Power of a Number using Recursion in C++

January 18, 2022

Power of a Number using Recursion in C++

Here, in this page we will discuss the program to find power of a number using recursion in C++ programming language. We are given with two integers values base and power respectively. We need to print the value representing the base raise to its power. We will design the program using recursion and also discuss the approach using iteration as well.

Example :

Input : 5 3
Output : 125
Explanation : 5³ = 125

Method 1 (Using Recursion):

Create a recursive function say power(int base, int x)
Base condition : if(x==0) return 1.
Otherwise, return (base* power(base, x-1))

Time and Space Complexity :

Time Complexity : O(x), x denotes the power.
Space Complexity : O(1)

Code to find Power of a Number using Recursion in C++

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

//Recursive Function
int power(int base, int x){

   if(x==0) //Base Condition
     return 1;

   return (base*power(base, x-1));
}

//Driver Code
int main(){

   int base = 5, x = 3;

   cout<<"Required Power is "<<power(base, x);

}

Output

Required Power is 125

Method 2 (Using Loop):

Create a function say power(int base, int x), that will return the integer value denoting the base^x.
Create a variable say result = 1, that hold the base^x.
Run a while loop that will terminate when x becomes 0.
Inside the loop set result = result * base.
After complete iteration return result.

Time and Space Complexity :

Time Complexity : O(x), x denotes the power.
Space Complexity : O(1)

Code to find Power of a Number using loop in C++

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

int power(int base, int x){

   int result=1;
   while(x--){
       result *= base;
   }

   return result;
}

//Driver Code
int main(){

    int base = 5, x = 3;

    cout<<"Required Power is "<<power(base, x);

}

Output

Required Power is 125