of trues function initialize_grid(w, h) local a = {} for i = 1, h do table.insert(a, {}) for j = 1, w do table.insert(a[i], true) end end return a end   -- average of a and b function avg(a, b) return (a + b) / 2 end     dirs = { {x = 0, y = -2}, -- north {x = 2, y = 0}, -- east {x = -2, y = 0}, -- west {x = 0, y = 2}, -- south }   function make_maze(w, h) w = w or 16 h = h or 8   local map = initialize_grid(w*2+1, h*2+1)   function walk(x, y) map[y][x] = false   local d = { 1, 2, 3, 4 } shuffle(d) for i, dirnum in ipairs(d) do local xx = x + dirs[dirnum].x local yy = y + dirs[dirnum].y if map[yy] and map[yy][xx] then map[avg(y, yy)][avg(x, xx)] = false walk(xx, yy) end end end   walk(math.random(1, w)*2, math.random(1, h)*2)   local s = {} for i = 1, h*2+1 do for j = 1, w*2+1 do if map[i][j] then table.insert(s, '#') else table.insert(s, ' ') end end table.insert(s, '\n') end return table.concat(s) end   print(make_maze())  
http://rosettacode.org/wiki/Matrix-exponentiation_operator
Matrix-exponentiation operator
Most programming languages have a built-in implementation of exponentiation for integers and reals only. Task Demonstrate how to implement matrix exponentiation as an operator.
#Wren
Wren
import "/matrix" for Matrix import "/fmt" for Fmt   var m = Matrix.new([[0, 1], [1, 1]]) System.print("Original:\n") Fmt.mprint(m, 2, 0) System.print("\nRaised to power of 10:\n") Fmt.mprint(m ^ 10, 3, 0)
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Lasso
Lasso
define map_range( a1, a2, b1, b2, number ) => (decimal(#b1) + (decimal(#number) - decimal(#a1)) * (decimal(#b2) - decimal(#b1)) / (decimal(#a2) - decimal(#a1))) -> asstring(-Precision = 1)   with number in generateSeries(1,10) do {^ #number ': ' map_range( 0, 10, -1, 0, #number) '<br />'   ^}'
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Liberty_BASIC
Liberty BASIC
For i = 0 To 10 Print "f(";i;") maps to ";mapToRange(i, 0, 10, -1, 0) Next i End   Function mapToRange(value, inputMin, inputMax, outputMin, outputMax) mapToRange = (((value - inputMin) * (outputMax - outputMin)) / (inputMax - inputMin)) + outputMin End Function  
http://rosettacode.org/wiki/Maximum_triangle_path_sum
Maximum triangle path sum
Starting from the top of a pyramid of numbers like this, you can walk down going one step on the right or on the left, until you reach the bottom row: 55 94 48 95 30 96 77 71 26 67 One of such walks is 55 - 94 - 30 - 26. You can compute the total of the numbers you have seen in such walk, in this case it's 205. Your problem is to find the maximum total among all possible paths from the top to the bottom row of the triangle. In the little example above it's 321. Task Find the maximum total in the triangle below: 55 94 48 95 30 96 77 71 26 67 97 13 76 38 45 07 36 79 16 37 68 48 07 09 18 70 26 06 18 72 79 46 59 79 29 90 20 76 87 11 32 07 07 49 18 27 83 58 35 71 11 25 57 29 85 14 64 36 96 27 11 58 56 92 18 55 02 90 03 60 48 49 41 46 33 36 47 23 92 50 48 02 36 59 42 79 72 20 82 77 42 56 78 38 80 39 75 02 71 66 66 01 03 55 72 44 25 67 84 71 67 11 61 40 57 58 89 40 56 36 85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52 06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93 Such numbers can be included in the solution code, or read from a "triangle.txt" file. This task is derived from the Euler Problem #18.
#VBScript
VBScript
  'Solution derived from http://stackoverflow.com/questions/8002252/euler-project-18-approach. Set objfso = CreateObject("Scripting.FileSystemObject") Set objinfile = objfso.OpenTextFile(objfso.GetParentFolderName(WScript.ScriptFullName) &_ "\triangle.txt",1,False)   row = Split(objinfile.ReadAll,vbCrLf)   For i = UBound(row) To 0 Step -1 row(i) = Split(row(i)," ") If i < UBound(row) Then For j = 0 To UBound(row(i)) If (row(i)(j) + row(i+1)(j)) > (row(i)(j) + row(i+1)(j+1)) Then row(i)(j) = CInt(row(i)(j)) + CInt(row(i+1)(j)) Else row(i)(j) = CInt(row(i)(j)) + CInt(row(i+1)(j+1)) End If Next End If Next   WScript.Echo row(0)(0)   objinfile.Close Set objfso = Nothing  
http://rosettacode.org/wiki/MD5
MD5
Task Encode a string using an MD5 algorithm.   The algorithm can be found on   Wikipedia. Optionally, validate your implementation by running all of the test values in   IETF RFC (1321)   for MD5. Additionally,   RFC 1321   provides more precise information on the algorithm than the Wikipedia article. Warning:   MD5 has known weaknesses, including collisions and forged signatures.   Users may consider a stronger alternative when doing production-grade cryptography, such as SHA-256 (from the SHA-2 family), or the upcoming SHA-3. If the solution on this page is a library solution, see   MD5/Implementation   for an implementation from scratch.
#Neko
Neko
/** MD5 in Neko Tectonics: nekoc md5.neko neko md5 */   var MD5 = $loader.loadprim("std@make_md5", 1); var base_encode = $loader.loadprim("std@base_encode", 2);   var result = MD5("The quick brown fox jumps over the lazy dog");   /* Output in lowercase hex */ $print(base_encode(result, "0123456789abcdef"));
http://rosettacode.org/wiki/Mandelbrot_set
Mandelbrot set
Mandelbrot set You are encouraged to solve this task according to the task description, using any language you may know. Task Generate and draw the Mandelbrot set. Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .
#D
D
void main() { import std.stdio, std.complex;   for (real y = -1.2; y < 1.2; y += 0.05) { for (real x = -2.05; x < 0.55; x += 0.03) { auto z = 0.complex; foreach (_; 0 .. 100) z = z ^^ 2 + complex(x, y); write(z.abs < 2 ? '#' : '.'); } writeln; } }
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#Icon_and_Unicon
Icon and Unicon
procedure main(A) n := integer(!A) | 3 write("Magic number: ",n*(n*n+1)/2) sq := buildSquare(n) showSquare(sq) end   procedure buildSquare(n) sq := [: |list(n)\n :] r := 0 c := n/2 every i := !(n*n) do { /sq[r+1,c+1] := i nr := (n+r-1)%n nc := (c+1)%n if /sq[nr+1,nc+1] then (r := nr,c := nc) else r := (r+1)%n } return sq end   procedure showSquare(sq) n := *sq s := *(n*n)+2 every r := !sq do every writes(right(!r,s)|"\n") end
http://rosettacode.org/wiki/Matrix_multiplication
Matrix multiplication
Task Multiply two matrices together. They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.
#F.23
F#
  let MatrixMultiply (matrix1 : _[,] , matrix2 : _[,]) = let result_row = (matrix1.GetLength 0) let result_column = (matrix2.GetLength 1) let ret = Array2D.create result_row result_column 0 for x in 0 .. result_row - 1 do for y in 0 .. result_column - 1 do let mutable acc = 0 for z in 0 .. (matrix1.GetLength 1) - 1 do acc <- acc + matrix1.[x,z] * matrix2.[z,y] ret.[x,y] <- acc ret    
http://rosettacode.org/wiki/Magic_squares_of_doubly_even_order
Magic squares of doubly even order
A magic square is an   N×N  square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column,   and   both diagonals are equal to the same sum   (which is called the magic number or magic constant). A magic square of doubly even order has a size that is a multiple of four   (e.g.     4, 8, 12). This means that the subsquares also have an even size, which plays a role in the construction. 1 2 62 61 60 59 7 8 9 10 54 53 52 51 15 16 48 47 19 20 21 22 42 41 40 39 27 28 29 30 34 33 32 31 35 36 37 38 26 25 24 23 43 44 45 46 18 17 49 50 14 13 12 11 55 56 57 58 6 5 4 3 63 64 Task Create a magic square of   8 × 8. Related tasks Magic squares of odd order Magic squares of singly even order See also Doubly Even Magic Squares (1728.org)
#Scala
Scala
object MagicSquareDoublyEven extends App { private val n = 8   private def magicSquareDoublyEven(n: Int): Array[Array[Int]] = { require(n >= 4 || n % 4 == 0, "Base must be a positive multiple of 4.")   // pattern of count-up vs count-down zones val (bits, mult, result, size) = (38505, n / 4, Array.ofDim[Int](n, n), n * n) var i = 0   for (r <- result.indices; c <- result(0).indices) { def bitPos = c / mult + (r / mult) * 4   result(r)(c) = if ((bits & (1 << bitPos)) != 0) i + 1 else size - i i += 1 } result }   magicSquareDoublyEven(n).foreach(row => println(row.map(x => f"$x%2s ").mkString)) println(f"---%nMagic constant: ${(n * n + 1) * n / 2}%d")   }
http://rosettacode.org/wiki/Magic_squares_of_doubly_even_order
Magic squares of doubly even order
A magic square is an   N×N  square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column,   and   both diagonals are equal to the same sum   (which is called the magic number or magic constant). A magic square of doubly even order has a size that is a multiple of four   (e.g.     4, 8, 12). This means that the subsquares also have an even size, which plays a role in the construction. 1 2 62 61 60 59 7 8 9 10 54 53 52 51 15 16 48 47 19 20 21 22 42 41 40 39 27 28 29 30 34 33 32 31 35 36 37 38 26 25 24 23 43 44 45 46 18 17 49 50 14 13 12 11 55 56 57 58 6 5 4 3 63 64 Task Create a magic square of   8 × 8. Related tasks Magic squares of odd order Magic squares of singly even order See also Doubly Even Magic Squares (1728.org)
#Sidef
Sidef
func double_even_magic_square(n) { assert(n%4 == 0, "Need multiple of four") var (bsize, max) = (n/4, n*n) var pre_pat = [true, false, false, true, false, true, true, false] pre_pat += pre_pat.flip var pattern = (pre_pat.map{|b| bsize.of(b)... } * bsize) pattern.map_kv{|k,v| v ? k+1 : max-k }.slices(n) }   func format_matrix(a) { var fmt = "%#{a.len**2 -> len}s" a.map { .map { fmt % _ }.join(' ') }.join("\n") }   say format_matrix(double_even_magic_square(8))
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Lox
Lox
fun A (k, xa, xb, xc, xd, xe) { print k; fun B() { k = k - 1; return A(k, B, xa, xb, xc, xd); } if (k <= 0) { return xd() + xe(); } else { return B(); } }   fun I0() { return 0; } fun I1() { return 1; } fun I_1() { return -1; }   print A(10, I1, I_1, I_1, I1, I0);
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Lua
Lua
function a(k,x1,x2,x3,x4,x5) local function b() k = k - 1 return a(k,b,x1,x2,x3,x4) end if k <= 0 then return x4() + x5() else return b() end end   function K(n) return function() return n end end   print(a(10, K(1), K(-1), K(-1), K(1), K(0)))
http://rosettacode.org/wiki/Matrix_transposition
Matrix transposition
Transpose an arbitrarily sized rectangular Matrix.
