Initial data commit

Task/Sudan-function/00-META.yaml

@@ -0,0 +1,6 @@
+---
+category:
+- Memoization
+- Classic CS problems and programs
+from: http://rosettacode.org/wiki/Sudan_function
+note: Recursion

Task/Sudan-function/00-TASK.txt

@@ -0,0 +1,14 @@
+The '''[[wp:Sudan function|Sudan function]]''' is a classic example of a recursive function, notable especially because it is not a [[wp:Primitive_recursive_function|primitive recursive function]]. This is also true of the better-known [[Ackermann function]]. The Sudan function was the first function having this property to be published.
+
+The Sudan function is usually defined as follows ([https://wikimedia.org/api/rest_v1/media/math/render/svg/59304f0b3ff0baad7dd21f5ce16ce6fa241111a2 svg]):
+
+<math>\begin{array}{lll}
+      F_0 (x, y) & = x+y \\
+      F_{n+1} (x, 0) & = x & \text{if } n \ge 0 \\
+      F_{n+1} (x, y+1) & = F_n (F_{n+1} (x, y), F_{n+1} (x, y) + y + 1) & \text{if } n\ge 0 \\
+      \end{array}
+    </math>
+
+;Task:
+Write a function which returns the value of F(x, y).
+

Task/Sudan-function/8080-Assembly/sudan-function.8080

@@ -0,0 +1,60 @@
+        org     100h
+        jmp     demo
+        ;; Sudan function. BC=N, DE=X, HL=Y; output in HL.
+sudan:  mov     a,b             ; N=0?
+        ora     c
+        jz      sdnbse
+        mov     a,h             ; Y=0?
+        ora     l
+        jz      sdnbse
+        push    b               ; Save N and Y (we don't need X)
+        push    h
+        dcx     h
+        call    sudan           ; Calculate result of inner call
+        xchg                    ; Set X = result of inner call
+        pop     h               ; Get Y
+        dad     d               ; Set Y = Y + result of inner call
+        pop     b               ; Get N
+        dcx     b               ; N = N-1
+        jmp     sudan           ; Calculate result of outer call
+sdnbse: dad     d               ; Return X+Y (base case)
+        ret
+
+        ;; Output routine (show 'sudan(N,X,Y) = value'), using CP/M call
+show:   push    h!      push    d!      push    b!      ; Copies of args
+        push    h!      push    d!      push    b!      ; For output
+        lxi     d,sdt!  call    pstr                    ; Print call
+        pop     h!      call    prhl
+        lxi     d,sdc!  call    pstr
+        pop     h!      call    prhl
+        lxi     d,sdc!  call    pstr
+        pop     h!      call    prhl
+        lxi     d,sdi!  call    pstr
+        pop     b!      pop     d!      pop     h!      ; Restore args
+        call    sudan!  call    prhl                    ; Find and print result
+        lxi     d,sdnl! jmp     pstr
+prhl:   lxi     d,numbuf!       push    d!      lxi     b,-10
+prdgt:  lxi     d,-1
+pdiv:   inx     d!              dad     b!      jc      pdiv
+        mvi     a,'0'+10!       add     l!      pop     h
+        dcx     h!              mov     m,a!    push    h
+        xchg!   mov     a,h!    ora     l!      jnz     prdgt
+        pop     d
+pstr:   mvi     c,9!    jmp     5
+
+        ;; Set up big system stack (using CP/M)
+demo:   lhld    6
+        sphl
+        ;; Show a couple of values
+        lxi     b,0!    lxi     d,0!    lxi     h,0!    call    show
+        lxi     b,1!    lxi     d,1!    lxi     h,1!    call    show
+        lxi     b,2!    lxi     d,1!    lxi     h,1!    call    show
+        lxi     b,3!    lxi     d,1!    lxi     h,1!    call    show
+        lxi     b,2!    lxi     d,2!    lxi     h,1!    call    show
+        rst     0
+sdt:    db      'sudan($'
+sdc:    db      ', $'
+sdi:    db      ') = $'
+        db      '.....'
+numbuf: db      '$'
+sdnl:   db      13,10,'$'

Task/Sudan-function/ALGOL-68/sudan-function.alg

@@ -0,0 +1,26 @@
+BEGIN # compute some values of the Sudan function                          #
+    PROC sudan = ( INT n, x, y )INT:
+         IF   n = 0 THEN x + y
+         ELIF y = 0 THEN x
+         ELSE
+             INT s = sudan( n, x, y - 1 );
+             sudan( n - 1, s, s + y )
+         FI # sudan # ;
+    FOR n FROM 0 TO 1 DO
+        print( ( "Values of F(", whole( n, 0 ), ", x, y):", newline ) );
+        print( ( "y/x    0   1   2   3   4   5",            newline ) );
+        print( ( "----------------------------",            newline ) );
+        FOR y FROM 0 TO 6 DO
+            print( ( whole( y, 0 ), "  |" ) );
+            FOR x FROM 0 TO 5 DO
+                print( ( whole( sudan( n, x, y ), -4 ) ) )
+            OD;
+            print( ( newline ) )
+        OD;
+        print( ( newline ) )
+    OD;
+    print( ( newline ) );
+    print( ( "F(2, 1, 1) = ", whole( sudan( 2, 1, 1 ), 0 ), newline ) );
+    print( ( "F(3, 1, 1) = ", whole( sudan( 3, 1, 1 ), 0 ), newline ) );
+    print( ( "F(2, 2, 1) = ", whole( sudan( 2, 2, 1 ), 0 ), newline ) )
+END

Task/Sudan-function/APL/sudan-function.apl

@@ -0,0 +1,6 @@
+ sudan←{
+    0∨.>⍺ ⍺⍺ ⍵:'Negative input'⎕SIGNAL 11
+    ⍺⍺=0:⍺+⍵
+    ⍵=0:⍺
+    tm((⍺⍺-1)∇∇)⍵+tm←⍺∇⍵-1
+ }

