Sudan function
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.
You are encouraged to solve this task according to the task description, using any language you may know.
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).
C
<lang C> //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;
} </lang>
Output
F1(3,3) = 35
C++
<lang cpp> //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;
} </lang> Output
F(1,3,3) = 35
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
<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
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
<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
<lang php>
- 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
<lang Python>
- 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
<lang rsplus>
- 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"
Wren
<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