#Excel
Excel
let transpose (mtx : _ [,]) = Array2D.init (mtx.GetLength 1) (mtx.GetLength 0) (fun x y -> mtx.[y,x])
http://rosettacode.org/wiki/Maze_generation
Maze generation
This page uses content from Wikipedia. The original article was at Maze generation algorithm. 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) Task Generate and show a maze, using the simple Depth-first search algorithm. Start at a random cell. Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor: If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell. Related tasks Maze solving.
#M2000_Interpreter
M2000 Interpreter
  Module Maze { width% = 40 height% = 20 \\ we can use DIM maze$(0 to width%,0 to height%)="#" \\ so we can delete the two For loops DIM maze$(0 to width%,0 to height%) FOR x% = 0 TO width% FOR y% = 0 TO height% maze$(x%, y%) = "#" NEXT y% NEXT x%   currentx% = INT(RND * (width% - 1)) currenty% = INT(RND * (height% - 1))   IF currentx% MOD 2 = 0 THEN currentx%++ IF currenty% MOD 2 = 0 THEN currenty%++ maze$(currentx%, currenty%) = " "   done% = 0 WHILE done% = 0 { FOR i% = 0 TO 99 oldx% = currentx% oldy% = currenty% SELECT CASE INT(RND * 4) CASE 0 IF currentx% + 2 < width% THEN currentx%+=2 CASE 1 IF currenty% + 2 < height% THEN currenty%+=2 CASE 2 IF currentx% - 2 > 0 THEN currentx%-=2 CASE 3 IF currenty% - 2 > 0 THEN currenty%-=2 END SELECT IF maze$(currentx%, currenty%) = "#" Then { maze$(currentx%, currenty%) = " " maze$(INT((currentx% + oldx%) / 2), ((currenty% + oldy%) / 2)) = " " } NEXT i% done% = 1 FOR x% = 1 TO width% - 1 STEP 2 FOR y% = 1 TO height% - 1 STEP 2 IF maze$(x%, y%) = "#" THEN done% = 0 NEXT y% NEXT x% }     FOR y% = 0 TO height% FOR x% = 0 TO width% PRINT maze$(x%, y%); NEXT x% PRINT NEXT y% } Maze  
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Logo
Logo
to interpolate :s :a1 :a2 :b1 :b2 output (:s-:a1) / (:a2-:a1) * (:b2-:b1) + :b1 end   for [i 0 10] [print interpolate :i 0 10 -1 0]
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Lua
Lua
function map_range( a1, a2, b1, b2, s ) return b1 + (s-a1)*(b2-b1)/(a2-a1) end   for i = 0, 10 do print( string.format( "f(%d) = %f", i, map_range( 0, 10, -1, 0, i ) ) ) end
http://rosettacode.org/wiki/Maximum_triangle_path_sum
Maximum triangle path sum
Starting from the top of a pyramid of numbers like this, you can walk down going one step on the right or on the left, until you reach the bottom row: 55 94 48 95 30 96 77 71 26 67 One of such walks is 55 - 94 - 30 - 26. You can compute the total of the numbers you have seen in such walk, in this case it's 205. Your problem is to find the maximum total among all possible paths from the top to the bottom row of the triangle. In the little example above it's 321. Task Find the maximum total in the triangle below: 55 94 48 95 30 96 77 71 26 67 97 13 76 38 45 07 36 79 16 37 68 48 07 09 18 70 26 06 18 72 79 46 59 79 29 90 20 76 87 11 32 07 07 49 18 27 83 58 35 71 11 25 57 29 85 14 64 36 96 27 11 58 56 92 18 55 02 90 03 60 48 49 41 46 33 36 47 23 92 50 48 02 36 59 42 79 72 20 82 77 42 56 78 38 80 39 75 02 71 66 66 01 03 55 72 44 25 67 84 71 67 11 61 40 57 58 89 40 56 36 85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52 06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93 Such numbers can be included in the solution code, or read from a "triangle.txt" file. This task is derived from the Euler Problem #18.
#Wren
Wren
var lines = [ " 55", " 94 48", " 95 30 96", " 77 71 26 67", " 97 13 76 38 45", " 07 36 79 16 37 68", " 48 07 09 18 70 26 06", " 18 72 79 46 59 79 29 90", " 20 76 87 11 32 07 07 49 18", " 27 83 58 35 71 11 25 57 29 85", " 14 64 36 96 27 11 58 56 92 18 55", " 02 90 03 60 48 49 41 46 33 36 47 23", " 92 50 48 02 36 59 42 79 72 20 82 77 42", " 56 78 38 80 39 75 02 71 66 66 01 03 55 72", " 44 25 67 84 71 67 11 61 40 57 58 89 40 56 36", " 85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52", " 06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15", "27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93" ] var f = lines[-1].split(" ") var d = f.map { |s| Num.fromString(s) }.toList for (row in lines.count-2..0) { var l = d[0] var i = 0 for (s in lines[row].trimStart().split(" ")) { var u = Num.fromString(s) var r = d[i+1] d[i] = (l > r) ? u + l : u + r l = r i = i + 1 } } System.print(d[0])
http://rosettacode.org/wiki/MD5
MD5
Task Encode a string using an MD5 algorithm.   The algorithm can be found on   Wikipedia. Optionally, validate your implementation by running all of the test values in   IETF RFC (1321)   for MD5. Additionally,   RFC 1321   provides more precise information on the algorithm than the Wikipedia article. Warning:   MD5 has known weaknesses, including collisions and forged signatures.   Users may consider a stronger alternative when doing production-grade cryptography, such as SHA-256 (from the SHA-2 family), or the upcoming SHA-3. If the solution on this page is a library solution, see   MD5/Implementation   for an implementation from scratch.
#Nemerle
Nemerle
using System; using System.Console; using System.Text; using System.Security.Cryptography; using Nemerle.Collections; using Nemerle.Collections.NCollectionsExtensions;   module Md5 { HashMD5(input : string) : string { BitConverter.ToString (MD5.Create().ComputeHash(Encoding.Default.GetBytes(input))).Replace("-", "").ToLower() }   IsValidMD5(text : string, hash : string) : bool { HashMD5(text) == hash.ToLower() }   Main() : void { def examples = ["The quick brown fox jumped over the lazy dog's back", "", "a", "abc", "message digest", "abcdefghijklmnopqrstuvwxyz", "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789", "12345678901234567890123456789012345678901234567890123456789012345678901234567890"]; def hashes = ["e38ca1d920c4b8b8d3946b2c72f01680", "d41d8cd98f00b204e9800998ecf8427e", "0cc175b9c0f1b6a831c399e269772661", "900150983cd24fb0d6963f7d28e17f72", "f96b697d7cb7938d525a2f31aaf161d0", "c3fcd3d76192e4007dfb496cca67e13b", "d174ab98d277d9f5a5611c2c9f419d9f", "57edf4a22be3c955ac49da2e2107b67a"]; def tests = Hashtable(ZipLazy(examples, hashes)); foreach (test in tests) Write($"$(IsValidMD5(test.Key, test.Value)) "); } }
http://rosettacode.org/wiki/Mandelbrot_set
Mandelbrot set
Mandelbrot set You are encouraged to solve this task according to the task description, using any language you may know. Task Generate and draw the Mandelbrot set. Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .
#Dart
Dart
class Complex { double _r,_i;   Complex(this._r,this._i); double get r => _r; double get i => _i; String toString() => "($r,$i)";   Complex operator +(Complex other) => new Complex(r+other.r,i+other.i); Complex operator *(Complex other) => new Complex(r*other.r-i*other.i,r*other.i+other.r*i); double abs() => r*r+i*i; }   void main() { double start_x=-1.5; double start_y=-1.0; double step_x=0.03; double step_y=0.1;   for(int y=0;y<20;y++) { String line=""; for(int x=0;x<70;x++) { Complex c=new Complex(start_x+step_x*x,start_y+step_y*y); Complex z=new Complex(0.0, 0.0); for(int i=0;i<100;i++) { z=z*(z)+c; if(z.abs()>2) { break; } } line+=z.abs()>2 ? " " : "*"; } print(line); } }
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#J
J
ms=: i:@<.@-: |."_1&|:^:2 >:@i.@,~
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#Java
Java
public class MagicSquare {   public static void main(String[] args) { int n = 5; for (int[] row : magicSquareOdd(n)) { for (int x : row) System.out.format("%2s ", x); System.out.println(); } System.out.printf("\nMagic constant: %d ", (n * n + 1) * n / 2); }   public static int[][] magicSquareOdd(final int base) { if (base % 2 == 0 || base < 3) throw new IllegalArgumentException("base must be odd and > 2");   int[][] grid = new int[base][base]; int r = 0, number = 0; int size = base * base;   int c = base / 2; while (number++ < size) { grid[r][c] = number; if (r == 0) { if (c == base - 1) { r++; } else { r = base - 1; c++; } } else { if (c == base - 1) { r--; c = 0; } else { if (grid[r - 1][c + 1] == 0) { r--; c++; } else { r++; } } } } return grid; } }
http://rosettacode.org/wiki/Matrix_multiplication
Matrix multiplication
Task Multiply two matrices together. They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.