Task/Sudan-function/AWK/sudan-function.awk

@@ -0,0 +1,32 @@
+# syntax: GAWK -f SUDAN_FUNCTION.AWK
+BEGIN {
+    for (n=0; n<=1; n++) {
+      printf("sudan(%d,x,y)\n",n)
+      printf("y/x    0   1   2   3   4   5\n")
+      printf("%s\n",strdup("-",28))
+      for (y=0; y<=6; y++) {
+        printf("%2d | ",y)
+        for (x=0; x<=5; x++) {
+          printf("%3d ",sudan(n,x,y))
+        }
+        printf("\n")
+      }
+      printf("\n")
+    }
+    n=1; x=3; y=3; printf("sudan(%d,%d,%d)=%d\n",n,x,y,sudan(n,x,y))
+    n=2; x=1; y=1; printf("sudan(%d,%d,%d)=%d\n",n,x,y,sudan(n,x,y))
+    n=2; x=2; y=1; printf("sudan(%d,%d,%d)=%d\n",n,x,y,sudan(n,x,y))
+    n=3; x=1; y=1; printf("sudan(%d,%d,%d)=%d\n",n,x,y,sudan(n,x,y))
+    exit(0)
+}
+function sudan(n,x,y) {
+    if (n == 0) { return(x+y) }
+    if (y == 0) { return(x) }
+    return sudan(n-1, sudan(n,x,y-1), sudan(n,x,y-1)+y)
+}
+function strdup(str,n,  i,new_str) {
+    for (i=1; i<=n; i++) {
+      new_str = new_str str
+    }
+    return(new_str)
+}

Task/Sudan-function/Ada/sudan-function.ada

@@ -0,0 +1,19 @@
+with Ada.Text_IO; use Ada.Text_IO;
+
+procedure Sudan_Function is
+
+   function F (N, X, Y : Natural) return Natural
+   is (if    N = 0 then X + Y
+       elsif Y = 0 then X
+       else  F (N => N - 1,
+                X => F (N, X, Y - 1),
+                Y => F (N, X, Y - 1) + Y));
+
+begin
+   Put_Line ("F0 (0, 0) = " & F (0, 0, 0)'Image);
+   Put_Line ("F1 (1, 1) = " & F (1, 1, 1)'Image);
+   Put_Line ("F1 (3, 3) = " & F (1, 3, 3)'Image);
+   Put_Line ("F2 (1, 1) = " & F (2, 1, 1)'Image);
+   Put_Line ("F2 (2, 1) = " & F (2, 2, 1)'Image);
+   Put_Line ("F3 (1, 1) = " & F (3, 1, 1)'Image);
+end Sudan_Function;

Task/Sudan-function/Arturo/sudan-function.arturo

@@ -0,0 +1,8 @@
+sudan: function [n, x, y][
+    if n = 0 -> return x + y
+    if y = 0 -> return x
+
+    sudan n-1 sudan n x y-1 y + sudan n x y-1
+]
+
+print sudan 1 3 3

Task/Sudan-function/BASIC256/sudan-function.basic

@@ -0,0 +1,24 @@
+for n = 0 to 1
+    print "Values of F(" & n & ", x, y):"
+    print "y/x    0   1   2   3   4   5"
+    print ("-"*28)
+    for y = 0 to 6
+        print y; "  |";
+        for x = 0 to 5
+            print rjust(string(F(n,x,y)),4);
+        next x
+        print
+    next y
+    print
+next n
+
+print "F(2,1,1) = "; F(2,1,1)
+print "F(3,1,1) = "; F(3,1,1)
+print "F(2,2,1) = "; F(2,2,1)
+end
+
+function F(n, x, y)
+    if n = 0 then return x + y
+    if y = 0 then return x
+    return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+end function

Task/Sudan-function/BCPL/sudan-function.bcpl

@@ -0,0 +1,30 @@
+get "libhdr"
+
+let sudan(n, x, y) =
+    n = 0 -> x + y,
+    y = 0 -> x,
+    sudan(n-1, sudan(n, x, y-1), sudan(n, x, y-1)+y)
+
+let showtable(f, n, x, y) be
+$(  writef("sudan(%N,x,y)*N", n)
+    writes("     ")
+    for i=0 to x do writed(i, 5)
+    for i=0 to y
+    $(  writef("*N%I4:", i)
+        for j=0 to x do writed(f(n, j, i), 5)
+    $)
+    writes("*N*N")
+$)
+
+let show(f, n, x, y) be
+    writef("sudan(%I4,%I4,%I4) = %I6*N", n, x, y, f(n, x, y))
+
+let start() be
+$(  showtable(sudan, 0, 6, 5)
+    showtable(sudan, 1, 6, 5)
+    wrch('*N')
+    show(sudan, 1, 3, 3)
+    show(sudan, 2, 1, 1)
+    show(sudan, 2, 2, 1)
+    show(sudan, 3, 1, 1)
+$)

Task/Sudan-function/BQN/sudan-function.bqn

@@ -0,0 +1,15 @@
+_sudan←{
+   x 0 _𝕣 y: x + y;
+   x n _𝕣 0: x;
+   x n _𝕣 y: k (n-1)_𝕣 y+k←x𝕊y-1
+}
+
+•Show "⍉(↕7) 0 _sudan⌜ ↕6:"
+•Show ⍉(↕7) 0 _sudan⌜ ↕6
+
+•Show "⍉(↕7) 1 _sudan⌜ ↕6:"
+•Show ⍉(↕7) 1 _sudan⌜ ↕6
+
+•Show "1 2 _sudan 1: "∾•Fmt 1 2 _sudan 1
+•Show "2 2 _sudan 1: "∾•Fmt 2 2 _sudan 1
+•Show "1 3 _sudan 1: "∾•Fmt 1 3 _sudan 1

Task/Sudan-function/C++/sudan-function.cpp

@@ -0,0 +1,21 @@
+//Aamrun , 11th July, 2022
+
+#include <iostream>
+using namespace std;
+
+int F(int n,int x,int y) {
+  if (n == 0) {
+    return x + y;
+  }
+
+  else if (y == 0) {
+    return x;
+  }
+
+  return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y);
+}
+
+int main() {
+  cout << "F(1,3,3) = "<<F(1,3,3)<<endl;
+  return 0;
+}

