# Maximize difference between the Sum of the two halves of the Array after removal of N elements

• Difficulty Level : Hard
• Last Updated : 29 Dec, 2020

Given an integer N and array arr[] consisting of 3 * N integers, the task is to find the maximum difference between first half and second half of the array after the removal of exactly N elements from the array.

Examples:

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Input: N = 2, arr[] = {3, 1, 4, 1, 5, 9}
Output: 1
Explanation:
Removal of arr and arr from the array maximizes the difference = (3 + 4) – (1 + 5) = 7 – 6 = 1.

Input: N = 1, arr[] = {1, 2, 3}
Output: -1

Approach:
Follow the steps given below to solve the problem

• Traverse the array from the beginning and keep updating the sum of the largest N elements from the beginning of the array.
• Similarly, keep updating the sum of the smallest N elements from the end of the array.
• Traverse these sums and calculate the differences at each point and update the maximum difference obtained.
• Print the maximum difference obtained.

Below is the implementation of the above approach:

## C++

 `// C++ Program to implement``// the above approach``#include ``using` `namespace` `std;` `// Function to print the maximum difference``// possible between the two halves of the array``long` `long` `FindMaxDif(vector<``long` `long``> a, ``int` `m)``{``    ``int` `n = m / 3;` `    ``vector<``long` `long``> l(m + 5), r(m + 5);` `    ``// Stores n maximum values from the start``    ``multiset<``long` `long``> s;` `    ``for` `(``int` `i = 1; i <= m; i++) {` `        ``// Insert first n elements``        ``if` `(i <= n) {` `            ``// Update sum of largest n``            ``// elements from left``            ``l[i] = a[i - 1] + l[i - 1];``            ``s.insert(a[i - 1]);``        ``}` `        ``// For the remaining elements``        ``else` `{``            ``l[i] = l[i - 1];` `            ``// Obtain minimum value``            ``// in the set``            ``long` `long` `d = *s.begin();` `            ``// Insert only if it is greater``            ``// than minimum value``            ``if` `(a[i - 1] > d) {` `                ``// Update sum from left``                ``l[i] -= d;``                ``l[i] += a[i - 1];` `                ``// Remove the minimum``                ``s.erase(s.find(d));` `                ``// Insert the current element``                ``s.insert(a[i - 1]);``            ``}``        ``}``    ``}` `    ``// Clear the set``    ``s.clear();` `    ``// Store n minimum elements from the end``    ``for` `(``int` `i = m; i >= 1; i--) {` `        ``// Insert the last n elements``        ``if` `(i >= m - n + 1) {` `            ``// Update sum of smallest n``            ``// elements from right``            ``r[i] = a[i - 1] + r[i + 1];``            ``s.insert(a[i - 1]);``        ``}` `        ``// For the remaining elements``        ``else` `{` `            ``r[i] = r[i + 1];` `            ``// Obtain the minimum``            ``long` `long` `d = *s.rbegin();` `            ``// Insert only if it is smaller``            ``// than maximum value``            ``if` `(a[i - 1] < d) {` `                ``// Update sum from right``                ``r[i] -= d;``                ``r[i] += a[i - 1];` `                ``// Remove the minimum``                ``s.erase(s.find(d));` `                ``// Insert the new element``                ``s.insert(a[i - 1]);``            ``}``        ``}``    ``}` `    ``long` `long` `ans = -9e18L;` `    ``for` `(``int` `i = n; i <= m - n; i++) {` `        ``// Compare the difference and``        ``// store the maximum``        ``ans = max(ans, l[i] - r[i + 1]);``    ``}` `    ``// Return the maximum``    ``// possible difference``    ``return` `ans;``}` `// Driver Code``int` `main()``{` `    ``vector<``long` `long``> vtr = { 3, 1, 4, 1, 5, 9 };``    ``int` `n = vtr.size();` `    ``cout << FindMaxDif(vtr, n);` `    ``return` `0;``}`

