pascalRow.php

<?php

// AUTHOR: algb12
// An implementation of the Pascal's triangle in PHP
// It is relatively fast, even with values in the 100s and 1000s
function pascalRow($n)
{
    // Every Pascal's triangle starts with a 1
    $row = [1];
    // If row number ($n) is 0, just return an array with 1 in it
    if ($n === 0) {
        return $row;
    }
    // No answer for a number less than 1
    if ($n < 1) {
        return;
    }
    // While current iteration ($i) is less than $n, process row
    for ($i = 0; $i < $n; ++$i) {
        // Adjust last index based on count to zero-based array by subtracting 1
        $lastIdx = count($row) - 1;
        // New row is initially an empty array
        $newRow = [];
        // First element in Pascal's triangle is always 1
        $newRow[0] = 1;
        // For each element in the row, do action below
        foreach ($row as $k => $v) {
            // If current element is last element
            if ($k === $lastIdx) {
                // Append a 1 to new row (rows always end in a 1)
                $newRow[$k + 1] = 1;
                // Set current row to new row
                $row = $newRow;
                // Exit this loop as end of row is reached
                break;
            }
            // If current element is not last element
            if ($k !== $lastIdx) {
                // Append sum of current element and next one to new row
                $newRow[$k + 1] = $row[$k] + $row[$k + 1];
            }
        }
    }

    return $row;
}

// Test with small integer
print_r(pascalRow(4));
// Test with another small integer
print_r(pascalRow(7));
// Test with a larger integer
print_r(pascalRow(43));
// Test with a very large integer
print_r(pascalRow(732));
// This is like nCr for n = 33 and r = 7
echo pascalRow(33)[7];