Question

MUST BE ANSWERED BY USING C++

Please explain the code as well.

Question 1

Write a recursive function defined by the following recursive formula:

foo (Y, X) =

    Y                                                            if X = 1

    0                                                             if X = Y

    (foo ( Y-1, X-1) + 3* foo ( Y-1, X))      if Y > X > 1

Write a driver to print out the value for foo (5, 4)    and foo (7, 5).

In addition, print out the total number of recursive function calls in each case.

Answer 1

#include <iostream>
using namespace std;

int count;

int foo(int X, int Y){
    count++;
    // Checking if X is 1
    if(X==1)
        return Y;
    // Checking if both X and Y are equal
    else if(X==Y)
        return 0;
    // Checking if both X and Y are greater than 1
    else if(Y>1 && X>1) 
        return foo ( Y-1, X-1) + 3* foo ( Y-1, X);
    // if all the above conditions not apply
    else 
        return 0;
}

int main()
{
    // testing function foo
    count = 0;
    cout<<"foo(5,4): "<<foo(5,4)<<endl;
    cout<<"The total number of recursive function calls: "<<count<<endl;
    count = 0;
    cout<<"foo(7,5): "<<foo(7,5)<<endl;
    cout<<"The total number of recursive function calls: "<<count<<endl;
    return 0;
}

foo(5,4): 947
The total number of recursive function calls: 19
foo(7,5): 20586
The total number of recursive function calls: 73