Task/Sudan-function/C-sharp/sudan-function.cs

@@ -0,0 +1,26 @@
+//Aamrun, 11th July 2022
+
+using System;
+
+namespace Sudan
+{
+  class Sudan
+  {
+  	static int F(int n,int x,int y) {
+  		if (n == 0) {
+    		return x + y;
+  		}
+
+  		else if (y == 0) {
+    		return x;
+  		}
+
+  		return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y);
+	}
+
+    static void Main(string[] args)
+    {
+      Console.WriteLine("F(1,3,3) = " + F(1,3,3));
+    }
+  }
+}

Task/Sudan-function/C/sudan-function.c

@@ -0,0 +1,20 @@
+//Aamrun, 11th July 2022
+
+#include <stdio.h>
+
+int F(int n,int x,int y) {
+  if (n == 0) {
+    return x + y;
+  }
+
+  else if (y == 0) {
+    return x;
+  }
+
+  return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y);
+}
+
+int main() {
+  printf("F1(3,3) = %d",F(1,3,3));
+  return 0;
+}

Task/Sudan-function/CLU/sudan-function.clu

@@ -0,0 +1,43 @@
+sudan = proc (n, x, y: int) returns (int)
+    if n=0 then
+        return(x + y)
+    elseif y=0 then
+        return(x)
+    else
+        k: int := sudan(n, x, y-1)
+        return(sudan(n-1, k, k+y))
+    end
+end sudan
+
+table = proc (n, xs, ys: int) returns (string)
+    ss: stream := stream$create_output()
+    stream$putl(ss, "sudan(" || int$unparse(n) || ",x,y):")
+    stream$puts(ss, "     ")
+    for x: int in int$from_to(0, xs)
+        do stream$putright(ss, int$unparse(x), 5) end
+    for y: int in int$from_to(0, ys) do
+        stream$putl(ss, "")
+        stream$putright(ss, int$unparse(y) || ":", 5)
+        for x: int in int$from_to(0, xs)
+            do stream$putright(ss, int$unparse(sudan(n, x, y)), 5) end
+    end
+    stream$putl(ss, "")
+    return(stream$get_contents(ss))
+end table
+
+show = proc (n, x, y: int) returns (string)
+    return("sudan(" || int$unparse(n)
+            || ", " || int$unparse(x)
+            || ", " || int$unparse(y)
+            || ") = " || int$unparse(sudan(n,x,y)))
+end show
+
+start_up = proc ()
+    po: stream := stream$primary_output()
+    stream$putl(po, table(0, 6, 5))
+    stream$putl(po, table(1, 6, 5))
+    stream$putl(po, show(1, 3, 3))
+    stream$putl(po, show(2, 1, 1))
+    stream$putl(po, show(2, 2, 1))
+    stream$putl(po, show(3, 1, 1))
+end start_up

Task/Sudan-function/Dart/sudan-function.dart

@@ -0,0 +1,13 @@
+int F(int n, int x, int y) {
+  if (n == 0) {
+    return x + y;
+  } else if (y == 0) {
+    return x;
+  }
+
+  return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y);
+}
+
+void main() {
+  print('F(1,3,3) = ${F(1, 3, 3)}');
+}

Task/Sudan-function/Delphi/sudan-function.delphi

@@ -0,0 +1,40 @@
+function SudanFunction(N,X,Y: integer): integer;
+begin
+if n = 0 then Result:=X + Y
+else if y = 0 then Result:=X
+else Result:=SudanFunction(N - 1, SudanFunction(N, X, Y - 1), SudanFunction(N, X, Y - 1) + Y);
+end;
+
+
+procedure ShowSudanFunction(Memo: TMemo; N,X,Y: integer);
+begin
+Memo.Lines.Add(Format('Sudan(%d,%d,%d)=%d',[n,x,y,SudanFunction(N,X,Y)]));
+end;
+
+
+procedure ShowSudanFunctions(Memo: TMemo);
+var N,X,Y: integer;
+var S: string;
+begin
+for N:=0 to 1 do
+	begin
+	Memo.Lines.Add(Format('Sudan(%d,X,Y)',[N]));
+	Memo.Lines.Add('Y/X    0   1   2   3   4   5');
+	Memo.Lines.Add('----------------------------');
+	for Y:=0 to 6 do
+		begin
+		S:=Format('%2d | ',[Y]);
+		for X:=0 to 5 do
+			begin
+			S:=S+Format('%3d ',[SudanFunction(N,X,Y)]);
+			end;
+		Memo.Lines.Add(S);
+		end;
+	Memo.Lines.Add('');
+	end;
+
+ShowSudanFunction(Memo, 1, 3, 3);
+ShowSudanFunction(Memo, 2, 1, 1);
+ShowSudanFunction(Memo, 2, 2, 1);
+ShowSudanFunction(Memo, 3, 1, 1);
+end;

Task/Sudan-function/Draco/sudan-function.draco

@@ -0,0 +1,38 @@
+proc sudan(word n, x, y) word:
+    word k;
+    if n=0 then
+        x + y
+    elif y=0 then
+        x
+    else
+        k := sudan(n, x, y-1);
+        sudan(n-1, k, k+y)
+    fi
+corp
+
+proc table(word n, xs, ys) void:
+    word x, y;
+    writeln("sudan(",n,",x,y):");
+    write("     ");
+    for x from 0 upto xs do write(x:5) od;
+    for y from 0 upto ys do
+        writeln();
+        write(y:4, ":");
+        for x from 0 upto xs do write(sudan(n,x,y):5) od;
+    od;
+    writeln();
+    writeln()
+corp
+
+proc show(word n, x, y) void:
+    writeln("sudan(", n:1, ",", x:3, ",", y:3, ") = ", sudan(n,x,y):5)
+corp
+
+proc main() void:
+    table(0, 6, 5);
+    table(1, 6, 5);
+    show(1, 3, 3);
+    show(2, 1, 1);
+    show(2, 2, 1);
+    show(3, 1, 1)
+corp

Task/Sudan-function/F-Sharp/sudan-function.fs

@@ -0,0 +1,5 @@
+let rec sudan = function
+   0L, x, y -> x + y
+  |_, x, 0L -> x
+  |n, x, y -> let x' = sudan (n, x, y-1L) in sudan (n-1L, x', x' + y)
+printfn "%d\n%d\n%d" (sudan(1L, 13L, 14L)) (sudan(2L, 5L, 1L)) (sudan(2L, 2L, 2L))

Task/Sudan-function/Factor/sudan-function-1.factor

@@ -0,0 +1,14 @@
+USING: combinators kernel math prettyprint ;
+
+: sudan ( n x y -- z )
+    {
+        { [ pick zero? ] [ nipd + ] }
+        { [ dup zero? ] [ drop nip ] }
+        [
+            [ 2drop 1 - ]
+            [ 1 - sudan dup ]
+            [ 2nip + sudan ] 3tri
+        ]
+    } cond ;
+
+3 1 1 sudan .

