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

Last Updated : 17 Jan, 2023

Method 1 (Using Nested Loops):
We can calculate power by using repeated addition.
For example to calculate 5^6.
1) First 5 times add 5, we get 25. (5^2)
2) Then 5 times add 25, we get 125. (5^3)
3) Then 5 times add 125, we get 625 (5^4)
4) Then 5 times add 625, we get 3125 (5^5)
5) Then 5 times add 3125, we get 15625 (5^6)

C++

// C++ code for power function 
#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; 
    int i, j; 
    for(i = 1; i < b; i++) 
    { 
        for(j = 1; j < a; j++) 
        { 
            answer += increment; 
        } 
        increment = answer; 
    } 
    return answer; 
} 

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

// This code is contributed by rathbhupendra

Output :

Time Complexity: O(a * b)

Auxiliary Space: O(1)

Method 2 (Using Recursion)
Recursively add a to get the multiplication of two numbers. And recursively multiply to get a raise to the power b.

C++

// C++ program to implement 
// the above approach
#include<bits/stdc++.h>
using namespace std;

// A recursive function 
// to get x*y
int multiply(int x, int y)
{
    if(y)
        return (x + multiply(x, 
                y - 1));
    else
        return 0;
}

// A recursive function to get 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);
    getchar();
    return 0;
}

// This code is contributed by Akanksha Rai

Output :

Time Complexity: O(b)

Auxiliary Space: O(b)

Method 3 (Using bit masking)

we can a^n (let's say 3^5) as 3^4 * 3^0 * 3^1 = 3^, so we can represent 5 as its binary i.e. 101

C++

// C++ program to implement
// the above approach
#include <iostream>
using namespace std;

// Function calculating power
long long pow(int a, int n)
{
    int ans = 1;
      while(n > 0)
      {
          // Calculate last bit(right most) 
          // bit of n
          int last_bit = n&1;
          
          // if last bit is 1 then multiply 
          // ans and a
          if(last_bit)
          {
            ans = ans*a;
          }
      
      // Make a equal to square of a as on 
      // every succeeding bit it got squared 
      // like a^0, a^1, a^2, a^4, a^8
      a = a * a;
      n = n >> 1;
    }
      return ans;
}

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