#Factor
Factor
( scratchpad ) USE: math.matrices { { 1 2 } { 3 4 } } { { -3 -8 3 } { -2 1 4 } } m. . { { -7 -6 11 } { -17 -20 25 } }
http://rosettacode.org/wiki/Magic_squares_of_doubly_even_order
Magic squares of doubly even order
A magic square is an   N×N  square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column,   and   both diagonals are equal to the same sum   (which is called the magic number or magic constant). A magic square of doubly even order has a size that is a multiple of four   (e.g.     4, 8, 12). This means that the subsquares also have an even size, which plays a role in the construction. 1 2 62 61 60 59 7 8 9 10 54 53 52 51 15 16 48 47 19 20 21 22 42 41 40 39 27 28 29 30 34 33 32 31 35 36 37 38 26 25 24 23 43 44 45 46 18 17 49 50 14 13 12 11 55 56 57 58 6 5 4 3 63 64 Task Create a magic square of   8 × 8. Related tasks Magic squares of odd order Magic squares of singly even order See also Doubly Even Magic Squares (1728.org)
#Stata
Stata
mata function magic(n) { if (mod(n,2)==1) { p = (n+1)/2-2 a = J(n,n,.) for (i=1; i<=n; i++) { for (j=1; j<=n; j++) { a[i,j] = n*mod(i+j+p,n)+mod(i+2*j-2,n)+1 } } } else if (mod(n,4)==0) { p = n^2+n+1 a = J(n,n,.) for (i=1; i<=n; i++) { for (j=1; j<=n; j++) { a[i,j] = mod(floor(i/2)-floor(j/2),2)==0 ? p-n*i-j : n*(i-1)+j } } } else { p = n/2 q = p*p k = (n-2)/4+1 a = magic(p) a = a,a:+2*q\a:+3*q,a:+q i = 1..p j = 1..k-1 if (k>2) j = j,n-k+3..n m = a[i,j]; a[i,j] = a[i:+p,j]; a[i:+p,j] = m j = 1,k m = a[k,j]; a[k,j] = a[k:+p,j]; a[k:+p,j] = m } return(a) } end
http://rosettacode.org/wiki/Magic_squares_of_doubly_even_order
Magic squares of doubly even order
A magic square is an   N×N  square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column,   and   both diagonals are equal to the same sum   (which is called the magic number or magic constant). A magic square of doubly even order has a size that is a multiple of four   (e.g.     4, 8, 12). This means that the subsquares also have an even size, which plays a role in the construction. 1 2 62 61 60 59 7 8 9 10 54 53 52 51 15 16 48 47 19 20 21 22 42 41 40 39 27 28 29 30 34 33 32 31 35 36 37 38 26 25 24 23 43 44 45 46 18 17 49 50 14 13 12 11 55 56 57 58 6 5 4 3 63 64 Task Create a magic square of   8 × 8. Related tasks Magic squares of odd order Magic squares of singly even order See also Doubly Even Magic Squares (1728.org)
#VBScript
VBScript
' Magic squares of doubly even order n=8 'multiple of 4 pattern="1001011001101001" size=n*n: w=len(size) mult=n\4 'how many multiples of 4 wscript.echo "Magic square : " & n & " x " & n i=0 For r=0 To n-1 l="" For c=0 To n-1 bit=Mid(pattern, c\mult+(r\mult)*4+1, 1) If bit="1" Then t=i+1 Else t=size-i l=l & Right(Space(w) & t, w) & " " i=i+1 Next 'c wscript.echo l Next 'r wscript.echo "Magic constant=" & (n*n+1)*n/2
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Mathematica.2FWolfram_Language
Mathematica/Wolfram Language
$RecursionLimit = 1665; (* anything less fails for k0 = 10 *) a[k0_, x1_, x2_, x3_, x4_, x5_] := Module[{k, b }, k = k0; b = (k--; a[k, b, x1, x2, x3, x4]) &; If[k <= 0, x4[] + x5[], b[]]] a[10, 1 &, -1 &, -1 &, 1 &, 0 &]
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Modula-3
Modula-3
MODULE Main; IMPORT IO;   TYPE Function = PROCEDURE ():INTEGER;   PROCEDURE A(k: INTEGER; x1, x2, x3, x4, x5: Function): INTEGER =   PROCEDURE B(): INTEGER = BEGIN DEC(k); RETURN A(k, B, x1, x2, x3, x4); END B;   BEGIN IF k <= 0 THEN RETURN x4() + x5(); ELSE RETURN B(); END; END A;   PROCEDURE F0(): INTEGER = BEGIN RETURN 0; END F0; PROCEDURE F1(): INTEGER = BEGIN RETURN 1; END F1; PROCEDURE Fn1(): INTEGER = BEGIN RETURN -1; END Fn1;   BEGIN IO.PutInt(A(10, F1, Fn1, Fn1, F1, F0)); IO.Put("\n"); END Main.
http://rosettacode.org/wiki/Matrix_transposition
Matrix transposition
Transpose an arbitrarily sized rectangular Matrix.
#F.23
F#
let transpose (mtx : _ [,]) = Array2D.init (mtx.GetLength 1) (mtx.GetLength 0) (fun x y -> mtx.[y,x])
http://rosettacode.org/wiki/Maze_generation
Maze generation
This page uses content from Wikipedia. The original article was at Maze generation algorithm. 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) Task Generate and show a maze, using the simple Depth-first search algorithm. Start at a random cell. Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor: If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell. Related tasks Maze solving.
#Mathematica.2FWolfram_Language
Mathematica/Wolfram Language
MazeGraphics[m_, n_] := Block[{$RecursionLimit = Infinity, unvisited = Tuples[Range /@ {m, n}], maze}, maze = Graphics[{Line[{{#, # - {0, 1}}, {#, # - {1, 0}}}] & /@ unvisited, Line[{{0, n}, {0, 0}, {m, 0}}]}]; {unvisited = DeleteCases[unvisited, #]; Do[If[MemberQ[unvisited, neighbor], maze = DeleteCases[ maze, {#, neighbor - {1, 1}} | {neighbor, # - {1, 1}}, {5}]; #0@ neighbor], {neighbor, RandomSample@{# + {0, 1}, # - {0, 1}, # + {1, 0}, # - {1, 0}}}]} &@RandomChoice@unvisited; maze]; maze = MazeGraphics[21, 13]
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Maple
Maple
  Map:=proc(a1,a2,b1,b2,s); return (b1+((s-a1)*(b2-b1)/(a2-a1))); end proc;   for i from 0 to 10 do printf("%a maps to ",i); printf("%a\n",Map(0,10,-1,0,i)); end do;  
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Mathematica.2FWolfram_Language
Mathematica/Wolfram Language
Rescale[#,{0,10},{-1,0}]&/@Range[0,10]
http://rosettacode.org/wiki/Maximum_triangle_path_sum
Maximum triangle path sum
Starting from the top of a pyramid of numbers like this, you can walk down going one step on the right or on the left, until you reach the bottom row: 55 94 48 95 30 96 77 71 26 67 One of such walks is 55 - 94 - 30 - 26. You can compute the total of the numbers you have seen in such walk, in this case it's 205. Your problem is to find the maximum total among all possible paths from the top to the bottom row of the triangle. In the little example above it's 321. Task Find the maximum total in the triangle below: 55 94 48 95 30 96 77 71 26 67 97 13 76 38 45 07 36 79 16 37 68 48 07 09 18 70 26 06 18 72 79 46 59 79 29 90 20 76 87 11 32 07 07 49 18 27 83 58 35 71 11 25 57 29 85 14 64 36 96 27 11 58 56 92 18 55 02 90 03 60 48 49 41 46 33 36 47 23 92 50 48 02 36 59 42 79 72 20 82 77 42 56 78 38 80 39 75 02 71 66 66 01 03 55 72 44 25 67 84 71 67 11 61 40 57 58 89 40 56 36 85 32 25 85 57 48 84 35 47 62 17 01 01 99 89 52 06 71 28 75 94 48 37 10 23 51 06 48 53 18 74 98 15 27 02 92 23 08 71 76 84 15 52 92 63 81 10 44 10 69 93 Such numbers can be included in the solution code, or read from a "triangle.txt" file. This task is derived from the Euler Problem #18.
#zkl
zkl
tri:=File("triangle.txt").pump(List,fcn(s){ s.strip().split(" ").apply("toInt") }).copy(); while(tri.len()>1){ t0:=tri.pop(); t1:=tri.pop(); tri.append( [[(it); t1.enumerate(); 'wrap([(i,t)]){ t + t0[i].max(t0[i+1]) }]]) } tri[0][0].println();
http://rosettacode.org/wiki/MD5
MD5
Task Encode a string using an MD5 algorithm.   The algorithm can be found on   Wikipedia. Optionally, validate your implementation by running all of the test values in   IETF RFC (1321)   for MD5. Additionally,   RFC 1321   provides more precise information on the algorithm than the Wikipedia article. Warning:   MD5 has known weaknesses, including collisions and forged signatures.   Users may consider a stronger alternative when doing production-grade cryptography, such as SHA-256 (from the SHA-2 family), or the upcoming SHA-3. If the solution on this page is a library solution, see   MD5/Implementation   for an implementation from scratch.
#NetRexx
NetRexx
/* NetRexx */   options replace format comments java crossref savelog symbols binary   import java.security.MessageDigest   MD5('The quick brown fox jumps over the lazy dog', '9e107d9d372bb6826bd81d3542a419d6') -- RFC 1321 MD5 test suite: MD5("", 'd41d8cd98f00b204e9800998ecf8427e') MD5("a", '0cc175b9c0f1b6a831c399e269772661') MD5("abc", '900150983cd24fb0d6963f7d28e17f72') MD5("message digest", 'f96b697d7cb7938d525a2f31aaf161d0') MD5("abcdefghijklmnopqrstuvwxyz", 'c3fcd3d76192e4007dfb496cca67e13b') MD5("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789", 'd174ab98d277d9f5a5611c2c9f419d9f') MD5("12345678901234567890123456789012345678901234567890123456789012345678901234567890", '57edf4a22be3c955ac49da2e2107b67a')   return   -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method MD5(messageText, verifyCheck) public static   algorithm = 'MD5' digestSum = getDigest(messageText, algorithm)   say '<Message>'messageText'</Message>' say Rexx('<'algorithm'>').right(12) || digestSum'</'algorithm'>' say Rexx('<Verify>').right(12) || verifyCheck'</Verify>' if digestSum == verifyCheck then say algorithm 'Confirmed' else say algorithm 'Failed'   return   -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method getDigest(messageText = Rexx, algorithm = Rexx 'MD5', encoding = Rexx 'UTF-8', lowercase = boolean 1) public static returns Rexx   algorithm = algorithm.upper encoding = encoding.upper   message = String(messageText) messageBytes = byte[] digestBytes = byte[] digestSum = Rexx ''   do messageBytes = message.getBytes(encoding) md = MessageDigest.getInstance(algorithm) md.update(messageBytes) digestBytes = md.digest   loop b_ = 0 to digestBytes.length - 1 bb = Rexx(digestBytes[b_]).d2x(2) if lowercase then digestSum = digestSum || bb.lower else digestSum = digestSum || bb.upper end b_ catch ex = Exception ex.printStackTrace end   return digestSum  
http://rosettacode.org/wiki/Mandelbrot_set
Mandelbrot set
Mandelbrot set You are encouraged to solve this task according to the task description, using any language you may know. Task Generate and draw the Mandelbrot set. Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .
