Recursive Function to Calculate Factorial of a Number in C++

In this exercise, you will implement a recursive function in C++ that calculates the factorial of a given number. The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It is denoted by n! and defined as:

n! = n × (n-1) × (n-2) × ... × 1

Recursion is a programming technique where a function calls itself to solve a smaller instance of the same problem. Factorials are a classic use case for practicing recursion and help reinforce your understanding of function calls, base cases, and recursion trees.

Implementation Details

1. The Base Case

Every recursive function needs a stop condition. If n == 0, we return 1. Without this, the function would call itself infinitely.

2. Recursive Call

For any number n > 0, the function returns n * factorial(n - 1), breaking the problem down into smaller steps.

3. User Validation

It is important to check if the input is negative, as factorials are only defined for non-negative integers.

Objective

1. Create a function named factorial that takes an integer as input.
2. Use an if statement to define the base case (n=0).
3. Return n multiplied by the recursive call factorial(n - 1).
4. Validate the input in main() to prevent negative values.

Example C++ Exercise

factorial_recursive.cpp Recursion

#include <iostream>

using namespace std;

// Recursive function to calculate the factorial of a number
int factorial(int n) {
    if (n == 0) {
        return 1; // Base case: factorial of 0 is 1
    }
    return n * factorial(n - 1); // Recursive call
}

int main() {
    int number;

    // Ask the user to enter a number
    cout << "Enter a non-negative integer: ";
    cin >> number;

    // Check if the number is negative
    if (number < 0) {
        cout << "Factorial is not defined for negative numbers." << endl;
    } else {
        // Call the recursive factorial function and print the result
        int result = factorial(number);
        cout << "Factorial of " << number << " is: " << result << endl;
    }

    return 0;
}

Example Output:

Enter a non-negative integer: 5
Factorial of 5 is: 120

Objective

Example C++ Exercise

Example Output:

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