Task/Sudan-function/Factor/sudan-function-2.factor

@@ -0,0 +1,8 @@
+USING: combinators kernel locals math prettyprint ;
+
+:: sudan ( n x y -- z )
+    {
+        { [ n zero? ] [ x y + ] }
+        { [ y zero? ] [ x ] }
+        [ n 1 - n x y 1 - sudan dup y + sudan ]
+    } cond ;

Task/Sudan-function/Free-Pascal-Lazarus/sudan-function.pas

@@ -0,0 +1,54 @@
+program Sudan;
+//trans  https://rosettacode.org/wiki/Sudan_function#Delphi
+{$IFDEF FPC} {$MODE DELPHI} {$OPTIMIZATION ON,ALL}{$ENDIF}
+{$IFDEF WINDOWS}{$APPTYPE CONSOLE}{$ENDIF}
+uses
+  sysutils;
+function SudanFunction(N,X,Y: UInt64): UInt64;
+begin
+  if n = 0 then
+    Result:=X + Y
+   else
+     if y = 0 then
+       Result:=X
+     else
+       Result:=SudanFunction(N - 1, SudanFunction(N, X, Y - 1), SudanFunction(N, X, Y - 1) + Y);
+end;
+
+procedure ShowSudanFunction(N,X,Y: UInt64);
+begin
+  writeln(Format('Sudan(%d,%d,%d)=%d',[n,x,y,SudanFunction(N,X,Y)]));
+end;
+
+procedure ShowSudanFunctions;
+var
+  N,X,Y: UInt64;
+  S: string;
+begin
+for N:=0 to 1 do
+	begin
+	writeln(Format('Sudan(%d,X,Y)',[N]));
+	writeln('Y/X    0   1   2   3   4   5');
+	writeln('----------------------------');
+	for Y:=0 to 6 do
+		begin
+		S:=Format('%2d | ',[Y]);
+		for X:=0 to 5 do
+			begin
+			S:=S+Format('%3d ',[SudanFunction(N,X,Y)]);
+			end;
+		writeln(S);
+		end;
+	writeln('');
+	end;
+end;	
+
+BEGIN
+  ShowSudanFunctions;
+  ShowSudanFunction( 1, 3, 3);
+  ShowSudanFunction( 2, 1, 1);
+  ShowSudanFunction( 2, 2, 1);
+  ShowSudanFunction( 2, 1, 2);
+  ShowSudanFunction( 3, 1, 1);
+  ShowSudanFunction( 2, 2, 2);
+END.

Task/Sudan-function/FreeBASIC/sudan-function.basic

@@ -0,0 +1,25 @@
+Function F(n As Integer, x As Integer, y As Integer) As Integer
+    If n = 0 Then Return x + y
+    If y = 0 Then Return x
+    Return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+End Function
+
+Dim As Integer n, x, y
+For n = 0 To 1
+    Print " Values of F(" & n & ", x, y):"
+    Print " y/x    0   1   2   3   4   5"
+    Print String(29, "-")
+    For y = 0 To 6
+        Print y; "  |";
+        For x = 0 To 5
+            Print Using "####"; F(n,x,y);
+        Next x
+        Print
+    Next y
+    Print
+Next n
+
+Print "F(2,1,1) ="; F(2,1,1)
+Print "F(3,1,1) ="; F(3,1,1)
+Print "F(2,2,1) ="; F(2,2,1)
+Sleep

Task/Sudan-function/Gambas/sudan-function.gambas

@@ -0,0 +1,31 @@
+Function F(n As Integer, x As Integer, y As Integer) As Integer
+
+  If n = 0 Then Return x + y
+  If y = 0 Then Return x
+  Return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+
+End Function
+
+Public Sub Main()
+
+  Dim n, x, y As Integer
+
+  For n = 0 To 1
+    Print " Values of F(" & n & ", x, y):"
+    Print " y/x    0   1   2   3   4   5"
+    Print String(29, "-") 'Print " ----------------------------"
+    For y = 0 To 6
+      Print y; "  | ";
+      For x = 0 To 5
+        Print Format$(F(n, x, y), "####");
+      Next
+      Print
+    Next
+    Print
+  Next
+
+  Print "F(2,1,1) = "; F(2, 1, 1)
+  Print "F(3,1,1) = "; F(3, 1, 1)
+  Print "F(2,2,1) = "; F(2, 2, 1)
+
+End

Task/Sudan-function/Go/sudan-function.go

@@ -0,0 +1,32 @@
+package main
+
+import "fmt"
+
+func F(n, x, y int) int {
+    if n == 0 {
+        return x + y
+    }
+    if y == 0 {
+        return x
+    }
+    return F(n-1, F(n, x, y-1), F(n, x, y-1)+y)
+}
+
+func main() {
+    for n := 0; n < 2; n++ {
+        fmt.Printf("Values of F(%d, x, y):\n", n)
+        fmt.Println("y/x    0   1   2   3   4   5")
+        fmt.Println("----------------------------")
+        for y := 0; y < 7; y++ {
+            fmt.Printf("%d  |", y)
+            for x := 0; x < 6; x++ {
+                fmt.Printf("%4d", F(n, x, y))
+            }
+            fmt.Println()
+        }
+        fmt.Println()
+    }
+    fmt.Printf("F(2, 1, 1) = %d\n", F(2, 1, 1))
+    fmt.Printf("F(3, 1, 1) = %d\n", F(3, 1, 1))
+    fmt.Printf("F(2, 2, 1) = %d\n", F(2, 2, 1))
+}

