C++ Program to Calculate Power Using Recursion

1. Introduction

In mathematics, raising a number to a power means multiplying the number by itself for a specified number of times. For instance, 3 raised to the power of 4 (3^4) is 3 x 3 x 3 x 3 = 81. In programming, one can compute powers in multiple ways, and recursion offers a clean and logical method for such tasks. This blog post will walk you through a C++ program that calculates the power of a number using recursion.

2. Program Overview

The program's mechanism is as follows:

1. Get base and exponent input from the user.

2. If the exponent is zero, return 1 (as any number raised to the power of 0 is 1).

3. Otherwise, recursively multiply the base by itself until the exponent becomes zero.

4. Display the computed result to the user.

3. Code Program

#include <iostream>
using namespace std;

// Function to calculate power using recursion
double power(double base, int exponent) {
    if(exponent == 0) {
        return 1;
    } else if(exponent < 0) {
        return 1 / power(base, -exponent);  // Dealing with negative exponents
    } else {
        return base * power(base, exponent - 1);
    }
}

int main() {
    double base;
    int exponent;

    // Taking user input
    cout << "Enter base: ";
    cin >> base;
    cout << "Enter exponent: ";
    cin >> exponent;

    cout << base << " raised to the power of " << exponent << " = " << power(base, exponent);

    return 0;  // Signal successful termination
}

Output:

For input values of base 3 and exponent 4, the output will be:
"3 raised to the power of 4 = 81"

4. Step By Step Explanation

1. Headers and Namespace: The I/O stream library is included, and the standard namespace is set up for simplified input and output operations.

#include <iostream>
using namespace std;

2. Recursive Function: The power function is the heart of this program. When the exponent is zero, the function returns 1. For negative exponents, the function calls itself with the positive value of the exponent and divides 1 by the result, giving the reciprocal. For positive exponents, the base is multiplied recursively.

// Function to calculate power using recursion
double power(double base, int exponent) {
    if(exponent == 0) {
        return 1;
    } else if(exponent < 0) {
        return 1 / power(base, -exponent);  // Dealing with negative exponents
    } else {
        return base * power(base, exponent - 1);
    }
}

3. Main Function: Here, the program begins. The base and exponent variables are initialized, and user input is taken using cin. The program then calls the power function and prints the result using cout.

int main() {
    double base;
    int exponent;

    // Taking user input
    cout << "Enter base: ";
    cin >> base;
    cout << "Enter exponent: ";
    cin >> exponent;

    cout << base << " raised to the power of " << exponent << " = " << power(base, exponent);

    return 0;  // Signal successful termination
}

4. Program Termination: The program ends and returns a value of 0, indicating successful execution.

    return 0;  // Signal successful termination