Implement power function without using multiplication and division operators (Iterative Approach)

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Implement power function without using multiplication and division operators (Iterative Approach)
vinaykhatri

Vinay Khatri
Last updated on May 22, 2024

    Problem

    Given two positive integers x and y, implement x y without using multiplication or division operator

    Sample Input

    x = 2
    y = 4
    

    Sample Output

    16

    Explanation

    24 = 16

    Approach

    We will use a nested loop to solve this problem. This method is very simple and obvious if you know the concept of exponentiation, as shown below. To calculate 24, use the below steps:

    1) 2 times add 2, we get 4. (2^2)

    2) 2 times add 4, we get 8. (2^3)

    3) 2 times add 8, we get 16 (2^4), which is our answer.

    Complexity Analysis

    The time complexity is O( x y ), and the space complexity is O(1)

    C++ Programming

    #include <bits/stdc++.h>
    using namespace std;
    
    // find exponent
    int solve(int x, int y)
    {
        if (y == 0)
            return 1;
    
        int ans = x;
        int temp = x;
        int i, j;
    
        for(i = 1; i < y; i++)
        {
            for(j = 1; j < x; j++)
            {
                ans += temp;
            }
            temp = ans;
        }
        return ans;
    }
    
    int main()
    {
        cout << solve(2, 4);
        return 0;
    }

    Output

    16

    Java Programming

    import java.io.*;
    // implement power function
    
    class Main {
        static int solve(int x, int y)
        {
            if (y == 0)
                return 1;
               
            int ans = x;
            int temp = x;
            int i, j;
            
            for (i = 1; i < y; i++) {
                for (j = 1; j < x; j++) {
                    ans += temp;
                }
                temp = ans;
            }
    
            return ans;
        }
    
        public static void main(String[] args)
        {
            System.out.println(solve(2, 4));
        }
    }

    Output

    16

    Python Programming

    # implement power function
    def solve(x,y):
        if(y==0):
            return 1
            
        ans=x
        temp=x
        
        for i in range(1,y):
            for j in range (1,x):
                ans+=temp
            temp=ans
        return ans
    
    print(solve(2,4))

    Output

    16

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