Task/Sudan-function/Haskell/sudan-function.hs

@@ -0,0 +1,37 @@
+import Control.Monad.Memo (Memo, memo, startEvalMemo)
+import Data.List.Split (chunksOf)
+import System.Environment (getArgs)
+import Text.Tabular (Header(..), Properties(..), Table(..))
+import Text.Tabular.AsciiArt (render)
+
+type SudanArgs = (Int, Integer, Integer)
+
+-- Given argument (n, x, y) calculate Fₙ(x, y).  For performance reasons we do
+-- the calculation in a memoization monad.
+sudan :: SudanArgs -> Memo SudanArgs Integer Integer
+sudan (0, x, y) = return $ x + y
+sudan (_, x, 0) = return x
+sudan (n, x, y) = memo sudan (n, x, y-1) >>= \x2 -> sudan (n-1, x2, x2 + y)
+
+-- A table of Fₙ(x, y) values, where the rows are y values and the columns are
+-- x values.
+sudanTable :: Int -> [Integer] -> [Integer] -> String
+sudanTable n xs ys = render show show show
+                   $ Table (Group NoLine $ map Header ys)
+                           (Group NoLine $ map Header xs)
+                   $ chunksOf (length xs)
+                   $ startEvalMemo
+                   $ sequence
+                   $ [sudan (n, x, y) | y <- ys, x <- xs]
+
+main :: IO ()
+main = do
+  args <- getArgs
+  case args of
+    [n, xlo, xhi, ylo, yhi] -> do
+      putStrLn $ "Fₙ(x, y), where the rows are y values " ++
+                 "and the columns are x values.\n"
+      putStr $ sudanTable (read n)
+                          [read xlo .. read xhi]
+                          [read ylo .. read yhi]
+    _ -> error "Usage: sudan n xmin xmax ymin ymax"

Task/Sudan-function/Hoon/sudan-function.hoon

@@ -0,0 +1,8 @@
+|=  [n=@ x=@ y=@]
+^-  @
+|-
+?:  =(n 0)
+  (add x y)
+?:  =(y 0)
+  x
+$(n (dec n), x $(n n, x x, y (dec y)), y (add $(n n, x x, y (dec y)) y))

Task/Sudan-function/J/sudan-function-1.j

@@ -0,0 +1,6 @@
+F=: {{ 'N X Y'=. y assert. N>:0
+  if. 0=N do. X+Y
+  elseif. Y=0 do. X
+  else. F (N-1),(F N,X,Y-1), Y+F N, X, Y-1
+  end.
+}}"1

Task/Sudan-function/J/sudan-function-2.j

@@ -0,0 +1,10 @@
+   F 0 0 0
+0
+   F 1 1 1
+3
+   F 2 1 1
+8
+   F 3 1 1
+10228
+   F 2 2 1
+27

Task/Sudan-function/Java/sudan-function.java

@@ -0,0 +1,20 @@
+//Aamrun, 11th July 2022
+
+public class Main {
+
+  private static int F(int n,int x,int y) {
+  	if (n == 0) {
+    	return x + y;
+  	}
+
+ 	 else if (y == 0) {
+    	return x;
+  	}
+
+  	return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y);
+ }
+
+  public static void main(String[] args) {
+    System.out.println("F(1,3,3) = " + F(1,3,3));
+  }
+}

Task/Sudan-function/JavaScript/sudan-function.js

@@ -0,0 +1,17 @@
+/**
+ * @param {bigint} n
+ * @param {bigint} x
+ * @param {bigint} y
+ * @returns {bigint}
+ */
+function F(n, x, y) {
+  if (n === 0) {
+    return x + y;
+  }
+
+  if (y === 0) {
+    return x;
+  }
+
+  return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y);
+}

Task/Sudan-function/Jq/sudan-function.jq

@@ -0,0 +1,13 @@
+def sudan(n;x;y):
+  if   n == 0 then x+y
+  elif y == 0 then x
+  else sudan(n-1; sudan(n;x;y-1); sudan(n;x;y-1) + y)
+  end;
+
+# For testing and syntactic convenience:
+def sudan:
+  "sudan(\(.[0]); \(.[1]); \(.[2])) => \(sudan(.[0]; .[1]; .[2]))";
+
+# Illustrations
+[0,0,0], [1,1,1], [2,1,1], [3,1,1], [2,2,1]
+| sudan

Task/Sudan-function/Julia/sudan-function.julia

@@ -0,0 +1,8 @@
+using Memoize
+
+@memoize function sudan(n, x, y)
+   return n == 0 ? x + y : y == 0 ? x : sudan(n - 1, sudan(n, x, y - 1), sudan(n, x, y - 1) + y)
+end
+
+foreach(t -> println("sudan($(t[1]), $(t[2]), $(t[3])) = ",
+   sudan(t[1], t[2], t[3])), ((0,0,0), (1,1,1), (2,1,1), (3,1,1), (2,2,1)))

Task/Sudan-function/Lua/sudan-function.lua

@@ -0,0 +1,23 @@
+function F (n, x, y)
+    if n == 0 then
+        return x + y
+    elseif y == 0 then
+        return x
+    else
+        return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+    end
+end
+
+local testCases = {
+    {0, 0, 0},
+    {1, 1, 1},
+    {1, 3, 3},
+    {2, 1, 1},
+    {2, 2, 1},
+    {3, 1, 1}
+}
+
+for _, v in pairs(testCases) do
+    io.write("F(" .. table.concat(v, ",") .. ") = ")
+    print(F(unpack(v)))
+end