#Dc
Dc
_2.1 sx # xmin = -2.1 0.7 sX # xmax = 0.7   _1.2 sy # ymin = -1.2 1.2 sY # ymax = 1.2   32 sM # maxiter = 32   80 sW # image width 25 sH # image height   8 k # precision   [ q ] sq # quitter helper macro   # for h from 0 to H-1 0 sh [ lh lH =q # quit if H reached   # for w from 0 to W-1 0 sw [ lw lW =q # quit if W reached   # (w,h) -> (R,I) # | | # | ymin + h*(ymax-ymin)/(height-1) # xmin + w*(xmax-xmin)/(width-1)   lX lx - lW 1 - / lw * lx + sR lY ly - lH 1 - / lh * ly + sI   # iterate for (R,I)   0 sr # r:=0 0 si # i:=0 0 sa # a:=0 (r squared) 0 sb # b:=0 (i squared) 0 sm # m:=0   # do while m!=M and a+b=<4 [ lm lM =q # exit if m==M la lb + 4<q # exit if >4   2 lr * li * lI + si # i:=2*r*i+I la lb - lR + sr # r:=a-b+R lm 1 + sm # m+=1 lr 2 ^ sa # a:=r*r li 2 ^ sb # b:=i*i   l0 x # loop ] s0 l0 x   lm 32 + P # print "pixel"   lw 1 + sw # w+=1 l1 x # loop ] s1 l1 x   A P # linefeed   lh 1 + sh # h+=1 l2 x # loop ] s2 l2 x
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#JavaScript
JavaScript
(function () {   // n -> [[n]] function magic(n) { return n % 2 ? rotation( transposed( rotation( table(n) ) ) ) : null; }   // [[a]] -> [[a]] function rotation(lst) { return lst.map(function (row, i) { return rotated( row, ((row.length + 1) / 2) - (i + 1) ); }) }   // [[a]] -> [[a]] function transposed(lst) { return lst[0].map(function (col, i) { return lst.map(function (row) { return row[i]; }) }); }   // [a] -> n -> [a] function rotated(lst, n) { var lng = lst.length, m = (typeof n === 'undefined') ? 1 : ( n < 0 ? lng + n : (n > lng ? n % lng : n) );   return m ? ( lst.slice(-m).concat(lst.slice(0, lng - m)) ) : lst; }   // n -> [[n]] function table(n) { var rngTop = rng(1, n);   return rng(0, n - 1).map(function (row) { return rngTop.map(function (x) { return row * n + x; }); }); }   // [m..n] function rng(m, n) { return Array.apply(null, Array(n - m + 1)).map( function (x, i) { return m + i; }); }   /******************** TEST WITH 3, 5, 11 ***************************/   // Results as right-aligned wiki tables function wikiTable(lstRows, blnHeaderRow, strStyle) { var css = strStyle ? 'style="' + strStyle + '"' : '';   return '{| class="wikitable" ' + css + lstRows.map( function (lstRow, iRow) { var strDelim = ((blnHeaderRow && !iRow) ? '!' : '|'), strDbl = strDelim + strDelim;   return '\n|-\n' + strDelim + ' ' + lstRow.join(' ' + strDbl + ' '); }).join('') + '\n|}'; }   return [3, 5, 11].map( function (n) { var w = 2.5 * n; return 'magic(' + n + ')\n\n' + wikiTable( magic(n), false, 'text-align:center;width:' + w + 'em;height:' + w + 'em;table-layout:fixed;' ) } ).join('\n\n') })();
http://rosettacode.org/wiki/Matrix_multiplication
Matrix multiplication
Task Multiply two matrices together. They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.
#Fantom
Fantom
  class Main { // multiply two matrices (with no error checking) public static Int[][] multiply (Int[][] m1, Int[][] m2) { Int[][] result := [,] m1.each |Int[] row1| { Int[] row := [,] m2[0].size.times |Int colNumber| { Int value := 0 m2.each |Int[] row2, Int index| { value += row1[index] * row2[colNumber] } row.add (value) } result.add (row) } return result }   public static Void main () { m1 := [[1,2,3],[4,5,6]] m2 := [[1,2],[3,4],[5,6]]   echo ("${m1} times ${m2} = ${multiply(m1,m2)}") } }  
http://rosettacode.org/wiki/Magic_squares_of_doubly_even_order
Magic squares of doubly even order
A magic square is an   N×N  square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column,   and   both diagonals are equal to the same sum   (which is called the magic number or magic constant). A magic square of doubly even order has a size that is a multiple of four   (e.g.     4, 8, 12). This means that the subsquares also have an even size, which plays a role in the construction. 1 2 62 61 60 59 7 8 9 10 54 53 52 51 15 16 48 47 19 20 21 22 42 41 40 39 27 28 29 30 34 33 32 31 35 36 37 38 26 25 24 23 43 44 45 46 18 17 49 50 14 13 12 11 55 56 57 58 6 5 4 3 63 64 Task Create a magic square of   8 × 8. Related tasks Magic squares of odd order Magic squares of singly even order See also Doubly Even Magic Squares (1728.org)
#Visual_Basic_.NET
Visual Basic .NET
Module MagicSquares   Function MagicSquareDoublyEven(n As Integer) As Integer(,) If n < 4 OrElse n Mod 4 <> 0 Then Throw New ArgumentException("base must be a positive multiple of 4") End If   'pattern of count-up vs count-down zones Dim bits = Convert.ToInt32("1001011001101001", 2) Dim size = n * n Dim mult As Integer = n / 4 ' how many multiples of 4   Dim result(n - 1, n - 1) As Integer   Dim i = 0 For r = 0 To n - 1 For c = 0 To n - 1 Dim bitPos As Integer = Math.Floor(c / mult) + Math.Floor(r / mult) * 4 Dim test = (bits And (1 << bitPos)) <> 0 If test Then result(r, c) = i + 1 Else result(r, c) = size - i End If   i = i + 1 Next Console.WriteLine() Next   Return result End Function   Sub Main() Dim n = 8 Dim result = MagicSquareDoublyEven(n) For i = 0 To result.GetLength(0) - 1 For j = 0 To result.GetLength(1) - 1 Console.Write("{0,2} ", result(i, j)) Next Console.WriteLine() Next Console.WriteLine() Console.WriteLine("Magic constant: {0} ", (n * n + 1) * n / 2)   Console.ReadLine() End Sub   End Module
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Nim
Nim
import sugar   proc a(k: int; x1, x2, x3, x4, x5: proc(): int): int = var k = k proc b(): int = dec k a(k, b, x1, x2, x3, x4) if k <= 0: x4() + x5() else: b()   echo a(10, () => 1, () => -1, () => -1, () => 1, () => 0)
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Objeck
Objeck
interface Arg { method : virtual : public : Run() ~ Int; }   class ManOrBoy { New() {}   function : A(mb : ManOrBoy, k : Int, x1 : Arg, x2 : Arg, x3 : Arg, x4 : Arg, x5 : Arg) ~ Int { if(k <= 0) { return x4->Run() + x5->Run(); };   return Base->New(mb, k, x1, x2, x3, x4) implements Arg { @mb : ManOrBoy; @k : Int; @x1 : Arg; @x2 : Arg; @x3 : Arg; @x4 : Arg; @m : Int;   New(mb : ManOrBoy, k : Int, x1 : Arg, x2 : Arg, x3 : Arg, x4 : Arg) { @mb := mb; @k := k; @x1 := x1; @x2 := x2; @x3 := x3; @x4 := x4; @m := @k; }   method : public : Run() ~ Int { @m -= 1; return @mb->A(@mb, @m, @self, @x1, @x2, @x3, @x4); } }->Run(); }   function : C(i : Int) ~ Arg { return Base->New(i) implements Arg { @i : Int; New(i : Int) { @i := i; }   method : public : Run() ~ Int { return @i; } }; }   function : Main(args : String[]) ~ Nil { mb := ManOrBoy->New(); mb->A(mb, 10, C(1), C(-1), C(-1), C(1), C(0))->PrintLine(); } }  
http://rosettacode.org/wiki/Matrix_transposition
Matrix transposition
Transpose an arbitrarily sized rectangular Matrix.
#Factor
Factor
( scratchpad ) { { 1 2 3 } { 4 5 6 } } flip . { { 1 4 } { 2 5 } { 3 6 } }
http://rosettacode.org/wiki/Maze_generation
Maze generation
This page uses content from Wikipedia. The original article was at Maze generation algorithm. 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) Task Generate and show a maze, using the simple Depth-first search algorithm. Start at a random cell. Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor: If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell. Related tasks Maze solving.
#MATLAB_.2F_Octave
MATLAB / Octave
function M = makeMaze(n) showProgress = false;   colormap([1,1,1;1,1,1;0,0,0]); set(gcf,'color','w');   NoWALL = 0; WALL = 2; NotVISITED = -1; VISITED = -2;   m = 2*n+3; M = NotVISITED(ones(m)); offsets = [-1, m, 1, -m];   M([1 2:2:end end],:) = WALL; M(:,[1 2:2:end end]) = WALL;   currentCell = sub2ind(size(M),3,3); M(currentCell) = VISITED;   S = currentCell;   while (~isempty(S)) moves = currentCell + 2*offsets; unvistedNeigbors = find(M(moves)==NotVISITED);   if (~isempty(unvistedNeigbors)) next = unvistedNeigbors(randi(length(unvistedNeigbors),1)); M(currentCell + offsets(next)) = NoWALL;   newCell = currentCell + 2*offsets(next); if (any(M(newCell+2*offsets)==NotVISITED)) S = [S newCell]; end   currentCell = newCell; M(currentCell) = VISITED; else currentCell = S(1); S = S(2:end); end   if (showProgress) image(M-VISITED); axis equal off; drawnow; pause(.01); end end   image(M-VISITED); axis equal off;
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Maxima
Maxima
maprange(a, b, c, d) := buildq([e: ratsimp(('x - a)*(d - c)/(b - a) + c)], lambda([x], e))$   f: maprange(0, 10, -1, 0);
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Nemerle
Nemerle
using System; using System.Console;   module Maprange { Maprange(a : double * double, b : double * double, s : double) : double { def (a1, a2) = a; def (b1, b2) = b;   b1 + (((s - a1) * (b2 - b1))/(a2 - a1)) }   Main() : void { foreach (i in [0 .. 10]) WriteLine("{0, 2:f0} maps to {1:f1}", i, Maprange((0.0, 10.0), (-1.0, 0.0), i)); } }
http://rosettacode.org/wiki/MD5
MD5
Task Encode a string using an MD5 algorithm.   The algorithm can be found on   Wikipedia. Optionally, validate your implementation by running all of the test values in   IETF RFC (1321)   for MD5. Additionally,   RFC 1321   provides more precise information on the algorithm than the Wikipedia article. Warning:   MD5 has known weaknesses, including collisions and forged signatures.   Users may consider a stronger alternative when doing production-grade cryptography, such as SHA-256 (from the SHA-2 family), or the upcoming SHA-3. If the solution on this page is a library solution, see   MD5/Implementation   for an implementation from scratch.
#NewLISP
NewLISP
;; using the crypto module from http://www.newlisp.org/code/modules/crypto.lsp.html ;; (import native functions from the crypto library, provided by OpenSSL) (module "crypto.lsp") (crypto:md5 "The quick brown fox jumped over the lazy dog's back")
http://rosettacode.org/wiki/Mandelbrot_set
Mandelbrot set
Mandelbrot set You are encouraged to solve this task according to the task description, using any language you may know. Task Generate and draw the Mandelbrot set. Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .
#Delphi
Delphi
const maxIter = 256;   var x, y, i : Integer; for y:=-39 to 39 do begin for x:=-39 to 39 do begin var c := Complex(y/40-0.5, x/40); var z := Complex(0, 0); for i:=1 to maxIter do begin z := z*z + c; if Abs(z)>=4 then Break; end; if i>=maxIter then Print('#') else Print('.'); end; PrintLn(''); end;
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#jq
jq
def odd_magic_square: if type != "number" or . % 2 == 0 or . <= 0 then error("odd_magic_square requires an odd positive integer") else . as $n | reduce range(1; 1 + ($n*$n)) as $i ( [0, (($n-1)/2), []]; .[0] as $x | .[1] as $y | .[2] | setpath([$x, $y]; $i ) | if getpath([(($x+$n-1) % $n), (($y+$n+1) % $n)]) then [(($x+$n+1) % $n), $y, .] else [ (($x+$n-1) % $n), (($y+$n+1) % $n), .] end ) | .[2] end ;
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#Julia
Julia
# v0.6.0   function magicsquareodd(base::Int) if base & 1 == 0 || base < 3; error("base must be odd and >3") end   square = fill(0, base, base) r, number = 1, 1 size = base * base   c = div(base, 2) + 1 while number ≤ size square[r, c] = number fr = r == 1 ? base : r - 1 fc = c == base ? 1 : c + 1 if square[fr, fc] != 0 fr = r == base ? 1 : r + 1 fc = c end r, c = fr, fc number += 1 end   return square end   for n in 3:2:7 println("Magic square with size $n - magic constant = ", div(n ^ 3 + n, 2)) println("----------------------------------------------------") square = magicsquareodd(n) for i in 1:n println(square[i, :]) end println() end
http://rosettacode.org/wiki/Matrix_multiplication
Matrix multiplication
Task Multiply two matrices together. They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.
