Php Program for Number of pairs with maximum sum

Write a PHP program for a given array arr[], count the number of pairs arr[i], arr[j] such that arr[i] + arr[j] is maximum and i < j.

Example:

Input : arr[] = {1, 1, 1, 2, 2, 2}
Output: 3
Explanation: The maximum possible pair sum where i<j is 4, which is given by 3 pairs, so the answer is 3 the pairs are (2, 2), (2, 2) and (2, 2)

Input: arr[] = {1, 4, 3, 3, 5, 1}
Output: 1
Explanation: The pair 4, 5 yields the maximum sum i.e, 9 which is given by 1 pair only

Php Program for Number of pairs with maximum sum using Naive Approach:

Traverse a loop i from 0 to n, i.e length of the array and another loop j from i+1 to n to find all possible pairs with i<j. Find the pair with the maximum possible sum, again traverse for all pairs and keep the count of the number of pairs which gives the pair sum equal to maximum .

Below is the Implementation of the above Approach:

PHP

<?php
// PHP program to count pairs
// with maximum sum.

// function to find the number
// of maximum pair sum
function sum( $a, $n)
{

    // traverse through all
    // the pairs
    $maxSum = PHP_INT_MIN;
    for($i = 0; $i < $n; $i++)
        for($j = $i + 1; $j < $n; $j++)
            $maxSum = max($maxSum, $a[$i] + $a[$j]);

    // traverse through all
    // pairs and keep a count
    // of the number of
    // maximum pairs
    $c = 0;
    for($i = 0; $i < $n; $i++)
        for($j = $i + 1; $j < $n; $j++)
            if ($a[$i] + $a[$j] == $maxSum)
                $c++;
    return $c;
}

    // Driver Code
    $array = array(1, 1, 1, 2, 2, 2);
    $n = count($array);
    echo sum($array, $n);

// This code is contributed by anuj_67.
?>

Output

3

Time complexity: O(n2)
Auxiliary Space: O(1)

Efficient Method:

• Maximum element is always part of solution.
• If maximum element appears more than once, then result is maxCount * (maxCount – 1)/2. We basically need to choose 2 elements from maxCount (^maxCountC2).
• If maximum element appears once, then result is equal to count of second maximum element. We can form a pair with every second max and max.

Below is the Implementation of the above Approach:

PHP

<?php
// PHP program to count
// pairs with maximum sum.

// function to find the number
// of maximum pair sums
function sum( $a, $n)
{
    // Find maximum and second
    // maximum elements. Also
    // find their counts.
    $maxVal = $a[0]; $maxCount = 1;
    $secondMax = PHP_INT_MIN;
    $secondMaxCount;
    for ( $i = 1; $i < $n; $i++)
    {
        if ($a[$i] == $maxVal)
            $maxCount++;
        else if ($a[$i] > $maxVal)
        {
            $secondMax = $maxVal;
            $secondMaxCount = $maxCount;
            $maxVal = $a[$i];
            $maxCount = 1;
        }
        else if ($a[$i] == $secondMax)
        {
            $secondMax = $a[$i];
            $secondMaxCount++;
        }
        else if ($a[$i] > $secondMax)
        {
            $secondMax = $a[$i];
            $secondMaxCount = 1;
        }
    }

    // If maximum element appears
    // more than once.
    if ($maxCount > 1)
        return $maxCount *
            ($maxCount - 1) / 2;

    // If maximum element
    // appears only once.
    return $secondMaxCount;
}

// Driver Code
$array = array(1, 1, 1, 2,
                2, 2, 3 );
$n = count($array);
echo sum($array, $n);

// This code is contributed by anuj_67.
?>

Output

3

Time complexity: O(n)
Auxiliary Space: O(1)

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