# Maximum equlibrium sum in an array

Given an array arr[]. Find 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]
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A Simple Solution is to one by one check the given condition (prefix sum equal to suffix sum) for every element and return 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; ` `} `

## Java

 `// java program to find maximum ` `// equilibrium sum. ` `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``// Function to find maximum  ` `    ``// equilibrium sum. ` `    ``static` `int` `findMaxSum(``int` `[]arr, ``int` `n) ` `    ``{ ` `        ``int` `res = Integer.MIN_VALUE; ` `         `  `        ``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 = Math.max(res, prefix_sum); ` `        ``} ` `         `  `        ``return` `res; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` `        ``int` `arr[] = {-``2``, ``5``, ``3``, ``1``, ``2``, ``6``, -``4``, ``2` `}; ` `        ``int` `n = arr.length; ` `        ``System.out.println(findMaxSum(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67. `

## Python3

# Python 3 program to find maximum
# equilibrium sum.
import sys

# Function to find maximum equilibrium sum.
def findMaxSum(arr, n):
res = -sys.maxsize – 1
for i in range(n):
prefix_sum = arr[i]
for j in range(i):
prefix_sum += arr[j]

suffix_sum = arr[i]
j = n – 1
while(j > i):
suffix_sum += arr[j]
j -= 1
if (prefix_sum == suffix_sum):
res = max(res, prefix_sum)

return res

# Driver Code
if __name__ == ‘__main__’:
arr = [-2, 5, 3, 1, 2, 6, -4, 2]
n = len(arr)
print(findMaxSum(arr, n))

# This code is contributed by
# Surendra_Gangwar

## C#

 `// C# program to find maximum ` `// equilibrium sum. ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``// Function to find maximum  ` `    ``// equilibrium sum. ` `    ``static` `int` `findMaxSum(``int` `[]arr, ``int` `n) ` `    ``{ ` `        ``int` `res = ``int``.MinValue; ` `         `  `        ``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 = Math.Max(res, prefix_sum); ` `        ``} ` `         `  `        ``return` `res; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main () ` `    ``{ ` `        ``int` `[]arr = {-2, 5, 3, 1, 2, 6, -4, 2 }; ` `        ``int` `n = arr.Length; ` `        ``Console.WriteLine(findMaxSum(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67. `

## PHP

 ` ``\$i``; ``\$j``--) ` `        ``\$suffix_sum` `+= ``\$arr``[``\$j``]; ` ` `  `    ``if` `(``\$prefix_sum` `== ``\$suffix_sum``) ` `        ``\$res` `= max(``\$res``, ``\$prefix_sum``); ` `    ``} ` `    ``return` `\$res``; ` `} ` ` `  `// Driver Code ` `\$arr` `= ``array``(-2, 5, 3, 1, ` `              ``2, 6, -4, 2 ); ` `\$n` `= ``count``(``\$arr``); ` `echo` `findMaxSum(``\$arr``, ``\$n``); ` ` `  `// This code is contributed by anuj_67. ` `?> `

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 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 there value with 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; ` `} `

## Java

 `// Java program to find maximum equilibrium sum. ` `import` `java.io.*; ` ` `  `public` `class` `GFG { ` `     `  ` `  `    ``// Function to find maximum ` `    ``// equilibrium sum. ` `    ``static` `int` `findMaxSum(``int` `[]arr, ``int` `n) ` `    ``{ ` `         `  `        ``// Array to store prefix sum. ` `        ``int` `[]preSum = ``new` `int``[n]; ` `     `  `        ``// Array to store suffix sum. ` `        ``int` `[]suffSum = ``new` `int``[n]; ` `     `  `        ``// Variable to store maximum sum. ` `        ``int` `ans = Integer.MIN_VALUE; ` `     `  `        ``// 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 = Math.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 = Math.max(ans, preSum[i]);  ` `        ``} ` `     `  `        ``return` `ans; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``static` `public` `void` `main (String[] args) ` `    ``{ ` `        ``int` `[]arr = { -``2``, ``5``, ``3``, ``1``, ``2``, ``6``, -``4``, ``2` `}; ` `        ``int` `n = arr.length; ` `         `  `        ``System.out.println( findMaxSum(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67 `

