Task:

Find the function of the Ackerman fuction A(m, n), using the recurrence relations:

Find the recursion depth.

Block-scheme of the solution:

C++ implementation:

#include<iostream> using namespace std; int depth; int Ackerman(int m, int n)//Ackerman function { depth++;//calculate the recursion depth if (m == 0) return n + 1;//end of the recursion else { if (n == 0) return Ackerman(m - 1, 1);//recursy else return Ackerman(m - 1, Ackerman(m, n - 1)); } } void main() { int m, n, result; cout << "Input m > 0, n > 0:" << endl; cin >> m >> n;//input m & n if (n >= 0 && m >= 0)//n & m must be >= 0 { result = Ackerman(m, n);//calculate solution, call Accerman function cout << "Ackerman(" << m << "," << n << ")=" << result << endl << "recursion depth = " << depth << endl;//output m, n, solution, recursion depth } else cout << "m or n < 0" << endl;//if m & n < 0 system("pause");//pause console }

Screenshots:

Let’s use the table of values of Ackerman function from the Wikipedia to ensure that the program works properly:

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