#Fermat
Fermat
  Array a[3,2] Array b[2,3] [a]:=[(2,3,5,7,11,13)] [b]:=[(1,1,2,3,5,8)] [a]*[b]  
http://rosettacode.org/wiki/Magic_squares_of_doubly_even_order
Magic squares of doubly even order
A magic square is an   N×N  square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column,   and   both diagonals are equal to the same sum   (which is called the magic number or magic constant). A magic square of doubly even order has a size that is a multiple of four   (e.g.     4, 8, 12). This means that the subsquares also have an even size, which plays a role in the construction. 1 2 62 61 60 59 7 8 9 10 54 53 52 51 15 16 48 47 19 20 21 22 42 41 40 39 27 28 29 30 34 33 32 31 35 36 37 38 26 25 24 23 43 44 45 46 18 17 49 50 14 13 12 11 55 56 57 58 6 5 4 3 63 64 Task Create a magic square of   8 × 8. Related tasks Magic squares of odd order Magic squares of singly even order See also Doubly Even Magic Squares (1728.org)
#Wren
Wren
import "/fmt" for Conv, Fmt   var magicSquareDoublyEven = Fn.new { |n| if (n < 4 || n%4 != 0) Fiber.abort("Base must be a positive multiple of 4")   // pattern of count-up vs count-down zones var bits = Conv.atoi("1001011001101001", 2) var size = n * n var mult = (n/4).floor // how many multiples of 4 var result = List.filled(n, null) for (i in 0...n) result[i] = List.filled(n, 0) var i = 0 for (r in 0...n) { for (c in 0...n) { var bitPos = (c/mult).floor + (r/mult).floor * 4 result[r][c] = ((bits & (1<<bitPos)) != 0) ? i + 1 : size - i i = i + 1 } } return result }   var n = 8 for (ia in magicSquareDoublyEven.call(n)) { for (i in ia) Fmt.write("$2d ", i) System.print() } System.print("\nMagic constant %((n * n + 1) * n / 2)")
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Objective-C
Objective-C
#import <Foundation/Foundation.h>   typedef NSInteger (^IntegerBlock)(void);   NSInteger A (NSInteger kParam, IntegerBlock x1, IntegerBlock x2, IntegerBlock x3, IntegerBlock x4, IntegerBlock x5) { __block NSInteger k = kParam; __block __weak IntegerBlock weak_B; IntegerBlock B; weak_B = B = ^ { return A(--k, weak_B, x1, x2, x3, x4); }; return k <= 0 ? x4() + x5() : B(); }   IntegerBlock K (NSInteger n) { return ^{return n;}; }   int main (int argc, const char * argv[]) { @autoreleasepool { NSInteger result = A(10, K(1), K(-1), K(-1), K(1), K(0)); NSLog(@"%d\n", result); } return 0; }
http://rosettacode.org/wiki/Matrix_transposition
Matrix transposition
Transpose an arbitrarily sized rectangular Matrix.
#Fermat
Fermat
  Array a[3,1] [a]:=[(1,2,3)] [b]:=Trans([a]) [a] [b]  
http://rosettacode.org/wiki/Maze_generation
Maze generation
This page uses content from Wikipedia. The original article was at Maze generation algorithm. 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) Task Generate and show a maze, using the simple Depth-first search algorithm. Start at a random cell. Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor: If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell. Related tasks Maze solving.
#Nim
Nim
import random, sequtils, strutils randomize()   iterator randomCover[T](xs: openarray[T]): T = var js = toSeq 0..xs.high for i in countdown(js.high, 0): let j = random(i) swap(js[i], js[j]) for j in js: yield xs[j]   const w = 14 h = 10   var vis = newSeqWith(h, newSeq[bool](w)) hor = newSeqWith(h+1, newSeqWith(w, "+---")) ver = newSeqWith(h, newSeqWith(w, "| ") & "|")   proc walk(x, y: int) = vis[y][x] = true for p in [[x-1,y], [x,y+1], [x+1,y], [x,y-1]].randomCover: if p[0] notin 0 ..< w or p[1] notin 0 ..< h or vis[p[1]][p[0]]: continue if p[0] == x: hor[max(y, p[1])][x] = "+ " if p[1] == y: ver[y][max(x, p[0])] = " " walk p[0], p[1]   walk rand(0..<w), rand(0..<h) for a,b in zip(hor, ver & @[""]).items: echo join(a & "+\n" & b)
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#NetRexx
NetRexx
/* NetRexx */ options replace format comments java crossref savelog symbols nobinary   A = [ 0.0, 10.0 ] B = [ -1.0, 0.0 ] incr = 1.0   say 'Mapping ['A[0]',' A[1]'] to ['B[0]',' B[1]'] in increments of' incr':' loop sVal = A[0] to A[1] by incr say ' f('sVal.format(3, 3)') =' mapRange(A, B, sVal).format(4, 3) end sVal   return   method mapRange(a = Rexx[], b = Rexx[], s_) public static return mapRange(a[0], a[1], b[0], b[1], s_)   method mapRange(a1, a2, b1, b2, s_) public static t_ = b1 + ((s_ - a1) * (b2 - b1) / (a2 - a1)) return t_  
http://rosettacode.org/wiki/MD5
MD5
Task Encode a string using an MD5 algorithm.   The algorithm can be found on   Wikipedia. Optionally, validate your implementation by running all of the test values in   IETF RFC (1321)   for MD5. Additionally,   RFC 1321   provides more precise information on the algorithm than the Wikipedia article. Warning:   MD5 has known weaknesses, including collisions and forged signatures.   Users may consider a stronger alternative when doing production-grade cryptography, such as SHA-256 (from the SHA-2 family), or the upcoming SHA-3. If the solution on this page is a library solution, see   MD5/Implementation   for an implementation from scratch.
#Nim
Nim
import md5   echo toMD5("The quick brown fox jumped over the lazy dog's back")
http://rosettacode.org/wiki/Mandelbrot_set
Mandelbrot set
Mandelbrot set You are encouraged to solve this task according to the task description, using any language you may know. Task Generate and draw the Mandelbrot set. Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .
#DWScript
DWScript
const maxIter = 256;   var x, y, i : Integer; for y:=-39 to 39 do begin for x:=-39 to 39 do begin var c := Complex(y/40-0.5, x/40); var z := Complex(0, 0); for i:=1 to maxIter do begin z := z*z + c; if Abs(z)>=4 then Break; end; if i>=maxIter then Print('#') else Print('.'); end; PrintLn(''); end;
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#Kotlin
Kotlin
// version 1.0.6   fun f(n: Int, x: Int, y: Int) = (x + y * 2 + 1) % n   fun main(args: Array<String>) { var n: Int while (true) { print("Enter the order of the magic square : ") n = readLine()!!.toInt() if (n < 1 || n % 2 == 0) println("Must be odd and >= 1, try again") else break } println() for (i in 0 until n) { for (j in 0 until n) print("%4d".format(f(n, n - j - 1, i) * n + f(n, j, i) + 1)) println() } println("\nThe magic constant is ${(n * n + 1) / 2 * n}") }
http://rosettacode.org/wiki/Matrix_multiplication
Matrix multiplication
Task Multiply two matrices together. They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.
#Forth
Forth
S" fsl-util.fs" REQUIRED S" fsl/dynmem.seq" REQUIRED : F+! ( addr -- ) ( F: r -- ) DUP F@ F+ F! ; : FSQR ( F: r1 -- r2 ) FDUP F* ; S" fsl/gaussj.seq" REQUIRED   3 3 float matrix A{{ 1e 2e 3e 4e 5e 6e 7e 8e 9e 3 3 A{{ }}fput 3 3 float matrix B{{ 3e 3e 3e 2e 2e 2e 1e 1e 1e 3 3 B{{ }}fput float dmatrix C{{ \ result   A{{ 3 3 B{{ 3 3 & C{{ mat* 3 3 C{{ }}fprint
http://rosettacode.org/wiki/Magic_squares_of_doubly_even_order
Magic squares of doubly even order
A magic square is an   N×N  square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column,   and   both diagonals are equal to the same sum   (which is called the magic number or magic constant). A magic square of doubly even order has a size that is a multiple of four   (e.g.     4, 8, 12). This means that the subsquares also have an even size, which plays a role in the construction. 1 2 62 61 60 59 7 8 9 10 54 53 52 51 15 16 48 47 19 20 21 22 42 41 40 39 27 28 29 30 34 33 32 31 35 36 37 38 26 25 24 23 43 44 45 46 18 17 49 50 14 13 12 11 55 56 57 58 6 5 4 3 63 64 Task Create a magic square of   8 × 8. Related tasks Magic squares of odd order Magic squares of singly even order See also Doubly Even Magic Squares (1728.org)
#zkl
zkl
class MagicSquareDoublyEven{ fcn init(n){ var result=magicSquareDoublyEven(n) } fcn toString{ sink,n:=Sink(String),result.len(); // num collumns fmt:="%2s "; foreach row in (result) { sink.write(row.apply('wrap(n){ fmt.fmt(n) }).concat(),"\n") } sink.write("\nMagic constant: %d".fmt((n*n + 1)*n/2)); sink.close(); } fcn magicSquareDoublyEven(n){ if (n<4 or n%4!=0 or n>16) throw(Exception.ValueError("base must be a positive multiple of 4")); bits,size,mult:=0b1001011001101001, n*n, n/4; result:=n.pump(List(),n.pump(List(),0).copy); // array[n,n] of zero   foreach i in (size){ bitsPos:=(i%n)/mult + (i/(n*mult)*4); value:=(bits.bitAnd((2).pow(bitsPos))) and i+1 or size-i; result[i/n][i%n]=value; } result; } } MagicSquareDoublyEven(8).println();
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#OCaml
OCaml
let rec a k x1 x2 x3 x4 x5 = if k <= 0 then x4 () + x5 () else let m = ref k in let rec b () = decr m; a !m b x1 x2 x3 x4 in b ()   let () = Printf.printf "%d\n" (a 10 (fun () -> 1) (fun () -> -1) (fun () -> -1) (fun () -> 1) (fun () -> 0))
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Ol
Ol
  ; Because argument "k" is a small number, it's a value, not an object. ; So we must 'pack' it in object - 'box' it; And 'unbox' when we try to get value.   (define (box x) (list x)) (define (unbox x) (car x)) (define (copy x) (box (unbox x)))   (define (A k x1 x2 x3 x4 x5) (define (B) (set-car! k (- (unbox k) 1)) (A (copy k) B x1 x2 x3 x4))   (if (<= (unbox k) 0) (+ (x4) (x5)) (B)))   (define (man-or-boy N) (A (box N) (lambda () 1) (lambda () -1) (lambda () -1) (lambda () 1) (lambda () 0)))   (print (man-or-boy 10)) (print (man-or-boy 15)) (print (man-or-boy 20))  
http://rosettacode.org/wiki/Matrix_transposition
Matrix transposition
Transpose an arbitrarily sized rectangular Matrix.