## Python3

 `# Python3 Program to implement``# the above approach` `# Function to print the maximum difference``# possible between the two halves of the array``def` `FindMaxDif(a, m) :` `    ``n ``=` `m ``/``/` `3` `    ``l ``=` `[``0``] ``*` `(m ``+` `5``)``    ``r ``=` `[``0``] ``*` `(m ``+` `5``)` `    ``# Stores n maximum values from the start``    ``s ``=` `[]` `    ``for` `i ``in` `range``(``1``, m ``+` `1``) :` `        ``# Insert first n elements``        ``if` `(i <``=` `n) :` `            ``# Update sum of largest n``            ``# elements from left``            ``l[i] ``=` `a[i ``-` `1``] ``+` `l[i ``-` `1``]``            ``s.append(a[i ``-` `1``])` `        ``# For the remaining elements``        ``else` `:``            ``l[i] ``=` `l[i ``-` `1``]` `            ``# Obtain minimum value``            ``# in the set``            ``s.sort()``            ``d ``=` `s[``0``]` `            ``# Insert only if it is greater``            ``# than minimum value``            ``if` `(a[i ``-` `1``] > d) :` `                ``# Update sum from left``                ``l[i] ``-``=` `d``                ``l[i] ``+``=` `a[i ``-` `1``]` `                ``# Remove the minimum``                ``s.remove(d)` `                ``# Insert the current element``                ``s.append(a[i ``-` `1``])` `    ``# Clear the set``    ``s.clear()` `    ``# Store n minimum elements from the end``    ``for` `i ``in` `range``(m, ``0``, ``-``1``) :` `        ``# Insert the last n elements``        ``if` `(i >``=` `m ``-` `n ``+` `1``) :` `            ``# Update sum of smallest n``            ``# elements from right``            ``r[i] ``=` `a[i ``-` `1``] ``+` `r[i ``+` `1``]``            ``s.append(a[i ``-` `1``])` `        ``# For the remaining elements``        ``else` `:` `            ``r[i] ``=` `r[i ``+` `1``]``            ``s.sort()``            ` `            ``# Obtain the minimum``            ``d ``=` `s[``-``1``]` `            ``# Insert only if it is smaller``            ``# than maximum value``            ``if` `(a[i ``-` `1``] < d) :` `                ``# Update sum from right``                ``r[i] ``-``=` `d``                ``r[i] ``+``=` `a[i ``-` `1``]` `                ``# Remove the minimum``                ``s.remove(d)` `                ``# Insert the new element``                ``s.append(a[i ``-` `1``])` `    ``ans ``=` `-``9e18` `    ``for` `i ``in` `range``(n, m ``-` `n ``+` `1``) :` `        ``# Compare the difference and``        ``# store the maximum``        ``ans ``=` `max``(ans, l[i] ``-` `r[i ``+` `1``])` `    ``# Return the maximum``    ``# possible difference``    ``return` `ans` `# Driver code ``vtr ``=` `[ ``3``, ``1``, ``4``, ``1``, ``5``, ``9` `]``n ``=` `len``(vtr)` `print``(FindMaxDif(vtr, n))` `# This code is contributed by divyesh072019`

## C#

 `// C# program to implement``// the above approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG{``    ` `// Function to print the maximum difference``// possible between the two halves of the array``static` `long` `FindMaxDif(List<``long``> a, ``int` `m)``{``    ``int` `n = m / 3;``    ` `    ``long``[] l = ``new` `long``[m + 5];``    ``long``[] r = ``new` `long``[m + 5];``  ` `    ``// Stores n maximum values from the start``    ``List<``long``> s = ``new` `List<``long``>();``  ` `    ``for``(``int` `i = 1; i <= m; i++)``    ``{``        ` `        ``// Insert first n elements``        ``if` `(i <= n)``        ``{``            ` `            ``// Update sum of largest n``            ``// elements from left``            ``l[i] = a[i - 1] + l[i - 1];``            ``s.Add(a[i - 1]);``        ``}``        ` `        ``// For the remaining elements``        ``else``        ``{``            ``l[i] = l[i - 1];``            ` `            ``s.Sort();``            ` `            ``// Obtain minimum value``            ``// in the set``            ``long` `d = s;``  ` `            ``// Insert only if it is greater``            ``// than minimum value``            ``if` `(a[i - 1] > d)``            ``{``                ` `                ``// Update sum from left``                ``l[i] -= d;``                ``l[i] += a[i - 1];``  ` `                ``// Remove the minimum``                ``s.Remove(d);``  ` `                ``// Insert the current element``                ``s.Add(a[i - 1]);``            ``}``        ``}``    ``}``  ` `    ``// Clear the set``    ``s.Clear();``  ` `    ``// Store n minimum elements from the end``    ``for``(``int` `i = m; i >= 1; i--)``    ``{``        ` `        ``// Insert the last n elements``        ``if` `(i >= m - n + 1)``        ``{``            ` `            ``// Update sum of smallest n``            ``// elements from right``            ``r[i] = a[i - 1] + r[i + 1];``            ``s.Add(a[i - 1]);``        ``}``  ` `        ``// For the remaining elements``        ``else``        ``{``            ``r[i] = r[i + 1];``            ` `            ``s.Sort();``            ` `            ``// Obtain the minimum``            ``long` `d = s[s.Count - 1];``  ` `            ``// Insert only if it is smaller``            ``// than maximum value``            ``if` `(a[i - 1] < d)``            ``{``                ` `                ``// Update sum from right``                ``r[i] -= d;``                ``r[i] += a[i - 1];``  ` `                ``// Remove the minimum``                ``s.Remove(d);``  ` `                ``// Insert the new element``                ``s.Add(a[i - 1]);``            ``}``        ``}``    ``}``  ` `    ``long` `ans = (``long``)(-9e18);``  ` `    ``for``(``int` `i = n; i <= m - n; i++)``    ``{``        ` `        ``// Compare the difference and``        ``// store the maximum``        ``ans = Math.Max(ans, l[i] - r[i + 1]);``    ``}``  ` `    ``// Return the maximum``    ``// possible difference``    ``return` `ans;``}` `// Driver Code``static` `void` `Main()``{``    ``List<``long``> vtr = ``new` `List<``long``>(``        ``new` `long``[]{ 3, 1, 4, 1, 5, 9 });``    ``int` `n = vtr.Count;``    ` `    ``Console.Write(FindMaxDif(vtr, n));``}``}` `// This code is contributed by divyeshrabadiya07`
Output:
`1`

Time Complexity: O(NlogN)
Auxiliary Space: O(N)

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