Algorithm and flowchart for finding factorial of a number

Introduction

In this tutorial, we will explore how to find the factorial of a number using an algorithm, a flowchart, and practical coding examples in C and C++. Understanding factorials is essential in mathematics and programming, particularly in combinatorics and recursive functions. This guide will provide you with a clear, step-by-step approach to implement this concept.

Step 1: Understanding Factorials

Factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n. The factorial of 0 is defined to be 1.

Key Points

• Factorial formula:
  n! = n × (n - 1) × (n - 2) × ... × 1
• Examples:
  • 5! = 5 × 4 × 3 × 2 × 1 = 120
  • 3! = 3 × 2 × 1 = 6

Step 2: Designing the Algorithm

An algorithm is a step-by-step procedure for solving a problem. Here’s a simple algorithm to calculate the factorial:

1. Start
2. Input a non-negative integer n
3. Initialize a variable result to 1
4. If n is 0, return result (which is 1)
5. For each integer i from 1 to n:
   • Multiply result by i
6. Output result
7. End

Step 3: Creating the Flowchart

To visualize the algorithm, you can create a flowchart. Here’s a simple outline of what it should contain:

• Start
• Input n
• Check if n is 0
  • If yes, output 1
  • If no, proceed to loop
• Loop from 1 to n
  • Multiply result by i
• Output result
• End

Step 4: Implementing the Code in C

Now, let's implement the factorial algorithm in C.

#include <stdio.h>

int factorial(int n) {
    int result = 1;
    if (n == 0) return result;
    for (int i = 1; i <= n; i++) {
        result *= i;
    }
    return result;
}

int main() {
    int number;
    printf("Enter a non-negative integer: ");
    scanf("%d", &number);
    printf("Factorial of %d is %d\n", number, factorial(number));
    return 0;
}

Step 5: Implementing the Code in C++

Here’s how you can write the same algorithm in C++.

#include <iostream>
using namespace std;

int factorial(int n) {
    int result = 1;
    if (n == 0) return result;
    for (int i = 1; i <= n; i++) {
        result *= i;
    }
    return result;
}

int main() {
    int number;
    cout << "Enter a non-negative integer: ";
    cin >> number;
    cout << "Factorial of " << number << " is " << factorial(number) << endl;
    return 0;
}

Conclusion

In this tutorial, we covered the concept of factorials, designed an algorithm, created a flowchart, and implemented the solution in both C and C++. Understanding how to compute factorials is a foundational skill in programming that opens the door to more complex algorithms and data structures. As a next step, consider experimenting with recursive methods for calculating factorials or applying this concept to solve combinatorial problems.