C++ Program To Find Power Without Using Multiplication(*) And Division(/) Operators

Given two non-negative integers a and b, the task is to calculate a raised to the power b without using the multiplication (*) and division (/) operators.

Multiplication can be replaced with repeated addition to calculate the power.
The same idea can be implemented using loops or recursion.

Example

For a = 5 and b = 3:
5^3 = 5 × 5 × 5 = 125

Approaches to Find Power Without Multiplication and Division

The power can be calculated using the following approaches:

1. Using Nested Loops

The idea is to replace every multiplication with repeated addition. For each power, the previous result is added a times.

For example, to calculate 5^3:

Add 5 five times to get 25 (5^2).
Add 25 five times to get 125 (5^3).

C++

#include <bits/stdc++.h>
using namespace std;

// Works only if a >= 0 and b >= 0
int pow(int a, int b)
{
    if (b == 0)
        return 1;

    int answer = a;
    int increment = a;

    for (int i = 1; i < b; i++)
    {
        for (int j = 1; j < a; j++)
        {
            answer += increment;
        }

        increment = answer;
    }

    return answer;
}

// Driver Code
int main()
{
    cout << pow(5, 3);
    return 0;
}

Output

Explanation

answer stores the current power, while increment stores the value that is repeatedly added.
The outer loop calculates each successive power, and the inner loop performs multiplication using repeated addition.
When b is 0, the function returns 1 because a^0 = 1.

2. Using Recursion

The multiplication of two numbers is first implemented using recursive addition. This multiplication function is then used recursively to calculate the power.

C++

#include <bits/stdc++.h>
using namespace std;

// Recursive function to calculate x * y
// using addition
int multiply(int x, int y)
{
    if (y)
        return x + multiply(x, y - 1);
    else
        return 0;
}

// Recursive function to calculate a^b
// Works only if a >= 0 and b >= 0
int pow(int a, int b)
{
    if (b)
        return multiply(a, pow(a, b - 1));
    else
        return 1;
}

// Driver Code
int main()
{
    cout << pow(5, 3);
    return 0;
}