Task/Sudan-function/MAD/sudan-function.mad

@@ -0,0 +1,39 @@
+            NORMAL MODE IS INTEGER
+
+          R  WE HAVE TO DEFINE OUR OWN STACK FIRST
+            DIMENSION STACK(1000)
+            SET LIST TO STACK
+
+          R  SUDAN FUNCTION
+            INTERNAL FUNCTION(N,X,Y)
+            ENTRY TO SUDAN.
+
+          R  BASE CASES
+            WHENEVER N.E.0, FUNCTION RETURN X+Y
+            WHENEVER Y.E.0, FUNCTION RETURN X
+
+          R  RECURSIVE CASE - WITH MANUAL STACK MANIPULATION
+          R  NOTE WE DON'T NEED X AFTER THE FIRST CALL
+            SAVE RETURN
+            SAVE DATA N,Y
+            K = SUDAN.(N,X,Y-1)
+            RESTORE DATA N,Y
+            RESTORE RETURN
+
+            SAVE RETURN
+            K = SUDAN.(N-1, K, K+Y)
+            RESTORE RETURN
+            FUNCTION RETURN K
+            END OF FUNCTION
+
+            INTERNAL FUNCTION(N,X,Y)
+            ENTRY TO SHOW.
+            VECTOR VALUES FMT = $7HSUDAN.(,I1,1H,,I1,1H,,I1,4H) = ,I8*$
+            PRINT FORMAT FMT,N,X,Y,SUDAN.(N,X,Y)
+            END OF FUNCTION
+
+            SHOW.(1,3,3)
+            SHOW.(2,1,1)
+            SHOW.(2,2,1)
+            SHOW.(3,1,1)
+            END OF PROGRAM

Task/Sudan-function/Modula-2/sudan-function.mod2

@@ -0,0 +1,34 @@
+MODULE Sudan;
+FROM InOut IMPORT WriteCard, WriteString, WriteLn;
+
+PROCEDURE sudan(n, x, y: CARDINAL): CARDINAL;
+    VAR k: CARDINAL;
+BEGIN
+    IF n = 0 THEN RETURN x+y
+    ELSIF y = 0 THEN RETURN x
+    ELSE
+        k := sudan(n, x, y-1);
+        RETURN sudan(n-1, k, k+y)
+    END
+END sudan;
+
+PROCEDURE Show(n, x, y: CARDINAL);
+BEGIN
+    WriteString("sudan(");
+    WriteCard(n, 0);
+    WriteString(", ");
+    WriteCard(x, 0);
+    WriteString(", ");
+    WriteCard(y, 0);
+    WriteString(") = ");
+    WriteCard(sudan(n,x,y), 0);
+    WriteLn
+END Show;
+
+BEGIN
+    Show(0, 0, 0);
+    Show(1, 1, 1);
+    Show(2, 1, 1);
+    Show(3, 1, 1);
+    Show(2, 2, 1)
+END Sudan.

Task/Sudan-function/Nim/sudan-function.nim

@@ -0,0 +1,16 @@
+import std/[unicode, strformat]
+
+func sudan(n, x, y: Natural): int =
+  if n == 0: return x + y
+  if y == 0: return x
+  let z = sudan(n, x, y - 1)
+  return sudan(n - 1, z, z + y)
+
+const Delta = ord("₀".toRunes()[0]) - ord('0')
+
+func subscript(n: Natural): string =
+  for c in $n:
+    result.add Rune(ord(c) + Delta)
+
+for (n, x, y) in [(0, 0, 0), (1, 1, 1), (2, 1, 1), (2, 2, 1), (2, 2, 2), (3, 1, 1)]:
+  echo &"F{subscript(n)}({x}, {y}) = {sudan(n, x, y)}"

Task/Sudan-function/OCaml/sudan-function.ocaml

@@ -0,0 +1,4 @@
+let rec sudan = function
+  | 0, x, y -> x + y
+  | _, x, 0 -> x
+  | n, x, y -> let x' = sudan (n, x, pred y) in sudan (pred n, x', x' + y)

Task/Sudan-function/PHP/sudan-function.php

@@ -0,0 +1,16 @@
+#Aamrun , 11th July 2022
+
+<?php
+function F(int $n,int $x,int $y) {
+  if ($n == 0) {
+    return $x + $y;
+  }
+
+  else if ($y == 0) {
+    return $x;
+  }
+
+  return F($n - 1, F($n, $x, $y - 1), F($n, $x, $y - 1) + $y);
+}
+echo "F(1,3,3) = " . F(1,3,3);
+?>

Task/Sudan-function/Perl/sudan-function.pl

@@ -0,0 +1,16 @@
+use v5.36;
+use experimental 'for_list';
+
+sub F1($n, $x, $y) { $n ? $y ? F1($n-1, F2($n,$x,$y-1), F3($n,$x,$y-1)+$y) : $x : $x+$y }
+
+sub F2($n, $x, $y) { $n == 0 ? $x+$y : $y == 0 ? $x : F2($n-1, F1($n,$x,$y-1), F3($n,$x,$y-1)+$y) }
+
+sub F3($n, $x, $y) {
+  return $x + $y if $n == 0;
+  return $x      if $y == 0;
+  F3($n-1, F1($n, $x, $y-1), F2($n, $x, $y-1) + $y)
+}
+
+for my($n,$x,$y) (0,0,0, 1,1,1, 2,1,1, 3,1,1, 2,2,1) {
+    say join ' ',F1($n,$x,$y), F2($n,$x,$y), F3($n,$x,$y)
+}

Task/Sudan-function/Phix/sudan-function.phix

@@ -0,0 +1,25 @@
+(phixonline)-->
+ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
+ <span style="color: #008080;">function</span> <span style="color: #000000;">F</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">y</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #008080;">if</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #004080;">integer</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">F</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">return</span> <span style="color: #000000;">F</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">+</span><span style="color: #000000;">y</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+
+ <span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
+     <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Values of F(%d, x, y):\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"y/x    0   1   2   3   4   5\n"</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"----------------------------\n"</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
+         <span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #000000;">F</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span><span style="color: #000000;">y</span><span style="color: #0000FF;">})</span>
+         <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d  |%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%4d"</span><span style="color: #0000FF;">)})</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+
+ <span style="color: #008080;">for</span> <span style="color: #000000;">t</span> <span style="color: #008080;">in</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}}</span> <span style="color: #008080;">do</span>
+     <span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span>
+     <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"F(%d, %d, %d) = %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">F</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">)})</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+<!--

