Calculating the factorial of a given number is a common programming problem that tests the ability to implement basic mathematical concepts and logical structures. In this article, we will discuss how to write a program to calculate the factorial of a given number using pseudocode.
First, let’s define what a factorial is. The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
To calculate the factorial of a given number, we can use a loop to multiply all positive integers less than or equal to the given number. Here’s the pseudocode for the program:
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Input: n (a non-negative integer) Output: factorial (the factorial of n) 1. Set factorial to 1 2. For i from 1 to n do the following: a. Set factorial to factorial x i 3. Output factorial |
Let’s go through each step of the pseudocode.
Step 1: We initialize the variable factorial
to 1, which is the starting point for the multiplication.
Step 2: We use a loop to multiply all positive integers less than or equal to n. We start the loop from 1 and iterate up to n. At each iteration, we multiply the current value of factorial
with the value of i
and assign it back to factorial
. This way, factorial
gets updated with the product of all positive integers less than or equal to n.
Step 3: We output the final value of factorial
, which is the factorial of the given number.
Here’s an example implementation of the program in Python:
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def factorial(n): factorial = 1 for i in range(1, n+1): factorial *= i return factorial |
In this implementation, we use a for
loop to iterate from 1 to n
. We use the range
function to generate a sequence of numbers from 1 to n
, and then multiply each number with factorial
and assign the result back to factorial
. Finally, we return the value of factorial
.
In conclusion, calculating the factorial of a given number is a fundamental programming problem that involves implementing basic mathematical concepts and logical structures. By using a loop to multiply all positive integers less than or equal to the given number, we can easily calculate the factorial of any non-negative integer.
Here’s how you can implement the pseudocode to calculate the factorial of a given number in Python, Java, and C:
Python:
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def factorial(n): factorial = 1 for i in range(1, n+1): factorial *= i return factorial # Example usage: print(factorial(5)) # Output: 120 |
Java:
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public class Factorial { public static int factorial(int n) { int factorial = 1; for (int i = 1; i <= n; i++) { factorial *= i; } return factorial; } // Example usage: public static void main(String[] args) { System.out.println(factorial(5)); // Output: 120 } } |
C:
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#include <stdio.h> int factorial(int n) { int factorial = 1; for (int i = 1; i <= n; i++) { factorial *= i; } return factorial; } // Example usage: int main() { printf("%d\n", factorial(5)); // Output: 120 return 0; } |
In all three languages, we define a function named factorial
that takes a non-negative integer n
as input and returns its factorial. We initialize the factorial
variable to 1 and use a for
loop to multiply all positive integers less than or equal to n
. Finally, we return the value of factorial
.
Note that the syntax of the code may vary slightly depending on the programming language, but the logic and algorithm remain the same.