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# Remove all occurrences of any element for maximum array sum

• Difficulty Level : Hard
• Last Updated : 27 May, 2021

Given an array of positive integers, remove all the occurrences of the element to get the maximum sum of the remaining array.

Examples:

Input : arr = {1, 1, 3}
Output : 3
On removing 1 from the array, we get {3}. The total value is 3

Input : arr = {1, 1, 3, 3, 2, 2, 1, 1, 1}
Output : 11
On removing 2 from the array, we get {1, 1, 3, 3, 1, 1, 1}. The total value is 11.

The Brute Force solution is to first find the sum of an array, after that, find all the frequencies of the elements in the array. Find the value contributed by them to the array sum. Select the minimum value among them. To get the maximum sum of the array after removing is the equal difference of the total value of the sum and minimum value contributed by the individual element’s total frequent value.
Time complexity: O(n2)

A better approach We first find the total sum of the array and then sort the array, count the individual frequencies while traversing the array and get the maximum value. After sorting, we can use frequencies of all elements in O(n) tine,
The time complexity of this approach is O(n Log n)

An Efficient Approach is to use hashing to count the frequencies of elements while traversing the array. Find the minimum value using the frequencies stored in the array

## C++

 `#include ``using` `namespace` `std;` `int` `maxSumArray(``int` `arr[], ``int` `n)``{``    ``// Find total sum and frequencies of elements``    ``int` `sum = 0;``    ``unordered_map<``int``, ``int``> mp;``    ``for` `(``int` `i = 0; i < n; i++) {``        ``sum += arr[i];``        ``mp[arr[i]]++;``    ``}` `    ``// Find minimum value to be subtracted.``    ``int` `minimum = INT_MAX;``    ``for` `(``auto` `x : mp)``        ``minimum = min(minimum, x.second * x.first);` `    ``// Find maximum sum after removal``    ``return` `(sum - minimum);``}` `// Drivers code``int` `main()``{``    ``int` `arr[] = { 1, 1, 3, 3, 2, 2, 1, 1, 1 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);``    ``cout << maxSumArray(arr, n);``    ``return` `0;``}`

## Java

 `// Java program to convert fractional decimal``// to binary number``import` `java.util.*;` `class` `GFG``{` `static` `int` `maxSumArray(``int` `arr[], ``int` `n)``{``    ``// Find total sum and frequencies of elements``    ``int` `sum = ``0``;``    ``Map m = ``new` `HashMap<>();``    ``for` `(``int` `i = ``0` `; i < n; i++)``    ``{``        ``sum += arr[i];``        ``if``(m.containsKey(arr[i]))``        ``{``            ``m.put(arr[i], m.get(arr[i])+``1``);``        ``}``        ``else``        ``{``            ``m.put(arr[i], ``1``);``        ``}``    ``}``    ` `    ``// Find minimum value to be subtracted.``    ``int` `minimum = Integer.MAX_VALUE;``    ``for` `(Map.Entry x : m.entrySet())``        ``minimum = Math.min(minimum, x.getValue() * x.getKey());` `    ``// Find maximum sum after removal``    ``return` `(sum - minimum);``}` `// Drivers code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``1``, ``1``, ``3``, ``3``, ``2``, ``2``, ``1``, ``1``, ``1` `};``    ``int` `n = arr.length;``    ``System.out.println(maxSumArray(arr, n));``}``}` `// This code contributed by Rajput-Ji`

## Python3

 `# Python3 program to convert``# fractional decimal to binary number``from` `sys ``import` `maxsize``def` `maxSumArray(arr, n):``    ` `    ``# Find total sum and frequencies of elements``    ``sum1 ``=` `0``    ``mp ``=` `{i:``0` `for` `i ``in` `range``(``4``)}``    ``for` `i ``in` `range``(n):``        ``sum1 ``+``=` `arr[i]``        ``mp[arr[i]] ``+``=` `1` `    ``# Find minimum value to be subtracted.``    ``minimum ``=` `maxsize``    ``for` `key, value ``in` `mp.items():``        ``if``(key ``=``=` `0``):``            ``continue``        ``minimum ``=` `min``(minimum, value ``*` `key)` `    ``# Find maximum sum after removal``    ``return` `(sum1 ``-` `minimum)` `# Driver Code``if` `__name__ ``=``=``'__main__'``:``    ``arr ``=` `[``1``, ``1``, ``3``, ``3``, ``2``, ``2``, ``1``, ``1``, ``1``]``    ``n ``=` `len``(arr)``    ``print``(maxSumArray(arr, n))``    ` `# This code is contributed by``# Surendra_Gangwar`

## C#

 `// C# program to convert fractional decimal``// to binary number``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{` `static` `int` `maxSumArray(``int` `[]arr, ``int` `n)``{``    ``// Find total sum and frequencies of elements``    ``int` `sum = 0;``    ``Dictionary<``int``,``int``> m = ``new` `Dictionary<``int``,``int``>();``    ``for` `(``int` `i = 0 ; i < n; i++)``    ``{``        ``sum += arr[i];``        ``if``(m.ContainsKey(arr[i]))``        ``{``            ``var` `val = m[arr[i]];``            ``m.Remove(arr[i]);``            ``m.Add(arr[i], val + 1);``        ``}``        ``else``        ``{``            ``m.Add(arr[i], 1);``        ``}``    ``}``    ` `    ``// Find minimum value to be subtracted.``    ``int` `minimum = ``int``.MaxValue;``    ``foreach``(KeyValuePair<``int``, ``int``> x ``in` `m)``        ``minimum = Math.Min(minimum, (x.Value * x.Key));` `    ``// Find maximum sum after removal``    ``return` `(sum - minimum);``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 1, 1, 3, 3, 2, 2, 1, 1, 1 };``    ``int` `n = arr.Length;``    ``Console.WriteLine(maxSumArray(arr, n));``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``
Output:
`11`

Time complexity: O(n)

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