Task/Sudan-function/PureBasic/sudan-function.basic

@@ -0,0 +1,30 @@
+Procedure.d F(n.i, x.i, y.i)
+  If n = 0
+    ProcedureReturn x + y
+  ElseIf y = 0
+    ProcedureReturn x
+  Else
+    ProcedureReturn F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+  EndIf
+EndProcedure
+
+OpenConsole()
+For n = 0 To 1
+  PrintN("Values of F(" + Str(n) + ", x, y):")
+  PrintN("y/x     0       1       2       3       4       5")
+  PrintN("---------------------------------------------------")
+  For y = 0 To 6
+    Print(Str(y) + " |")
+    For x = 0 To 5
+      Print(#TAB$ + F(n,x,y))
+    Next x
+    PrintN("")
+  Next y
+  PrintN("")
+Next n
+
+PrintN("F(2,1,1) = " + Str(F(2,1,1)))
+PrintN("F(3,1,1) = " + Str(F(3,1,1)))
+PrintN("F(2,2,1) = " + Str(F(2,2,1)))
+Input()
+CloseConsole()

Task/Sudan-function/Python/sudan-function.py

@@ -0,0 +1,12 @@
+# Aamrun, 11th July 2022
+
+def F(n,x,y):
+  if n==0:
+    return x + y
+  elif y==0:
+    return x
+  else:
+    return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+
+
+print("F(1,3,3) = ", F(1,3,3))

Task/Sudan-function/QBasic/sudan-function.basic

@@ -0,0 +1,16 @@
+FUNCTION F(n,x,y)
+    IF n = 0 THEN
+       LET F = x + y
+    ELSE
+       IF y = 0 THEN
+          LET F = x
+       ELSE
+          LET F = F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+       END IF
+    END IF
+END FUNCTION
+
+PRINT "F(2,1,1) = "; F(2, 1, 1)
+PRINT "F(3,1,1) = "; F(3, 1, 1)
+PRINT "F(2,2,1) = "; F(2, 2, 1)
+END

Task/Sudan-function/Quackery/sudan-function.quackery

@@ -0,0 +1,20 @@
+  [ rot dup 0 = iff
+      [ drop + ] done
+    over 0 = iff
+      2drop      done
+    over temp put
+    dup 1 -
+    swap 2swap 1 -
+    recurse
+    dup temp take +
+    again ]           is sudan ( n x y --> f(n) )
+
+  ' [ [ 0 0 0 ]
+      [ 1 1 1 ]
+      [ 1 3 3 ]
+      [ 2 1 1 ]
+      [ 2 2 1 ]
+      [ 3 1 1 ] ]
+  witheach
+    [ dup echo say " = "
+    do sudan echo cr ]

Task/Sudan-function/R/sudan-function.r

@@ -0,0 +1,18 @@
+#Aamrun, 11th July 2022
+
+F <- function(n, x, y) {
+  if(n==0){
+  	F <- x+y
+    return (F)
+  }
+
+  else if(y == 0) {
+    F <- x
+    return (F)
+  }
+
+  F <- F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+  return (F)
+}
+
+print(paste("F(1,3,3) = " , F(1,3,3)))

Task/Sudan-function/REXX/sudan-function.rexx

@@ -0,0 +1,25 @@
+/* REXX implement the SUDAN function */
+Say '+---++-------------------------+'
+Say '| y ||x= 0   1   2   3   4   5 |'
+Say '+===++=========================+'
+Do y=0 To 6
+  s='|' y '||'
+  Do x=0 To 5
+    s=s format(sudan(x,y),3)
+    End
+  Say s '|'
+  End
+Say '+===++=========================+'
+Exit
+
+sudan: Procedure
+  Parse Arg x,y
+  Return sudan1(1,x,y)
+
+sudan1: Procedure
+  Parse Arg n,x,y
+  Select
+    When n=0 Then Return x+y
+    When y=0 Then Return x
+    Otherwise Return sudan1(n-1,sudan1(n,x,y-1),sudan1(n,x,y-1)+y)
+    End

Task/Sudan-function/Raku/sudan-function.raku

@@ -0,0 +1,11 @@
+multi F (0, $x, $y) { $x + $y }
+multi F ($n where * > 0, $x, 0) { $x }
+multi F ($n, $x, $y) { F($n-1, F($n, $x, $y-1), F($n, $x, $y-1) + $y) }
+
+# Testing
+for 0, 6, 1, 15 -> $f, $g {
+    my @range = ^$g;
+    say "\{|class=\"wikitable\"\n", "|+ F\<sub>$f\</sub> (x,y)\n" ~ '!x\y!!', join '!!', @range;
+    -> $r { say "|-\n" ~ '|' ~ join '||', $r, @range.map:{ F($f, $r, $_) } } for @range;
+    say( "|}" );
+}

Task/Sudan-function/Ruby/sudan-function.rb

@@ -0,0 +1,6 @@
+def sudan(n, x, y)
+  return x + y if n == 0
+  return x if y == 0
+
+  sudan(n - 1, sudan(n, x, y - 1), sudan(n, x, y - 1) + y)
+end

Task/Sudan-function/Run-BASIC/sudan-function.basic

@@ -0,0 +1,16 @@
+FUNCTION F(n,x,y)
+    IF n = 0 THEN
+       LET F = x + y
+    ELSE
+       IF y = 0 THEN
+          LET F = x
+       ELSE
+          LET F = F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+       END IF
+    END IF
+END FUNCTION
+
+PRINT "F(2,1,1) = "; F(2, 1, 1)
+PRINT "F(3,1,1) = "; F(3, 1, 1)
+PRINT "F(2,2,1) = "; F(2, 2, 1)
+END

Task/Sudan-function/Swift/sudan-function-1.swift

@@ -0,0 +1,15 @@
+//Aamrun, 3rd February 2023
+
+func F(n: Int,x: Int,y: Int) -> Int {
+  if (n == 0) {
+    return x + y;
+  }
+
+  else if (y == 0) {
+    return x;
+  }
+
+    return F(n: n - 1, x: F(n: n, x: x, y: y - 1), y: F(n: n, x: x, y: y - 1) + y);
+}
+
+print("F1(3,3) = " + String(F(n: 1,x: 3,y: 3)));

Task/Sudan-function/Swift/sudan-function-2.swift

@@ -0,0 +1,15 @@
+//Aamrun, 3rd February 2023
+
+func F(n: Int,x: Int,y: Int) -> Int {
+  if n == 0 {
+    return x + y
+  }
+
+  else if y == 0 {
+    return x
+  }
+
+    return F(n: n - 1, x: F(n: n, x: x, y: y - 1), y: F(n: n, x: x, y: y - 1) + y)
+}
+
+print("F1(3,3) = " + String(F(n: 1,x: 3,y: 3)))

