Question

in code c++ describe a recursive algorithm for multiplying two nonnegative integers x and y based on the fact that xy = 2(x · (y/2)) when y is even and xy = 2(x · ⌊y/2⌋) + x when y is odd, together with the initial condition xy = 0 when y = 0.

Answer 1

// C++ Program to find Product
// of 2 Numbers using Recursion
#include <bits/stdc++.h>
#include <math.h>
using namespace std;

// recursive function to calculate
// multiplication of two numbers
int product(int x, int y)
{    if(y==0) //return ) if y is 0 intial condition
       return 0;
   // if y is even
   else if (y%2==0)
       return (2*product(x, y/2));

   // if y is odd
   else
       return (x + 2*product(x, floor((y - 1)/2)));

   // if any of the two numbers is
   // zero return zero
   }

// Driver Code
int main()
{
   int x = 23, y = 3;
   cout << product(x, y);
   return 0;
}
Output :

69

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