Question

Without using a division or multiplication operator and without using iteration , define a recursive method named product that accepts two int parameter , m and k, and calculates and returns the integer product of m times k . you can count on m>=0 and k>=0.

Answer 1

I will be using the language C++. Given the problem specification, there are an large variety of solving the problem, ranging from simple addition, to more complicated bit testing and selection. But since the problem isn't exactly high performance or practical, I'll use simple addition. For a recursive function, you need to create a condition that will prevent further recursion, I'll use the condition of multiplying by 0. Also, you need to define what your recursion is.
To wit, consider the following math expression 
 f(m,k) = 0 if m = 0, otherwise f(m-1,k) + k 
 If you calculate f(0,k), you'll get 0 which is exactly what 0 * k is. 
 If you calculate f(1,k), you'll get 0 + k, which is exactly what 1 * k is.   
 So here's the function   
 int product(int m, int k) 
 { 
  if (m == 0) return 0; 
  return product(m-1,k) + k;  
}