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# C++ Program for Maximum equilibrium sum in an array

• Last Updated : 31 Jan, 2022

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

## C++

 `// CPP program to find ` `// maximum equilibrium sum.` `#include ` `using` `namespace` `std;`   `// Function to find ` `// maximum equilibrium sum.` `int` `findMaxSum(``int` `arr[], ``int` `n)` `{` `    ``int` `res = INT_MIN;` `    ``for` `(``int` `i = 0; i < n; i++)` `    ``{` `    ``int` `prefix_sum = arr[i];` `    ``for` `(``int` `j = 0; j < i; j++)` `        ``prefix_sum += arr[j];`   `    ``int` `suffix_sum = arr[i];` `    ``for` `(``int` `j = n - 1; j > i; j--)` `        ``suffix_sum += arr[j];`   `    ``if` `(prefix_sum == suffix_sum)` `        ``res = max(res, prefix_sum);` `    ``}` `    ``return` `res;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = {-2, 5, 3, 1, ` `                  ``2, 6, -4, 2 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``cout << findMaxSum(arr, n);` `    ``return` `0;` `}`

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.

## C++

 `// CPP program to find ` `// maximum equilibrium sum.` `#include ` `using` `namespace` `std;`   `// Function to find maximum` `// equilibrium sum.` `int` `findMaxSum(``int` `arr[], ``int` `n)` `{` `    ``// Array to store prefix sum.` `    ``int` `preSum[n];`   `    ``// Array to store suffix sum.` `    ``int` `suffSum[n];`   `    ``// Variable to store maximum sum.` `    ``int` `ans = INT_MIN;`   `    ``// Calculate prefix sum.` `    ``preSum[0] = arr[0];` `    ``for` `(``int` `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` `(``int` `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` `int` `main()` `{` `    ``int` `arr[] = { -2, 5, 3, 1,` `                   ``2, 6, -4, 2 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``cout << findMaxSum(arr, n);` `    ``return` `0;` `}`

Output:

`7`

Time Complexity: O(n)
Auxiliary Space: O(n)

Further Optimization :
We can avoid the use of extra space by first computing the total sum, then using it to find the current prefix and suffix sums.

## C++

 `// CPP program to find` `// maximum equilibrium sum.` `#include ` `using` `namespace` `std;`   `// Function to find ` `// maximum equilibrium sum.` `int` `findMaxSum(``int` `arr[], ``int` `n)` `{` `    ``int` `sum = accumulate(arr, arr + n, 0);` `    ``int` `prefix_sum = 0, res = INT_MIN;` `    ``for` `(``int` `i = 0; i < n; i++)` `    ``{` `    ``prefix_sum += arr[i]; ` `    ``if` `(prefix_sum == sum)` `        ``res = max(res, prefix_sum); ` `    ``sum -= arr[i];` `    ``}` `    ``return` `res;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { -2, 5, 3, 1, ` `                   ``2, 6, -4, 2 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``cout << findMaxSum(arr, n);` `    ``return` `0;` `}`

Output :

`7`

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

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

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