Task/Sudan-function/True-BASIC/sudan-function.basic

@@ -0,0 +1,16 @@
+FUNCTION F(n,x,y)
+    IF n = 0 THEN
+       LET F = x + y
+    ELSE
+       IF y = 0 THEN
+          LET F = x
+       ELSE
+          LET F = F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+       END IF
+    END IF
+END FUNCTION
+
+PRINT "F(2,1,1) = "; F(2, 1, 1)
+PRINT "F(3,1,1) = "; F(3, 1, 1)
+PRINT "F(2,2,1) = "; F(2, 2, 1)
+END

Task/Sudan-function/V-(Vlang)/sudan-function.v

@@ -0,0 +1,29 @@
+fn sudan(n int, x int, y int) int {
+    if n == 0 {
+       return x + y
+    }
+    if y == 0 {
+        return x
+    }
+    return sudan(n-1, sudan(n, x, y-1), sudan(n, x, y-1) + y)
+}
+
+fn main() {
+    for n := 0; n < 2; n++ {
+        println("Values of F($n, x, y):")
+        println("y/x    0   1   2   3   4   5")
+        println("----------------------------")
+        for y := 0; y < 7; y++ {
+            print("$y  |")
+            for x := 0; x < 6; x++ {
+                s := sudan(n, x, y)
+                print("${s:4}")
+            }
+            println('')
+        }
+        println('')
+    }
+    println("F(2, 1, 1) = ${sudan(2, 1, 1)}")
+    println("F(3, 1, 1) = ${sudan(3, 1, 1)}")
+    println("F(2, 2, 1) = ${sudan(2, 2, 1)}")
+}

Task/Sudan-function/Wren/sudan-function.wren

@@ -0,0 +1,25 @@
+import "./fmt" for Fmt
+
+var F = Fn.new { |n, x, y|
+    if (n == 0) return x + y
+    if (y == 0) return x
+    return F.call(n - 1, F.call(n, x, y-1), F.call(n, x, y-1) + y)
+}
+
+for (n in 0..1) {
+    System.print("Values of F(%(n), x, y):")
+    System.print("y/x    0   1   2   3   4   5")
+    System.print("----------------------------")
+    for (y in 0..6) {
+        System.write("%(y)  |")
+        for (x in 0..5) {
+            var sudan = F.call(n, x, y)
+            Fmt.write("$4d", sudan)
+        }
+        System.print()
+    }
+    System.print()
+}
+System.print("F(2, 1, 1) = %(F.call(2, 1, 1))")
+System.print("F(3, 1, 1) = %(F.call(3, 1, 1))")
+System.print("F(2, 2, 1) = %(F.call(2, 2, 1))")

Task/Sudan-function/XBasic/sudan-function.basic

@@ -0,0 +1,40 @@
+PROGRAM	"Sudan function"
+VERSION	"0.0000"
+
+DECLARE FUNCTION Entry ()
+DECLARE FUNCTION F (n, x, y)
+
+FUNCTION Entry ()
+FOR n = 0 TO 1
+    PRINT " Values of F("; n; ", x, y ):"
+    PRINT " y/x    0   1   2   3   4   5"
+    PRINT " ----------------------------"
+    FOR y = 0 TO 6
+        PRINT y; "  |";
+        FOR x = 0 TO 5
+            PRINT FORMAT$("####", F(n, x, y));
+        NEXT x
+        PRINT
+    NEXT y
+    PRINT
+NEXT n
+
+PRINT "F(2,1,1) ="; F(2, 1, 1)
+PRINT "F(3,1,1) ="; F(3, 1, 1)
+PRINT "F(2,2,1) ="; F(2, 2, 1)
+
+END FUNCTION
+
+FUNCTION F (n, x, y)
+    IF n = 0 THEN
+        RETURN x + y
+    ELSE
+        IF y = 0 THEN
+            RETURN x
+        ELSE
+            RETURN F (n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+        ENDIF
+    ENDIF
+
+END FUNCTION
+END PROGRAM

Task/Sudan-function/XPL0/sudan-function.xpl0

@@ -0,0 +1,24 @@
+func F; int N, X, Y;
+[if N = 0 then return X + Y;
+ if Y = 0 then return X;
+return F(N-1, F(N, X, Y-1), F(N, X, Y-1) + Y);
+];
+
+int N, X, Y;
+[Format(4, 0);
+for N:= 0 to 1 do
+    [Text(0, "Values of F("); IntOut(0, N);  Text(0, ", X, Y):^m^j");
+     Text(0, "Y/X    0   1   2   3   4   5^m^j");
+     Text(0, "----------------------------^m^j");
+     for Y:= 0 to 6 do
+        [IntOut(0, Y);  Text(0, "  |");
+        for X:= 0 to 5 do
+            RlOut(0, float(F(N, X, Y)));
+        CrLf(0);
+        ];
+    CrLf(0);
+    ];
+Text(0, "F(2, 1, 1) = ");  IntOut(0, F(2, 1, 1));  CrLf(0);
+Text(0, "F(3, 1, 1) = ");  IntOut(0, F(3, 1, 1));  CrLf(0);
+Text(0, "F(2, 2, 1) = ");  IntOut(0, F(2, 2, 1));  CrLf(0);
+]

Task/Sudan-function/Yabasic/sudan-function.basic

@@ -0,0 +1,24 @@
+for n = 0 to 1
+    print "Values of F(", n, ", x, y):"
+    print "y/x    0   1   2   3   4   5"
+    print "----------------------------"
+    for y = 0 to 6
+        print y, "  | ";
+        for x = 0 to 5
+            print F(n,x,y) using ("###");
+        next x
+        print
+    next y
+    print
+next n
+
+print "F(2,1,1) = ", F(2,1,1)
+print "F(3,1,1) = ", F(3,1,1)
+print "F(2,2,1) = ", F(2,2,1)
+end
+
+sub F(n, x, y)
+    if n = 0  return x + y
+    if y = 0  return x
+    return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)
+end sub