Finding Unique Number Pairs in Large Datasets Using PHP

Introduction

Hello, coding enthusiast! Welcome to a new challenge in your journey to mastering programming and problem-solving. Today, we're diving into combinatorial problems that involve working with large datasets and multiple pairs of numbers. We'll learn to solve significant problems efficiently using smart data structures like PHP associative arrays, which will help us avoid expensive operations such as iterating over large arrays. Are you ready? Let's dive in!

Task Statement

In this unit's task, you will be given a large array composed of pairs of distinct, positive integers, with up to 1,000,000 elements. Your challenge is to write a PHP function to count the number of indices (i, j) (i not equals j) where the i-th pair does not share a common element with the j-th pair. A crucial point to remember is that a pair (a, b) is considered identical to (b, a), meaning the order of elements in a pair is irrelevant in this case. It is guaranteed that no two pairs are element-wise equal. For example, given the array [[2, 5], [1, 6], [3, 2], [4, 2], [5, 1], [6, 3]], the output should be 8 . The required index pairs are the following: (0, 1), (0, 5), (1, 2), (1, 3), (2, 4), (3, 4), (3, 5), (4, 5) .

Understanding the Solution: The Idea

n \sdot (n - 1) / 2

Solution Building: Step 1

n \sdot (n - 1) / 2

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PHP

<?php

function nonCommonPairs($pairs) {
    $indices = [];
    $totalPairs = count($pairs) * (count($pairs) - 1) / 2;
    
    // (The rest of the code will be added in subsequent steps)
    return $totalPairs; // Temporary return to avoid errors
}

// Testing code will be added later

?>

PHP

<?php

function nonCommonPairs($pairs) {
    $indices = [];
    $totalPairs = count($pairs) * (count($pairs) - 1) / 2;
    
    foreach ($pairs as $index => $pair) {
        foreach ($pair as $num) {
            if (!isset($indices[$num])) {
                $indices[$num] = [];
            }
            $indices[$num][] = $index;
        }
    }
    
    // (The rest of the code will be added in the next step)
    return $totalPairs; // Temporary return to avoid errors
}

?>

PHP

<?php

function nonCommonPairs($pairs) {
    $indices = [];
    $totalPairs = count($pairs) * (count($pairs) - 1) / 2;
    
    foreach ($pairs as $index => $pair) {
        foreach ($pair as $num) {
            if (!isset($indices[$num])) {
                $indices[$num] = [];
            }
            $indices[$num][] = $index;
        }
    }

    $commonPairs = 0;
    foreach ($indices as $list) {
        $size = count($list);
        $commonPairs += $size * ($size - 1) / 2;
    }
    
    return $totalPairs - $commonPairs;
}

// Test the function with a sample array
$pairs = [[2, 5], [1, 6], [3, 2], [4, 2], [5, 1], [6, 3]];
echo "Count of non-common pairs: " . nonCommonPairs($pairs);

?>

PHP

<?php

function nonCommonPairs($pairs) {
    $indices = [];
    $totalPairs = count($pairs) * (count($pairs) - 1) / 2;
    
    foreach ($pairs as $index => $pair) {
        foreach ($pair as $num) {
            if (!isset($indices[$num])) {
                $indices[$num] = [];
            }
            $indices[$num][] = $index;
        }
    }
    
    // (The rest of the code will be added in the next step)
    return $totalPairs; // Temporary return to avoid errors
}

?>

PHP

<?php

function nonCommonPairs($pairs) {
    $indices = [];
    $totalPairs = count($pairs) * (count($pairs) - 1) / 2;
    
    foreach ($pairs as $index => $pair) {
        foreach ($pair as $num) {
            if (!isset($indices[$num])) {
                $indices[$num] = [];
            }
            $indices[$num][] = $index;
        }
    }

    $commonPairs = 0;
    foreach ($indices as $list) {
        $size = count($list);
        $commonPairs += $size * ($size - 1) / 2;
    }
    
    return $totalPairs - $commonPairs;
}

// Test the function with a sample array
$pairs = [[2, 5], [1, 6], [3, 2], [4, 2], [5, 1], [6, 3]];
echo "Count of non-common pairs: " . nonCommonPairs($pairs);

?>

Introduction

Task Statement

Understanding the Solution: The Idea

Solution Building: Step 1

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Solution Building: Step 2

Solution Building: Step 3

Lesson Summary