Sudan function

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Revision as of 18:43, 11 July 2022 by Jquorning (talk | contribs) (Ada version)
Task
Sudan function
You are encouraged to solve this task according to the task description, using any language you may know.

The Sudan function is a classic example of a recursive function, notable especially because it is not a 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 (svg): 

  <big>
    :<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>
  </big>
Task

Write a function which returns the value of F(x, y).

Ada

Translation of: Javascript

<lang Ada>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;</lang>

Output:
F0 (0, 0) =  0
F1 (1, 1) =  3
F1 (3, 3) =  35
F2 (1, 1) =  8
F2 (2, 1) =  27
F3 (1, 1) =  10228

C

Translation of: Javascript

<lang C> //Aamrun, 11th July 2022

  1. 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;

} </lang>

Output 

F1(3,3) = 35

C++

Translation of: C

<lang cpp> //Aamrun , 11th July, 2022

  1. 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;

} </lang> Output 

F(1,3,3) = 35

C#

Translation of: C

<lang csharp> //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));    
   }
 }

} </lang> Output 

F(1,3,3) = 35

Go

Translation of: Wren

<lang go>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))

}</lang>

Output:
Identical to Wren example.

Hoon

<lang Hoon> |= [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)) </lang>

J

Translation of: Javascript

This is, of course, not particularly efficient and some results are too large for a computer to represent. <lang J>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</lang>

Examples: <lang J> 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</lang>

Java

Translation of: C

<lang Java> //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));
 }

} </lang> Output 

F(1,3,3) = 35

JavaScript

<lang Javascript> /** 

* @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);

} </lang>

PHP

Translation of: C

<lang php>

  1. 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); ?> </lang> Output 

F(1,3,3) = 35

Julia

<lang ruby>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)))

</lang>

Output:
sudan(0, 0, 0) = 0
sudan(1, 1, 1) = 3
sudan(2, 1, 1) = 8
sudan(3, 1, 1) = 10228
sudan(2, 2, 1) = 27

Python

Translation of: Javascript

<lang Python>

  1. 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)) </lang>

Output 

F(1,3,3) =  35

R

Translation of: C

<lang rsplus>

  1. 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))) </lang> Output 

[1] "F(1,3,3) =  35"

Vlang

Translation of: Wren

<lang ruby>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)}")

}</lang>

Output:
Identical to Wren example.

Wren

Library: Wren-fmt

<lang ecmascript>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))")</lang>

Output:
Values of F(0, x, y):
y/x    0   1   2   3   4   5
----------------------------
0  |   0   1   2   3   4   5
1  |   1   2   3   4   5   6
2  |   2   3   4   5   6   7
3  |   3   4   5   6   7   8
4  |   4   5   6   7   8   9
5  |   5   6   7   8   9  10
6  |   6   7   8   9  10  11

Values of F(1, x, y):
y/x    0   1   2   3   4   5
----------------------------
0  |   0   1   2   3   4   5
1  |   1   3   5   7   9  11
2  |   4   8  12  16  20  24
3  |  11  19  27  35  43  51
4  |  26  42  58  74  90 106
5  |  57  89 121 153 185 217
6  | 120 184 248 312 376 440

F(2, 1, 1) = 8
F(3, 1, 1) = 10228
F(2, 2, 1) = 27
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