C++ Program to Calculate Power of a Number

The power of a number can be calculated as x^y where x is the number and y is its power.

For example.

Let’s say, x = 2 and y = 10
   x^y =1024
   Here, x^y is 2^10

Power of a number can be calculated using recursive and non-recursive programs. Each of these are given as follows.

Power of a Number Using Non-Recursive Program

The program to find the power of a number using a non-recursive program is given as follows −

Example

#include<iostream>
using namespace std;
int power(int x, int y) {
   int i,power=1;
   if(y == 0)
   return 1;
   for(i=1;i<=y;i++)
   power=power*x;
   return power;
}
int main() {
   int x = 3;
   int y = 4;
   cout<<"x = "<<x<<endl;;
   cout<<"y = "<<y<<endl;
   cout<<"x^y = "<<power(x,y);
   return 0;
}

x = 3
y = 4
x^y = 81

In the above program, the function power() is used to calculate the power of a number. It is a non-recursive function. In the function, a for loop is used which runs from 1 to y. For each iteration of the loop, x is multiplied with power.

So, x is multiplied with itself y times and the result is stored in power. This leads to x^y being stored in power. Then power is returned to the main() function.

The following code snippet demonstrates this −

int power(int x, int y) {
   int i, power = 1;
   if(y==0)
   return 1;
   for(i=1;i<=y;i++)
   power = power*x;
   return power;
}

In main(), the values of x, y and x^y are displayed. This is shown in the code snippet given below −

cout<<"x = "<<x<<endl;;
cout<<"y = "<<y<<endl;
cout<<"x^y = "<<power(x,y);

Power of a Number Using Recursive Program

The program to find the power of a number using a recursive program is given as follows.

Example

#include<iostream>
using namespace std;
int power(int x, int y) {
   if (y == 0)
   return 1;
   else if (y%2 == 0)
   return power(x, y/2)*power(x, y/2);
   else
   return x*power(x, y/2)*power(x, y/2);
}
int main() {
   int x = 3;
   int y = 4;
   cout<<"x = "<<x<<endl;;
   cout<<"y = "<<y<<endl;
   cout<<"x^y = "<<power(x,y);
   return 0;
}

Output

x = 3
y = 4
x^y = 81

In the above program, power() is a recursive function. If the value of y is 0, it returns 1. If y is even, it recursively calls itself with the values x and y/2 and returns power(x, y/2)*power(x, y/2). If y is odd, it recursively calls itself with the values x and y/2 and returns x*power(x, y/2)*power(x, y/2). This is demonstrated by the following code snippet.

int power(int x, int y) {
   if (y == 0)
   return 1;
   else if (y%2 == 0)
   return power(x, y/2)*power(x, y/2);
   else
   return x*power(x, y/2)*power(x, y/2);
}

In main(), the values of x, y and x^y are displayed. This is shown in the code snippet given below.

cout<<"x = "<<x<<endl;;
cout<<"y = "<<y<<endl;
cout<<"x^y = "<<power(x,y);