Algorithm and flowchart for finding factorial of a number
Table of Contents
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:
- Start
- Input a non-negative integer n
- Initialize a variable result to 1
- If n is 0, return result (which is 1)
- For each integer i from 1 to n:
- Multiply result by i
- Output result
- 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.