C program to generate the value of x power n using recursive function

In C programming, calculating xⁿ (x raised to the power n) can be efficiently done using recursive functions. This approach breaks down the problem into smaller subproblems, making the solution elegant and mathematically intuitive.

Syntax

long int power(int x, int n);

Algorithm

The recursive algorithm uses the following mathematical properties −

• If n = 1, then xⁿ = x (base case)
• If n is even, then xⁿ = (x^n/2)²
• If n is odd, then xⁿ = x × x^n-1

Example: Recursive Power Function

Here's a complete C program that calculates xⁿ using recursion −

#include <stdio.h>
#include <math.h>

long int power(int x, int n) {
    if (n == 1)
        return x;
    else if (n % 2 == 0)
        return pow(power(x, n/2), 2); /* if n is even */
    else
        return x * power(x, n-1); /* if n is odd */
}

int main() {
    long int x, n, result;
    
    printf("Enter the values of X and N: 
");
    scanf("%ld %ld", &x, &n);
    
    result = power(x, n);
    printf("X to the power N = %ld
", result);
    
    return 0;
}

Enter the values of X and N: 
5 4
X to the power N = 625

How It Works

For the input x=5, n=4, the recursive calls work as follows −

• power(5, 4): n is even, so calculate pow(power(5, 2), 2)
• power(5, 2): n is even, so calculate pow(power(5, 1), 2)
• power(5, 1): base case, returns 5
• Back to power(5, 2): returns pow(5, 2) = 25
• Back to power(5, 4): returns pow(25, 2) = 625

Key Points

• The algorithm has O(log n) time complexity due to the divide-and-conquer approach
• Using pow() function requires #include <math.h>
• The base case prevents infinite recursion

Conclusion

Recursive power calculation provides an efficient solution with logarithmic time complexity. The divide-and-conquer strategy significantly reduces the number of multiplications compared to iterative approaches.