PHP Program for Maximum Equilibrium Sum in an Array

Last Updated : 22 Jul, 2024
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Given an array arr[]. Find the maximum value of prefix sum which is also suffix sum for index i in arr[].

Examples: 

Input : arr[] = {-1, 2, 3, 0, 3, 2, -1}
Output : 4
Prefix sum of arr[0..3] = Suffix sum of arr[3..6]

Input : arr[] = {-2, 5, 3, 1, 2, 6, -4, 2}
Output : 7
Prefix sum of arr[0..3] = Suffix sum of arr[3..7]

A Simple Solution is to check one by one of the given condition (prefix sum equal to suffix sum) for every element and returns the element that satisfies the given condition with maximum value. 

PHP 
<?php
// PHP program to find
// maximum equilibrium sum.

// Function to find
// maximum equilibrium sum.
function findMaxSum($arr, $n) {
    $res = PHP_INT_MIN;
    for ($i = 0; $i < $n; $i++) {
        $prefix_sum = $arr[$i];
        for ($j = 0; $j < $i; $j++) {
            $prefix_sum += $arr[$j];
        }

        $suffix_sum = $arr[$i];
        for ($j = $n - 1; $j > $i; $j--) {
            $suffix_sum += $arr[$j];
        }

        if ($prefix_sum == $suffix_sum) {
            $res = max($res, $prefix_sum);
        }
    }
    return $res;
}

// Driver Code
$arr = [-2, 5, 3, 1, 2, 6, -4, 2];
$n = count($arr);
echo findMaxSum($arr, $n);

?>

Output
7

Time Complexity: O(n2)

Auxiliary Space: O(n)

A Better Approach is to traverse the array and store prefix sum for each index in array presum[], in which presum[i] stores sum of subarray arr[0..i]. Do another traversal of the array and store suffix sum in another array suffsum[], in which suffsum[i] stores sum of subarray arr[i..n-1]. After this for each index check if presum[i] is equal to suffsum[i] and if they are equal then compare their value with the overall maximum so far.

PHP 
<?php
// PHP program to find maximum equilibrium sum

// Function to find maximum equilibrium sum.
function findMaxSum($arr, $n) {
    
    // Array to store prefix sum.
    $preSum[$n] = [];

    // Array to store suffix sum.
    $suffSum[$n] = [];

    // Variable to store maximum sum.
    $ans = PHP_INT_MIN;

    // Calculate prefix sum.
    $preSum[0] = $arr[0];
    for ($i = 1; $i < $n; $i++) {
        $preSum[$i] = $preSum[$i - 1] + $arr[$i];
    }

    // Calculate suffix sum and compare
    // it with prefix sum. Update ans
    // accordingly.
    $suffSum[$n - 1] = $arr[$n - 1];
    if ($preSum[$n - 1] == $suffSum[$n - 1]) {
        $ans = max($ans, $preSum[$n - 1]);
    }

    for ($i = $n - 2; $i >= 0; $i--) {
        $suffSum[$i] = $suffSum[$i + 1] + $arr[$i];
        if ($suffSum[$i] == $preSum[$i]) {
            $ans = max($ans, $preSum[$i]);
        }
    }

    return $ans;
}

// Driver Code
$arr = [-2, 5, 3, 1, 2, 6, -4, 2];
$n = sizeof($arr);
echo findMaxSum($arr, $n);

?>

Output
7

Time Complexity: O(n) 

Auxiliary Space: O(n)

Please refer complete article on Maximum equilibrium sum in an array for more details!


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