## C#

 `// C# program to find maximum equilibrium sum. ` `using` `System; ` ` `  `public` `class` `GFG { ` `     `  ` `  `    ``// Function to find maximum ` `    ``// equilibrium sum. ` `    ``static` `int` `findMaxSum(``int` `[]arr, ``int` `n) ` `    ``{ ` `         `  `        ``// Array to store prefix sum. ` `        ``int` `[]preSum = ``new` `int``[n]; ` `     `  `        ``// Array to store suffix sum. ` `        ``int` `[]suffSum = ``new` `int``[n]; ` `     `  `        ``// Variable to store maximum sum. ` `        ``int` `ans = ``int``.MinValue; ` `     `  `        ``// 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 = Math.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 = Math.Max(ans, preSum[i]);  ` `        ``} ` `     `  `        ``return` `ans; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``static` `public` `void` `Main () ` `    ``{ ` `        ``int` `[]arr = { -2, 5, 3, 1, 2, 6, -4, 2 }; ` `        ``int` `n = arr.Length; ` `         `  `        ``Console.WriteLine( findMaxSum(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67 `

## PHP

 `= 0; ``\$i``--)  ` `    ``{ ` `        ``\$suffSum``[``\$i``] = ``\$suffSum``[``\$i` `+ 1] + ``\$arr``[``\$i``]; ` `        ``if` `(``\$suffSum``[``\$i``] == ``\$preSum``[``\$i``])  ` `            ``\$ans` `= max(``\$ans``, ``\$preSum``[``\$i``]);  ` `    ``} ` ` `  `    ``return` `\$ans``; ` `} ` ` `  `// Driver Code ` `\$arr` `= ``array``( -2, 5, 3, 1, 2, 6, -4, 2 ); ` `\$n` `= sizeof(``\$arr``); ` `echo` `findMaxSum(``\$arr``, ``\$n``); ` ` `  `// This code is contibuted by ajit. ` `?> `

Output:

```7
```

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

Further Optimization :
We can avoid use of extra space by first computing total sum, then using it to find 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; ` `} `

## Java

 `// Java program to find maximum equilibrium ` `// sum. ` `import` `java.lang.Math.*; ` `import` `java.util.stream.*; ` ` `  `class` `GFG { ` `     `  `    ``// Function to find maximum equilibrium ` `    ``// sum. ` `    ``static` `int` `findMaxSum(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``int` `sum = IntStream.of(arr).sum(); ` `        ``int` `prefix_sum = ``0``, ` `        ``res = Integer.MIN_VALUE; ` `         `  `        ``for` `(``int` `i = ``0``; i < n; i++) ` `        ``{ ` `            ``prefix_sum += arr[i];  ` `             `  `            ``if` `(prefix_sum == sum) ` `                ``res = Math.max(res, prefix_sum);  ` `            ``sum -= arr[i]; ` `        ``} ` `         `  `        ``return` `res; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[] = { -``2``, ``5``, ``3``, ``1``,  ` `                    ``2``, ``6``, -``4``, ``2` `}; ` `        ``int` `n = arr.length; ` `        ``System.out.print(findMaxSum(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by Smitha. `

## C#

 `// C# program to find maximum equilibrium sum. ` `using` `System.Linq; ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``static` `int` `Add(``int` `x, ``int` `y) {  ` `        ``return` `x + y;  ` `    ``}  ` `     `  `    ``// Function to find maximum equilibrium ` `    ``// sum. ` `    ``static` `int` `findMaxSum(``int` `[]arr, ``int` `n) ` `    ``{ ` `        ``int` `sum = arr.Aggregate(func:Add); ` `        ``int` `prefix_sum = 0, ` `        ``res = ``int``.MinValue; ` `         `  `        ``for` `(``int` `i = 0; i < n; i++) ` `        ``{ ` `            ``prefix_sum += arr[i];  ` `             `  `            ``if` `(prefix_sum == sum) ` `                ``res = Math.Max(res, prefix_sum);  ` `            ``sum -= arr[i]; ` `        ``} ` `         `  `        ``return` `res; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[]arr = { -2, 5, 3, 1,  ` `                    ``2, 6, -4, 2 }; ` `        ``int` `n = arr.Length; ` `        ``Console.Write(findMaxSum(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by Smitha. `

Output :

```7
```

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

This article is attributed to GeeksforGeeks.org

code

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