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Remove all occurrences of any element for maximum array sum
• Difficulty Level : Hard
• Last Updated : 01 Jul, 2019

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

Examples:

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

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

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

Brute Force solution is to first find the sum of array after that find all the frequencies of element in the array. Find the value contributed by them to array sum. Select the minimum value among them. To get maximum sum of array after removing is equal difference of total value of sum and minimum value contributed by individual element total frequent value.

Time complexity: O(n2)

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

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 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`
Output:
```11
```

Time complexity: O(n)

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