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Learn C++: The Complete Course for Beginners

Calculating the Factorial of a Number

Explore how to calculate the factorial of a number in C++ using recursion. Understand the base case for stopping recursion, handling invalid inputs, and how the function calls itself to compute factorials. This lesson guides you through writing and running a recursive factorial function for non-negative integers.

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Introduction

Let’s consider the example of the recursive factorial function. In this lesson, we will calculate the factorial of a number n denoted by n!.

📝 The factorial of a given number is the product of the number by all the numbers smaller than it until it reaches 1.

📝 We can only calculate the factorial for the non-negative integers.

Illustration

Consider the illustration below for n = 5. You will see that we can represent the factorial problem in terms of itself, and eventually, reach a case that can be solved directly. When we reach that case, we will start returning value to the calling function.

Example program

Run the program below and see the output!

C++
#include <iostream>
using namespace std;
// Recursive factorial function
int factorial(int n) {
  // Invalid value
  if (n < 0){
    return -1;
  }
  // Base case
  if (n == 1 || n == 0) {
    return 1;
  } 
  // Recursive Case
  else {
    return n * factorial(n - 1);
  }
}
// main function
int main() {
  int n = 5;
  int result;
  // Call factorial function in main and store the returned value in result
  result = factorial(n);
  // Prints value of result
  cout << "Factorial of " << n << " = " << result;
  return 0;
}

Explanation

factorial function

Line No. 6: The recursive factorial function takes a value of type int, whose factorial is to be calculated in its input parameters, and returns the factorial of value in the output.

Line No. 8: Since we cannot calculate the factorial of negative integers for n < 0, factorial simply returns -1 in the output. -1 indicates that we have entered an invalid value.

Line No. 12: If n = 1 or n = 0, the function terminates after returning 1 to the calling point. There are no recursive calls in the factorial body since we cannot break the expression anymore. This is the base case of the factorial function.

Line No. 17: If n > 1, the factorial returns the product of n by the factorial (n-1). This is the recursive case.

Let’s run our code for n = 5 and see what happens inside the recursive factorial function.

In the above illustration, we see how to use the results of the inner function call to terminate the outer function call.

Quiz

1.

If n = 6, what is the output of the following function?

int factorial(int n) {
  if (n < 0){
    return -1;
  }
  if (n == 1 || n == 0) {
    return 1;
  } 
  else {
    return n * factorial(n - 1);
  }
}
A.

120

B.

720

C.

5040

D.

40320

1 / 1

Let’s learn about the difference between recursion and iteration in the upcoming lesson.