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]

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++

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// CPP program to find 
// maximum equilibrium sum.
#include <bits/stdc++.h>
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;
}

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Java

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// 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.

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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#

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// 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.

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PHP

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<?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 = array(-2, 5, 3, 1,
              2, 6, -4, 2 );
$n = count($arr);
echo findMaxSum($arr, $n);
  
// This code is contributed by anuj_67.
?>

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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++

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// CPP program to find 
// maximum equilibrium sum.
#include <bits/stdc++.h>
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;
}

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Java

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// 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

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C#

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// 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

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PHP

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<?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();
  
    // Array to store suffix sum.
    $suffSum[$n] = array();
  
    // 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 = array( -2, 5, 3, 1, 2, 6, -4, 2 );
$n = sizeof($arr);
echo findMaxSum($arr, $n);
  
// This code is contibuted by ajit.
?>

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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++

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// CPP program to find
// maximum equilibrium sum.
#include <bits/stdc++.h>
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;
}

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Java

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// 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.

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C#

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// 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.

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Output :

7

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



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