Sample Assignments: The One on Recursive Functions


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

\left\{\begin{matrix}A(0, n) = n + 1, \\ A(m, 0) = A(m - 1, 1), \\ A(m,n) = A(m - 1,A(m, n - 1)). \end{matrix}\right.

Find the recursion depth.

Block-scheme of the solution:


C++ implementation:

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
		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





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


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