Adding Extremely Large Numbers Using PHP Strings | CodeSignal Learn

Adding Extremely Large Numbers Using PHP Strings | CodeSignal Learn

Before we dive into the code, let's first discuss the strategy we're going to follow. Remember that every digit in a number carries value, and the position of the digit determines its influence on the total value of the number. This system is known as place-value notation.

The first step involves initializing our variables. We'll use two integers, $i and $j, to point to the current digit in $num1 and $num2, respectively. We'll also need an integer variable named $carry to hold the carryovers from each addition operation. Lastly, we'll use an array named $result to store our resultant number, where each digit from the addition is appended to the front.

We start iterating from the end (rightmost side) of each string because the rightmost digit is the least significant digit, and this is where we begin when performing manual addition. Processing the least significant digits first allows us to handle carryover operations easily and propagate any necessary changes to the more significant digits on the left.

PHP

<?php

function addLargeNumbers($num1, $num2) {
    $i = strlen($num1) - 1;
    $j = strlen($num2) - 1;
    $carry = 0;
    $result = [];

After initializing our variables, it's time to move on to the next step. Here, we'll scan through $num1 and $num2 from right to left, moving from the least significant digit to the most significant one.

For each iteration, we extract the digits $n1 from $num1 and $n2 from $num2. If $i or $j is less than 0, that means we've processed all the digits in one of the numbers. Therefore, we treat any additional digits as 0.

PHP

<?php

function addLargeNumbers($num1, $num2) {
    $i = strlen($num1) - 1;
    $j = strlen($num2) - 1;
    $carry = 0;
    $result = [];
    
    while ($i >= 0 || $j >= 0 || $carry != 0) {
        $n1 = ($i >= 0) ? ord($num1[$i]) - ord('0') : 0;
        $n2 = ($j >= 0) ? ord($num2[$j]) - ord('0') : 0;

After obtaining digits $n1 and $n2, our next step is to add them. This addition also includes the $carry, which accumulates any overflow from the addition of previous column digits. This sum results in a one- or two-digit number, where the "tens" place becomes a new $carry and the "units" place is the result digit.

Subsequently, we add $current to the $result array and decrement both $i and $j before starting the next iteration. Finally, we reverse $result and join the digits together to obtain our result.

PHP

<?php

function addLargeNumbers($num1, $num2) {
    $i = strlen($num1) - 1;
    $j = strlen($num2) - 1;
    $carry = 0;
    $result = [];
    
    while ($i >= 0 || $j >= 0 || $carry != 0) {
        $n1 = ($i >= 0) ? ord($num1[$i]) - ord('0') : 0;
        $n2 = ($j >= 0) ? ord($num2[$j]) - ord('0') : 0;
        $current = $n1 + $n2 + $carry;
        $carry = intdiv($current, 10);
        $current = $current % 10;
        array_unshift($result, chr($current + ord('0')));
        $i--;
        $j--;
    }

    return implode('', $result);
}

// Example usage
echo addLargeNumbers("1454178195297", "8458263917502");
// Outputs 9912442112799
?>