Remove all occurrences of any element for maximum array sum

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

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++

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#include <bits/stdc++.h>
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;
}

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Java

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// 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<Integer,Integer> 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<Integer,Integer> 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

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Python3

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# 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

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C#

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// 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

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Output:

11

Time complexity: O(n)



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