PHP Program to Generate Pascal’s Triangle

Posted in PHP Tutorial

Updated on Nov 22, 2024

By Mari Selvan

👁️ 94 - Views

⏳ 4 mins

💬 1 Comment

PHP Program to Generate Pascal's Triangle

Photo Credit to CodeToFun

🙋 Introduction

Pascal's Triangle is a mathematical construct named after the French mathematician Blaise Pascal.

It is an arrangement of numbers in a triangular shape where each number is the sum of the two numbers directly above it. This triangle has many interesting properties and applications in combinatorics and algebra.

In this tutorial, we will explore a PHP program that generates Pascal's Triangle and prints it to the screen.

📄 Example

Let's delve into the PHP code that generates Pascal's Triangle.

generatePascalsTriangle.php

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<?php
$col = 1;

echo "-----This is the pascal triangle pattern-----\n\n";
function generatePascalsTriangle($row) {
for ($i = 0; $i < $row; $i++) {
    echo "\t";
    for ($ws = 1; $ws <= $row - $i; $ws++) {
        echo "  ";
    }
        
    for ($j = 0; $j <= $i; $j++) {
        if ($j == 0 || $i == 0)
            $col = 1;
        else
            $col = $col * ($i - $j + 1) / $j;
        echo $col . "   ";
    }
    echo "\n";
}
}
generatePascalsTriangle(6);
?>

💻 Testing the Program

To test the program with a different number of rows, simply replace the value of $numRows in the code.

Output

Run the script to see Pascal's Triangle printed to the screen.

🧠 How the Program Works

The program defines a function generatePascalsTriangle that takes the number of rows as input and prints Pascal's Triangle up to the specified number of rows.
Inside the function, two nested loops are used. The outer loop iterates through each row, and the inner loop calculates and prints the coefficients of each row.
The coefficients are calculated using the formula C(n, k) = n! / (k! * (n-k)!), where n is the row number, and k is the position in the row.

🧐 Understanding the Concept of Pascal's Triangle

Pascal's Triangle is a triangular array of numbers in which each number is the sum of the two numbers directly above it.The first few rows of Pascal's Triangle look like this:

Each number in the triangle represents a binomial coefficient, also known as "n choose k," denoted as C(n, k). These coefficients have many applications in probability, algebra, and combinatorics.

🎢 Optimizing the Program

While the provided program is straightforward, consider exploring ways to optimize it for larger triangle sizes or implementing additional features, such as formatting the triangle for better readability.

Feel free to incorporate and modify this code as needed for your specific use case. Happy coding!