Question

I have the following function:

int mult(int y, int z)
{
  if (z == 0)
    return 0;
  else if (z % 2 == 1)
    return mult(2 * y, z / 2) + y;
  else 
    return mult(2 * y, z / 2);
}

What I need to do is prove its correctness by induction. Now the trouble I’m having is that even though I know it works since I ran it I can’t follow each individual step.

What is confusing me is that y only shows up as an argument and in no place does it show up in a return except in the recursive part, and yet the function actually returns y as the answer.

How does this happen? I need to be able to follow everything that happens so that I can do the iterations of it for the proof.

Answer 1

step-by-step analisis

final result: 100
 mult(10, 10)
 {
     makes 100
     mult(20, 5)
     {
         makes 100
         mult(40, 2) + 20
         {
              makes 80
             mult(80, 1)
             {
                   makes 80
                  mult(160, 0) + 80
                  {
                        return 0;
                  }
             }
         }
     }
 }