#Forth
Forth
S" fsl-util.fs" REQUIRED S" fsl/dynmem.seq" REQUIRED : F+! ( addr -- ) ( F: r -- ) DUP F@ F+ F! ; : FSQR ( F: r1 -- r2 ) FDUP F* ; S" fsl/gaussj.seq" REQUIRED   5 3 float matrix a{{ 1e 2e 3e 4e 5e 6e 7e 8e 9e 10e 11e 12e 13e 14e 15e 5 3 a{{ }}fput float dmatrix b{{   a{{ 5 3 & b{{ transpose 3 5 b{{ }}fprint
http://rosettacode.org/wiki/Maze_generation
Maze generation
This page uses content from Wikipedia. The original article was at Maze generation algorithm. 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) Task Generate and show a maze, using the simple Depth-first search algorithm. Start at a random cell. Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor: If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell. Related tasks Maze solving.
#Node.js
Node.js
  'use strict'; /* * Imported from http://rosettacode.org/wiki/Maze_generation#JavaScript * Added asynchronous behaviour to the maze generation. * * Port by sigmasoldier */   /** * Generates the maze asynchronously. * @param {Number} x Width of the maze. * @param {Number} y Height of the maze. * @returns {Promise} finished when resolved. */ function maze(x,y) { return new Promise((resolve, reject) => { let n=x*y-1; if (n<0) { reject(new Error(`illegal maze dimensions (${x} x ${y} < 1)`)); } else { let horiz =[]; for (let j= 0; j<x+1; j++) horiz[j]= []; let verti =[]; for (let j= 0; j<x+1; j++) verti[j]= []; let here = [Math.floor(Math.random()*x), Math.floor(Math.random()*y)]; let path = [here]; let unvisited = []; for (let j = 0; j<x+2; j++) { unvisited[j] = []; for (let k= 0; k<y+1; k++) unvisited[j].push(j>0 && j<x+1 && k>0 && (j != here[0]+1 || k != here[1]+1)); } while (0<n) { let potential = [[here[0]+1, here[1]], [here[0],here[1]+1], [here[0]-1, here[1]], [here[0],here[1]-1]]; let neighbors = []; for (let j = 0; j < 4; j++) if (unvisited[potential[j][0]+1][potential[j][1]+1]) neighbors.push(potential[j]); if (neighbors.length) { n = n-1; let next= neighbors[Math.floor(Math.random()*neighbors.length)]; unvisited[next[0]+1][next[1]+1]= false; if (next[0] == here[0]) horiz[next[0]][(next[1]+here[1]-1)/2]= true; else verti[(next[0]+here[0]-1)/2][next[1]]= true; path.push(here = next); } else here = path.pop(); } resolve({x: x, y: y, horiz: horiz, verti: verti}); } }); }   /** * A mere way of generating text. * The text (Since it can be large) is generated in a non-blocking way. * @param {Object} m Maze object. * @param {Stream} writeTo Optinally, include here a function to write to. * @returns {Promise} finished when the text is generated. */ function display(m, writeTo) { return new Promise((resolve, reject) => { let text = []; for (let j= 0; j<m.x*2+1; j++) { let line = []; if (0 == j%2) for (let k=0; k<m.y*4+1; k++) if (0 == k%4) line[k] = '+'; else if (j>0 && m.verti[j/2-1][Math.floor(k/4)]) line[k] = ' '; else line[k] = '-'; else for (let k=0; k<m.y*4+1; k++) if (0 == k%4) if (k>0 && m.horiz[(j-1)/2][k/4-1]) line[k] = ' '; else line[k] = '|'; else line[k] = ' '; if (0 == j) line[1] = line[2] = line[3] = ' '; if (m.x*2-1 == j) line[4*m.y]= ' '; text.push(line.join('')+'\r\n'); } const OUTPUT = text.join(''); if (typeof writeTo === 'function') writeTo(OUTPUT); resolve(OUTPUT); }); }   module.exports = { maze: maze, display: display }  
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Nim
Nim
import strformat   type FloatRange = tuple[s, e: float]   proc mapRange(a, b: FloatRange; s: float): float = b.s + (s - a.s) * (b.e - b.s) / (a.e - a.s)   for i in 0..10: let m = mapRange((0.0,10.0), (-1.0, 0.0), float(i)) echo &"{i:>2} maps to {m:4.1f}"
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Objeck
Objeck
  bundle Default { class Range { function : MapRange(a1:Float, a2:Float, b1:Float, b2:Float, s:Float) ~ Float { return b1 + (s-a1)*(b2-b1)/(a2-a1); }   function : Main(args : String[]) ~ Nil { "Mapping [0,10] to [-1,0] at intervals of 1:"->PrintLine(); for(i := 0.0; i <= 10.0; i += 1;) { IO.Console->Print("f(")->Print(i->As(Int))->Print(") = ")->PrintLine(MapRange(0.0, 10.0, -1.0, 0.0, i)); }; } } }  
http://rosettacode.org/wiki/MD5
MD5
Task Encode a string using an MD5 algorithm.   The algorithm can be found on   Wikipedia. Optionally, validate your implementation by running all of the test values in   IETF RFC (1321)   for MD5. Additionally,   RFC 1321   provides more precise information on the algorithm than the Wikipedia article. Warning:   MD5 has known weaknesses, including collisions and forged signatures.   Users may consider a stronger alternative when doing production-grade cryptography, such as SHA-256 (from the SHA-2 family), or the upcoming SHA-3. If the solution on this page is a library solution, see   MD5/Implementation   for an implementation from scratch.
#Oberon-2
Oberon-2
  MODULE MD5; IMPORT Crypto:MD5, Crypto:Utils, Strings, Out; VAR h: MD5.Hash; str: ARRAY 128 OF CHAR; BEGIN h := MD5.NewHash(); h.Initialize; str := "The quick brown fox jumped over the lazy dog's back"; h.Update(str,0,Strings.Length(str)); h.GetHash(str,0); Out.String("MD5: ");Utils.PrintHex(str,0,h.size);Out.Ln END MD5.  
http://rosettacode.org/wiki/Mandelbrot_set
Mandelbrot set
Mandelbrot set You are encouraged to solve this task according to the task description, using any language you may know. Task Generate and draw the Mandelbrot set. Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .
#EasyLang
EasyLang
for y0 range 300 cy = (y0 - 150) / 120 for x0 range 300 cx = (x0 - 220) / 120 x = 0 y = 0 color3 0 0 0 for n range 128 if x * x + y * y > 4 color3 n / 16 0 0 break 1 . h = x * x - y * y + cx y = 2 * x * y + cy x = h . move x0 / 3 y0 / 3 rect 0.4 0.4 . .
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#Liberty_BASIC
Liberty BASIC
  Dim m(1,1)   Call magicSquare 5 Call magicSquare 17   End   Sub magicSquare n ReDim m(n,n) inc = 1 count = 1 row = 1 col=(n+1)/2 While count <= n*n m(row,col) = count count = count + 1 If inc < n Then inc = inc + 1 row = row - 1 col = col + 1 If row <> 0 Then If col > n Then col = 1 Else row = n End If Else inc = 1 row = row + 1 End If Wend Call printSquare n End Sub   Sub printSquare n 'Arbitrary limit to fit width of A4 paper If n < 23 Then Print n;" x ";n;" Magic Square --- "; Print "Magic constant is ";Int((n*n+1)/2*n) For row = 1 To n For col = 1 To n Print Using("####",m(row,col)); Next col Print Print Next row Else Notice "Magic Square will not fit on one sheet of paper." End If End Sub  
http://rosettacode.org/wiki/Matrix_multiplication
Matrix multiplication
Task Multiply two matrices together. They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.
#Fortran
Fortran
real, dimension(n,m) :: a = reshape( [ (i, i=1, n*m) ], [ n, m ] ) real, dimension(m,k) :: b = reshape( [ (i, i=1, m*k) ], [ m, k ] ) real, dimension(size(a,1), size(b,2)) :: c ! C is an array whose first dimension (row) size ! is the same as A's first dimension size, and ! whose second dimension (column) size is the same ! as B's second dimension size.   c = matmul( a, b )   print *, 'A' do i = 1, n print *, a(i,:) end do   print *, print *, 'B' do i = 1, m print *, b(i,:) end do   print *, print *, 'C = AB' do i = 1, n print *, c(i,:) end do
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Oz
Oz
declare fun {A K X1 X2 X3 X4 X5} ReturnA = {NewCell undefined} fun {B} ReturnB = {NewCell undefined} in K := @K - 1 ReturnA := {A {NewCell @K} B X1 X2 X3 X4} ReturnB := @ReturnA @ReturnB end in if @K =< 0 then ReturnA := {X4} + {X5} else _ = {B} end @ReturnA end   fun {C V} fun {$} V end end in {Show {A {NewCell 10} {C 1} {C ~1} {C ~1} {C 1} {C 0}}}
http://rosettacode.org/wiki/Matrix_transposition
Matrix transposition
Transpose an arbitrarily sized rectangular Matrix.
#Fortran
Fortran
integer, parameter :: n = 3, m = 5 real, dimension(n,m) :: a = reshape( (/ (i,i=1,n*m) /), (/ n, m /) ) real, dimension(m,n) :: b   b = transpose(a)   do i = 1, n print *, a(i,:) end do   do j = 1, m print *, b(j,:) end do
http://rosettacode.org/wiki/Maze_generation
Maze generation
This page uses content from Wikipedia. The original article was at Maze generation algorithm. 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) Task Generate and show a maze, using the simple Depth-first search algorithm. Start at a random cell. Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor: If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell. Related tasks Maze solving.
