Multiplying using recursive function C++ - c++

Question

I did a recursive function to calculate x*y with x and y are all integers (x and y >= 0). My formula is:
x * y =
0, if x is equal 0
(x >> 1)*(y << 1), if x is an even number
(x >> 1)*(y << 1) + y, if x is an odd number
"<<" and ">>" are Left Shift and Right Shift Bitwise Operator. Here is my code:
int multiply(int x, int y) {
int y1 = 0;
if (x == 0) return 0;
else if (x % 3 == 0) {
y1 = y;
x = x >> 1;
y = y << 1;
return (multiply(x, y) + y1);
}
else if (x % 2 == 0) {
x = x >> 1;
y = y << 1;
return multiply(x, y);
}
}
The recursive function above is supposed to return (x*y) value but they were all wrong when i tested and i don't know why. What did i do wrong? How can i fix this?

Answer 1

Your problem is wit x % 3, what happens if x = 5? you skip it. Here is improved version of your code.
int multiply(int x, int y) {
if (x == 0)
return 0;
else if (x % 2 == 1)
return (multiply(x >> 1, y << 1) + y);
return multiply(x >> 1, y << 1);
}
or maybe even this:
int multiply(int x, int y) {
if (x == 0)
return 0;
int m = multiply(x >> 1, y << 1);
if (x % 2 == 1)
m += y;
return m;
}
Here is super fast version suggested by Andy:
int multiply(int x, int y) {
if (x == 0)
return 0;
int m = multiply(x >> 1, y << 1);
if (x & 1)
m += y;
return m;
}
As a challenge of speed, here is non recursive version:
int multiply (int x, int y) {
int y1 = 0;
for (; x > 0; x = (x >> 1), y = (y << 1))
if (x&1)
y1 += y;
return y1;
}
NOTE: I know this question is about recursive method but just as a challenge I wrote non-recursive algorithm.

Answer 2

You are not checking if x is odd correctly here:
else if (x % 3 == 0) { // e.g. fails on x = 1
Instead, you need to do
else if (x % 2 == 1) {
Here's a demo.
Note that this makes the following else check for even values of x redundant:
else if (x % 2 == 0) { // can just be an unconditional else
Also, since you are returning from the x == 0, and x % 2 == 1 branches, the else conditions can be removed as well. You can also factor out the repeated code to make the function simpler, like this:
int multiply(int x, int y) {
if (x == 0) return 0;
if (x % 2 == 1)
return (multiply(x >> 1, y << 1) + y);
else
return multiply(x >> 1, y << 1);
}
Here's a demo.

Answer 3

This is what i feel is the simplest approach to carry out recursive multiplication.
Do let me know if its efficient enough for you.
#include<iostream>
using namespace std;
float multiply(float a, float b) {
//no zeros bro
if (b == 0)
return 0;
//let the recursion begin
if (b > 0)
return x + multiply(a, b - 1);
//negatives stay away pliz
if (y < 0)
return -multiply(a, -b);
}
int main() {
float a, b, result;
cout << "Enter the two numbers";
cin >> a >> b;
result = multiply(a, b);
//And the result is.................
cout << result;
return 0;
}

Answer 4

Recursive function related to multiplication of natural numbers:
int multCool(int a, int b)
{
return (b==1 ? a: a+ multCool(a,b-1));
}