Factorial

#include <iostream>
using namespace std;

int factorial(int n) {

    // Base case: If n is 0, the factorial of 0 is defined as 1
    if(n == 0)
        return 1;

    // Recursive call: Solve the smaller problem (factorial of n-1)
    int smallerProblem = factorial(n - 1);

    // Combine the result of the smaller problem with the current n to solve the bigger problem
    int biggerProblem = n * smallerProblem;

    // Return the solution to the bigger problem
    return biggerProblem;
}

int main() {
    int number = 5;
    cout << "Factorial of " << number << " is " << factorial(number) << endl;
    return 0;
}

Example Walkthrough

• Call 1: factorial(5)
  • Calls factorial(4) (recursive case)
• Call 2: factorial(4)
  • Calls factorial(3) (recursive case)
• Call 3: factorial(3)
  • Calls factorial(2) (recursive case)
• Call 4: factorial(2)
  • Calls factorial(1) (recursive case)
• Call 5: factorial(1)
  • Calls factorial(0) (recursive case)
• Call 6: factorial(0)
  • Reaches the base case and returns 1.

Now, the function begins to return the values as follows:

• factorial(1) returns 1 * 1 = 1
• factorial(2) returns 2 * 1 = 2
• factorial(3) returns 3 * 2 = 6
• factorial(4) returns 4 * 6 = 24
• factorial(5) returns 5 * 24 = 120

So, the factorial of 5 is 120.