## Ackermann function with C++

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is notprimitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.

After Ackermann’s publication[1] of his function (which had three nonnegative integer arguments), many authors modified it to suit various purposes, so that today “the Ackermann function” may refer to any of numerous variants of the original function. One common version, the two-argument Ackermann–Péter function, is defined as follows for nonnegative integers m and n:

Its value grows rapidly, even for small inputs. For example A(4,2) is an integer of 19,729 decimal digits.

```#include <stdio.h>
/* The three conditions can be found here:
http://en.wikipedia.org/wiki/Ackermann%27s_function
*/
int acker(int m, int n){
if (m == 0) return (n + 1);
else if ((m > 0) && (n == 0)){
return acker(m-1, 1);
}
else if ((m > 0) && (n > 0)){
return acker(m-1, acker(m, n-1));
}
}
/*sample usage*/
int main(){
/*iterate through the first 4 "pairs"
1 3 7 61
*/
for(int i = 0; i < 4; i++){
printf("%d ", acker(i,i));
}
return 0;
}```