#OCaml
OCaml
let seen = Hashtbl.create 7 let mark t = Hashtbl.add seen t true let marked t = Hashtbl.mem seen t   let walls = Hashtbl.create 7 let ord a b = if a <= b then (a,b) else (b,a) let join a b = Hashtbl.add walls (ord a b) true let joined a b = Hashtbl.mem walls (ord a b)   let () = let nx = int_of_string Sys.argv.(1) in let ny = int_of_string Sys.argv.(2) in   let shuffle lst = let nl = List.map (fun c -> (Random.bits (), c)) lst in List.map snd (List.sort compare nl) in   let get_neighbours (x,y) = let lim n k = (0 <= k) && (k < n) in let bounds (x,y) = lim nx x && lim ny y in List.filter bounds [(x-1,y);(x+1,y);(x,y-1);(x,y+1)] in   let rec visit cell = mark cell; let check k = if not (marked k) then (join cell k; visit k) in List.iter check (shuffle (get_neighbours cell)) in   let print_maze () = begin for i = 1 to nx do print_string "+---";done; print_endline "+"; let line n j k l s t u = for i = 0 to n do print_string (if joined (i,j) (i+k,j+l) then s else t) done; print_endline u in for j = 0 to ny-2 do print_string "| "; line (nx-2) j 1 0 " " "| " "|"; line (nx-1) j 0 1 "+ " "+---" "+"; done; print_string "| "; line (nx-2) (ny-1) 1 0 " " "| " "|"; for i = 1 to nx do print_string "+---";done; print_endline "+"; end in   Random.self_init(); visit (Random.int nx, Random.int ny); print_maze ();
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#OCaml
OCaml
let map_range (a1, a2) (b1, b2) s = b1 +. ((s -. a1) *. (b2 -. b1) /. (a2 -. a1))   let () = print_endline "Mapping [0,10] to [-1,0] at intervals of 1:"; for i = 0 to 10 do Printf.printf "f(%d) = %g\n" i (map_range (0.0, 10.0) (-1.0, 0.0) (float i)) done
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Oforth
Oforth
: mapRange(p1, p2, s) s p1 first - p2 second p2 first - * p1 second p1 first - asFloat / p2 first + ;
http://rosettacode.org/wiki/MD5
MD5
Task Encode a string using an MD5 algorithm.   The algorithm can be found on   Wikipedia. Optionally, validate your implementation by running all of the test values in   IETF RFC (1321)   for MD5. Additionally,   RFC 1321   provides more precise information on the algorithm than the Wikipedia article. Warning:   MD5 has known weaknesses, including collisions and forged signatures.   Users may consider a stronger alternative when doing production-grade cryptography, such as SHA-256 (from the SHA-2 family), or the upcoming SHA-3. If the solution on this page is a library solution, see   MD5/Implementation   for an implementation from scratch.
#Objeck
Objeck
  class MD5 { function : Main(args : String[]) ~ Nil { in := "The quick brown fox jumped over the lazy dog's back"->ToByteArray(); hash := Encryption.Hash->MD5(in); hash->ToHexString()->PrintLine(); } }  
http://rosettacode.org/wiki/Mandelbrot_set
Mandelbrot set
Mandelbrot set You are encouraged to solve this task according to the task description, using any language you may know. Task Generate and draw the Mandelbrot set. Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .
#eC
eC
void drawMandelbrot(Bitmap bmp, float range, Complex center, ColorAlpha * palette, int nPalEntries, int nIterations, float scale) { int x, y; int w = bmp.width, h = bmp.height; ColorAlpha * picture = (ColorAlpha *)bmp.picture; double logOf2 = log(2); Complex d { w > h ? range : range * w / h, h > w ? range : range * h / w }; Complex C0 { center.a - d.a/2, center.b - d.b/2 }; Complex C = C0; double delta = d.a / w;   for(y = 0; y < h; y++, C.a = C0.a, C.b += delta) { for(x = 0; x < w; x++, picture++, C.a += delta) { Complex Z { }; int i; double ii = 0; bool out = false; double Za2 = Z.a * Z.a, Zb2 = Z.b * Z.b; for(i = 0; i < nIterations; i++) { double z2; Z = { Za2 - Zb2, 2*Z.a*Z.b }; Z.a += C.a; Z.b += C.b; Za2 = Z.a * Z.a, Zb2 = Z.b * Z.b; z2 = Za2 + Zb2;   if(z2 >= 2*2) { ii = (double)(i + 1 - log(0.5 * log(z2)) / logOf2); out = true; break; } } if(out) { float si = (float)(ii * scale); int i0 = ((int)si) % nPalEntries; *picture = palette[i0]; } else *picture = black; } } }
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#Lua
Lua
rp[v_, pos_] := RotateRight[v, (Length[v] + 1)/2 - pos]; rho[m_] := MapIndexed[rp, m]; magic[n_] := rho[Transpose[rho[Table[i*n + j, {i, 0, n - 1}, {j, 1, n}]]]];   square = magic[11] // Grid Print["Magic number is ", Total[square[[1, 1]]]]
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#Mathematica.2FWolfram_Language
Mathematica/Wolfram Language
rp[v_, pos_] := RotateRight[v, (Length[v] + 1)/2 - pos]; rho[m_] := MapIndexed[rp, m]; magic[n_] := rho[Transpose[rho[Table[i*n + j, {i, 0, n - 1}, {j, 1, n}]]]];   square = magic[11] // Grid Print["Magic number is ", Total[square[[1, 1]]]]
http://rosettacode.org/wiki/Matrix_multiplication
Matrix multiplication
Task Multiply two matrices together. They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.
#FreeBASIC
FreeBASIC
type Matrix dim as double m( any , any ) declare constructor ( ) declare constructor ( byval x as uinteger , byval y as uinteger ) end type   constructor Matrix ( ) end constructor   constructor Matrix ( byval x as uinteger , byval y as uinteger ) redim this.m( x - 1 , y - 1 ) end constructor   operator * ( byref a as Matrix , byref b as Matrix ) as Matrix dim as Matrix ret dim as uinteger i, j, k if ubound( a.m , 2 ) = ubound( b.m , 1 ) and ubound( a.m , 1 ) = ubound( b.m , 2 ) then redim ret.m( ubound( a.m , 1 ) , ubound( b.m , 2 ) ) for i = 0 to ubound( a.m , 1 ) for j = 0 to ubound( b.m , 2 ) for k = 0 to ubound( b.m , 1 ) ret.m( i , j ) += a.m( i , k ) * b.m( k , j ) next k next j next i end if return ret end operator   'some garbage matrices for demonstration dim as Matrix a = Matrix(4 , 2) a.m(0 , 0) = 1 : a.m(0 , 1) = 0 a.m(1 , 0) = 0 : a.m(1 , 1) = 1 a.m(2 , 0) = 2 : a.m(2 , 1) = 3 a.m(3 , 0) = 0.75 : a.m(3 , 1) = -0.5 dim as Matrix b = Matrix( 2 , 4 ) b.m(0 , 0) = 3.1 : b.m(0 , 1) = 1.6 : b.m(0 , 2) = -99 : b.m (0, 3) = -8 b.m(1 , 0) = 2.7 : b.m(1 , 1) = 0.6 : b.m(1 , 2) = 0 : b.m(1,3) = 21 dim as Matrix c = a * b print c.m(0, 0), c.m(0, 1), c.m(0, 2), c.m(0, 3) print c.m(1, 0), c.m(1, 1), c.m(1, 2), c.m(1, 3) print c.m(2, 0), c.m(2, 1), c.m(2, 2), c.m(2, 3) print c.m(3, 0), c.m(3, 1), c.m(3, 2), c.m(3, 3)  
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Pascal
Pascal
program manorboy(output);   function zero: integer; begin zero := 0 end; function one: integer; begin one := 1 end; function negone: integer; begin negone := -1 end;   function A( k: integer; function x1: integer; function x2: integer; function x3: integer; function x4: integer; function x5: integer ): integer;   function B: integer; begin k := k - 1; B := A(k, B, x1, x2, x3, x4) end;   begin if k <= 0 then A := x4 + x5 else A := B end;   begin writeln(A(10, one, negone, negone, one, zero)) end.
http://rosettacode.org/wiki/Matrix_transposition
Matrix transposition
Transpose an arbitrarily sized rectangular Matrix.
#FreeBASIC
FreeBASIC
Dim matriz(0 To 3, 0 To 4) As Integer = {{78,19,30,12,36},_ {49,10,65,42,50},_ {30,93,24,78,10},_ {39,68,27,64,29}} Dim As Integer mtranspuesta(Lbound(matriz, 2) To Ubound(matriz, 2), Lbound(matriz, 1) To Ubound(matriz, 1)) Dim As Integer fila, columna   For fila = Lbound(matriz,1) To Ubound(matriz,1) For columna = Lbound(matriz,2) To Ubound(matriz,2) mtranspuesta(columna, fila) = matriz(fila, columna) Print ; matriz(fila,columna); " "; Next columna Print Next fila Print   For fila = Lbound(mtranspuesta,1) To Ubound(mtranspuesta,1) For columna = Lbound(mtranspuesta,2) To Ubound(mtranspuesta,2) Print ; mtranspuesta(fila,columna); " "; Next columna Print Next fila Sleep
http://rosettacode.org/wiki/Maze_generation
Maze generation
This page uses content from Wikipedia. The original article was at Maze generation algorithm. 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) Task Generate and show a maze, using the simple Depth-first search algorithm. Start at a random cell. Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor: If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell. Related tasks Maze solving.
#Ol
Ol
  ; maze generation (import (otus random!)) (define WIDTH 30) (define HEIGHT 8)   (define maze (map (lambda (?) (repeat #b01111 WIDTH)) ; 0 - unvisited, 1111 - all walls exists (iota HEIGHT))) (define (at x y) (list-ref (list-ref maze y) x))   (define (unvisited? x y) (if (and (< -1 x WIDTH) (< -1 y HEIGHT)) (zero? (band (at x y) #b10000)))) (define neighbors '((-1 . 0) (0 . -1) (+1 . 0) (0 . +1))) (define walls '( #b10111 #b11011 #b11101 #b11110)) (define antiwalls '( #b11101 #b11110 #b10111 #b11011))   (let loop ((x (rand! WIDTH)) (y (rand! HEIGHT))) (list-set! (list-ref maze y) x (bor (at x y) #b10000)) (let try () (if (or (unvisited? (- x 1) y) ; left (unvisited? x (- y 1)) ; top (unvisited? (+ x 1) y) ; right (unvisited? x (+ y 1))) ; bottom (let*((p (rand! 4)) (neighbor (list-ref neighbors p))) (let ((nx (+ x (car neighbor))) (ny (+ y (cdr neighbor)))) (if (unvisited? nx ny) (let ((ncell (at nx ny))) (list-set! (list-ref maze y) x (band (at x y) (list-ref walls p))) (list-set! (list-ref maze ny) nx (band ncell (list-ref antiwalls p))) (loop nx ny))) (try))))))  
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#PARI.2FGP
PARI/GP
map(r1,r2,x)=r2[1]+(x-r1[1])*(r2[2]-r2[1])/(r1[2]-r1[1])
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Pascal
Pascal
Program Map(output);   function MapRange(fromRange, toRange: array of real; value: real): real; begin MapRange := (value-fromRange[0]) * (toRange[1]-toRange[0]) / (fromRange[1]-fromRange[0]) + toRange[0]; end;   var i: integer; begin for i := 0 to 10 do writeln (i, ' maps to: ', MapRange([0.0, 10.0], [-1.0, 0.0], i):4:2); end.
http://rosettacode.org/wiki/MD5
MD5
Task Encode a string using an MD5 algorithm.   The algorithm can be found on   Wikipedia. Optionally, validate your implementation by running all of the test values in   IETF RFC (1321)   for MD5. Additionally,   RFC 1321   provides more precise information on the algorithm than the Wikipedia article. Warning:   MD5 has known weaknesses, including collisions and forged signatures.   Users may consider a stronger alternative when doing production-grade cryptography, such as SHA-256 (from the SHA-2 family), or the upcoming SHA-3. If the solution on this page is a library solution, see   MD5/Implementation   for an implementation from scratch.
#Objective-C
Objective-C
NSString *myString = @"The quick brown fox jumped over the lazy dog's back"; NSData *digest = [[myString dataUsingEncoding:NSUTF8StringEncoding] md5Digest]; // or another encoding of your choosing NSLog(@"%@", [digest hexadecimalRepresentation]);
http://rosettacode.org/wiki/Mandelbrot_set
Mandelbrot set
Mandelbrot set You are encouraged to solve this task according to the task description, using any language you may know. Task Generate and draw the Mandelbrot set. Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .
#EchoLisp
EchoLisp
  (lib 'math) ;; fractal function (lib 'plot)   ;; (fractal z zc n) iterates z := z^2 + c, n times ;; 100 iterations (define (mset z) (if (= Infinity (fractal 0 z 100)) Infinity z))   ;; plot function argument inside square (-2 -2), (2,2) (plot-z-arg mset -2 -2)   ;; result here [http://www.echolalie.org/echolisp/help.html#fractal]  
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#Maxima
Maxima
wrap1(i):= if i>%n% then 1 else if i<1 then %n% else i; wrap(P):=maplist('wrap1, P);   uprigth(P):= wrap(P + [-1, 1]); down(P):= wrap(P + [1, 0]);   magic(n):=block([%n%: n, M: zeromatrix (n, n), P: [1, (n + 1)/2], m: 1, Pc], do ( M[P[1],P[2]]: m, m: m + 1, if m>n^2 then return(M), Pc: uprigth(P), if M[Pc[1],Pc[2]]=0 then P: Pc else while(M[P[1],P[2]]#0) do P: down(P)));
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#Nim
Nim
import strutils   proc magic(n: int) = let length = len($(n * n)) for row in 1 .. n: for col in 1 .. n: let cell = (n * ((row + col - 1 + n div 2) mod n) + ((row + 2 * col - 2) mod n) + 1) stdout.write ($cell).align(length), ' ' echo "" echo "\nAll sum to magic number ", (n * n + 1) * n div 2   for n in [3, 5, 7]: echo "\nOrder ", n, "\n=======" magic(n)
http://rosettacode.org/wiki/Matrix_multiplication
Matrix multiplication
Task Multiply two matrices together. They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.
#Frink
Frink
matprod[a is array, b is array] := { c = makeArray[[length[a], length[b@0]], 0]   a_row = length[a]-1 a_col = length[a@0]-1 b_col = length[b]-1   for row = 0 to a_row for col = 0 to b_col for inc = 0 to a_col c@row@col = c@row@col + (a@row@inc * b@inc@col)   return c }
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Perl
Perl
sub A { my ($k, $x1, $x2, $x3, $x4, $x5) = @_; my($B); $B = sub { A(--$k, $B, $x1, $x2, $x3, $x4) }; $k <= 0 ? &$x4 + &$x5 : &$B; }   print A(10, sub{1}, sub {-1}, sub{-1}, sub{1}, sub{0} ), "\n";
http://rosettacode.org/wiki/Matrix_transposition
Matrix transposition
Transpose an arbitrarily sized rectangular Matrix.
#Frink
Frink
  a = [[1,2,3], [4,5,6], [7,8,9]] join["\n",a.transpose[]]  
http://rosettacode.org/wiki/Maze_generation
Maze generation
This page uses content from Wikipedia. The original article was at Maze generation algorithm. 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) Task Generate and show a maze, using the simple Depth-first search algorithm. Start at a random cell. Mark the current cell as visited, and get a list of its neighbors. For each neighbor, starting with a randomly selected neighbor: If that neighbor hasn't been visited, remove the wall between this cell and that neighbor, and then recurse with that neighbor as the current cell. Related tasks Maze solving.
#Perl
Perl
use List::Util 'max';   my ($w, $h) = @ARGV; $w ||= 26; $h ||= 127; my $avail = $w * $h;   # cell is padded by sentinel col and row, so I don't check array bounds my @cell = (map([(('1') x $w), 0], 1 .. $h), [('') x ($w + 1)]); my @ver = map([("| ") x $w], 1 .. $h); my @hor = map([("+--") x $w], 0 .. $h);   sub walk { my ($x, $y) = @_; $cell[$y][$x] = ''; $avail-- or return; # no more bottles, er, cells   my @d = ([-1, 0], [0, 1], [1, 0], [0, -1]); while (@d) { my $i = splice @d, int(rand @d), 1; my ($x1, $y1) = ($x + $i->[0], $y + $i->[1]);   $cell[$y1][$x1] or next;   if ($x == $x1) { $hor[ max($y1, $y) ][$x] = '+ ' } if ($y == $y1) { $ver[$y][ max($x1, $x) ] = ' ' } walk($x1, $y1); } }   walk(int rand $w, int rand $h); # generate   for (0 .. $h) { # display print @{$hor[$_]}, "+\n"; print @{$ver[$_]}, "|\n" if $_ < $h; }
http://rosettacode.org/wiki/Map_range
Map range
Given two ranges:   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   and   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]} ;   then a value   s {\displaystyle s}   in range   [ a 1 , a 2 ] {\displaystyle [a_{1},a_{2}]}   is linearly mapped to a value   t {\displaystyle t}   in range   [ b 1 , b 2 ] {\displaystyle [b_{1},b_{2}]}   where:   t = b 1 + ( s − a 1 ) ( b 2 − b 1 ) ( a 2 − a 1 ) {\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}} Task Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range. Use this function to map values from the range   [0, 10]   to the range   [-1, 0]. Extra credit Show additional idiomatic ways of performing the mapping, using tools available to the language.
#Perl
Perl
#!/usr/bin/perl -w use strict ;   sub mapValue { my ( $range1 , $range2 , $number ) = @_ ; return ( $range2->[ 0 ] + (( $number - $range1->[ 0 ] ) * ( $range2->[ 1 ] - $range2->[ 0 ] ) ) / ( $range1->[ -1 ] - $range1->[ 0 ] ) ) ; } my @numbers = 0..10 ; my @interval = ( -1 , 0 ) ; print "The mapped value for $_ is " . mapValue( \@numbers , \@interval , $_ ) . " !\n" foreach @numbers ;  
http://rosettacode.org/wiki/MD5
MD5
Task Encode a string using an MD5 algorithm.   The algorithm can be found on   Wikipedia. Optionally, validate your implementation by running all of the test values in   IETF RFC (1321)   for MD5. Additionally,   RFC 1321   provides more precise information on the algorithm than the Wikipedia article. Warning:   MD5 has known weaknesses, including collisions and forged signatures.   Users may consider a stronger alternative when doing production-grade cryptography, such as SHA-256 (from the SHA-2 family), or the upcoming SHA-3. If the solution on this page is a library solution, see   MD5/Implementation   for an implementation from scratch.
#OCaml
OCaml
# Digest.to_hex(Digest.string "The quick brown fox jumped over the lazy dog's back") ;; - : string = "e38ca1d920c4b8b8d3946b2c72f01680"
http://rosettacode.org/wiki/Mandelbrot_set
Mandelbrot set
Mandelbrot set You are encouraged to solve this task according to the task description, using any language you may know. Task Generate and draw the Mandelbrot set. Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .
#Elixir
Elixir
defmodule Mandelbrot do def set do xsize = 59 ysize = 21 minIm = -1.0 maxIm = 1.0 minRe = -2.0 maxRe = 1.0 stepX = (maxRe - minRe) / xsize stepY = (maxIm - minIm) / ysize Enum.each(0..ysize, fn y -> im = minIm + stepY * y Enum.map(0..xsize, fn x -> re = minRe + stepX * x 62 - loop(0, re, im, re, im, re*re+im*im) end) |> IO.puts end) end   defp loop(n, _, _, _, _, _) when n>=30, do: n defp loop(n, _, _, _, _, v) when v>4.0, do: n-1 defp loop(n, re, im, zr, zi, _) do a = zr * zr b = zi * zi loop(n+1, re, im, a-b+re, 2*zr*zi+im, a+b) end end   Mandelbrot.set
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#Oforth
Oforth
: magicSquare(n) | i j wd | n sq log asInteger 1+ ->wd n loop: i [ n loop: j [ i j + 1- n 2 / + n mod n * i j + j + 2 - n mod 1 + + System.Out swap <<w(wd) " " << drop ] printcr ] System.Out "Magic constant is : " << n sq 1 + 2 / n * << cr ;
http://rosettacode.org/wiki/Magic_squares_of_odd_order
Magic squares of odd order
A magic square is an   NxN   square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column,   and   both long (main) diagonals are equal to the same sum (which is called the   magic number   or   magic constant). The numbers are usually (but not always) the first   N2   positive integers. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. 8 1 6 3 5 7 4 9 2 Task For any odd   N,   generate a magic square with the integers   1 ──► N,   and show the results here. Optionally, show the magic number. You should demonstrate the generator by showing at least a magic square for   N = 5. Related tasks Magic squares of singly even order Magic squares of doubly even order See also MathWorld™ entry: Magic_square Odd Magic Squares (1728.org)
#PARI.2FGP
PARI/GP
magicSquare(n)={ my(M=matrix(n,n),j=n\2+1,i=1); for(l=1,n^2, M[i,j]=l; if(M[(i-2)%n+1,j%n+1], i=i%n+1 , i=(i-2)%n+1; j=j%n+1 ) ); M; } magicSquare(7)
http://rosettacode.org/wiki/Matrix_multiplication
Matrix multiplication
Task Multiply two matrices together. They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.
#Futhark
Futhark
  fun main(x: [n][m]int, y: [m][p]int): [n][p]int = map (fn xr => map (fn yc => reduce (+) 0 (zipWith (*) xr yc)) (transpose y)) x  
http://rosettacode.org/wiki/Man_or_boy_test
Man or boy test
Man or boy test You are encouraged to solve this task according to the task description, using any language you may know. Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers' — Donald Knuth Task: Imitate Knuth's example in Algol 60 in another language, as far as possible. Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem. In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation. So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree. Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67. Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments. The table below shows the result, call depths, and total calls for a range of k: k 0 1 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 27 28 29 30 A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658 A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827 61,786,266 134,202,509 292,011,464       A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608             B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826             B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607             Related tasks   Jensen's Device
#Phix
Phix
without js -- allocate() forward function A(integer k, object x1, x2, x3, x4, x5) function B(sequence s) object {kptr,x1,x2,x3,x4} = s integer k = peek4s(kptr)-1 poke4(kptr,k) return A(k,{kptr,x1,x2,x3,x4},x1,x2,x3,x4) end function function A(integer k, object x1, x2, x3, x4, x5) if k<=0 then return iff(sequence(x4)?B(x4):x4)+ iff(sequence(x5)?B(x5):x5) end if atom kptr = allocate(4,1) poke4(kptr,k) return B({kptr,x1,x2,x3,x4}) end function for k=0 to 23 do printf(1,"A(%d) = %d\n",{k,A(k,1,-1,-1,1,0)}) end for