Maximize the Sum of the given array using given operations

Last Updated : 05 Oct, 2022

Given two arrays A[] and B[] consisting of N integers and an integer K, the task is to maximize the sum calculated from the array A[] by the following operations:

For every index in B[] containing 0, the corresponding index in A[] is added to the sum.
For every index in B[] containing 1, add the value at the corresponding index in A[] to the sum for atmost K such indices. For the remaining indices, subtract from the sum.

Examples:

Input: A[] = {5, 4, 6, 2, 8}, B[] = {1, 0, 1, 1, 0}, K = 2
Output: 21
Explanation:
Add A[1] and A[4] to the sum as B[1] = B[4] = 0
Therefore, sum = 4 + 8 = 12.
Now, add A[0] and A[3] to the sum as K elements can be added.
Finally, subtract 2 from the sum.
Therefore, the maximum possible sum = 12 + 5 + 6 - 2 = 21
Input: A[] = {5, 2, 1, 8, 10, 5}, B[] = {1, 1, 1, 1, 0, 0}, K = 3
Output: 29

Approach:

Follow the steps below to solve the problem:

Sort the array A[] in decreasing order.
To maximize the sum, add first K elements from the sorted array corresponding to which the index in B[] contains 1. Subtract the remaining such elements.
Add to the sum all the values in A[] corresponding to an index in B[] containing 0.

Below is the implementation of the above approach:

C++

// C++ Program to maximize the
// sum of the given array
#include <bits/stdc++.h>
using namespace std;

// Comparator to sort the array
// in ascending order
bool compare(pairs<int, int> p1,
             pairs<int, int> p2)
{
    return p1.first > p2.first;
}

// Function to maximize the sum of
// the given array
int maximizeScore(int A[], int B[],
                  int K, int N)
{

    // Stores {A[i], B[i]} pairs
    vector<pairs<int, int> > pairs(N);
    for (int i = 0; i < N; i++) {
        pairs[i] = make_pairs(A[i], B[i]);
    }

    // Sort in descending order of the
    // values in the array A[]
    sort(pairs.begin(), pairs.end(), compare);

    // Stores the maximum sum
    int sum = 0;
    for (int i = 0; i < N; i++) {

        // If B[i] is equal to 0
        if (pairs[i].second == 0) {

            // Simply add A[i] to the sum
            sum += pairs[i].first;
        }

        else if (pairs[i].second == 1) {

            // Add the highest K numbers
            if (K > 0) {
                sum += pairs[i].first;
                K--;
            }

            // Subtract from the sum
            else {
                sum -= pairs[i].first;
            }
        }
    }

    // Return the sum
    return sum;
}

// Driver Code
int main()
{

    int A[] = { 5, 4, 6, 2, 8 };
    int B[] = { 1, 0, 1, 1, 0 };
    int K = 2;
    int N = sizeof(A) / sizeof(int);
    cout << maximizeScore(A, B, K, N);
    return 0;
}

Java

// Java program to maximise the
// sum of the given array
import java.util.*;

class Pairs implements Comparable<Pairs>
{
    int first, second;
    Pairs(int x, int y)
    {
        first = x;
        second = y;
    }
    public int compareTo(Pairs p) 
    {
        return p.first - first; 
    }
}

class GFG{
    
// Function to maximise the sum of
// the given array
static int maximiseScore(int A[], int B[],
                         int K, int N)
{

    // Stores {A[i], B[i]} pairs
    ArrayList<Pairs> pairs = new ArrayList<>();
    for(int i = 0; i < N; i++)
    {
        pairs.add(new Pairs(A[i], B[i]));
    }

    // Sort in descending order of the
    // values in the array A[]
    Collections.sort(pairs);

    // Stores the maximum sum
    int sum = 0;
    for(int i = 0; i < N; i++)
    {
        
        // If B[i] is equal to 0
        if (pairs.get(i).second == 0)
        {
            
            // Simply add A[i] to the sum
            sum += pairs.get(i).first;
        }

        else if (pairs.get(i).second == 1) 
        {
            
            // Add the highest K numbers
            if (K > 0)
            {
                sum += pairs.get(i).first;
                K--;
            }

            // Subtract from the sum
            else 
            {
                sum -= pairs.get(i).first;
            }
        }
    }

    // Return the sum
    return sum;
}

// Driver Code
public static void main(String[] args)
{

    int A[] = { 5, 4, 6, 2, 8 };
    int B[] = { 1, 0, 1, 1, 0 };
    int K = 2;
    int N = A.length;
    
    System.out.print(maximiseScore(A, B, K, N));
}
}

// This code is contributed by jrishabh99

Python3

# Python Program to maximise the 
# sum of the given array 

# Comparator to sort the array 
# in ascending order 
def compare(p1, p2):
    return p1[0] > p2[0]

# Function to maximise the sum of 
# the given array 
def maximiseScore(A, B, K, N):
    
    # Stores {A[i], B[i]} pairs 
    pairs = []
    for i in range(N):
        pairs.append([A[i], B[i]])
    
    # Sort in descending order of the 
    # values in the array A[] 
    pairs.sort(key = lambda x:x[0], reverse = True)

    # Stores the maximum sum 
    Sum = 0

    for i in range(N):
      
        # If B[i] is equal to 0 
        if(pairs[i][1] == 0):
          
            # Simply add A[i] to the sum 
            Sum += pairs[i][0]
        elif(pairs[i][1] == 1):
            
            # Add the highest K numbers 
            if(K > 0):
                Sum += pairs[i][0]
                K -= 1
                
            # Subtract from the sum 
            else:
                Sum -= pairs[i][0]
    
    # Return the sum 
    return Sum

# Driver Code 
A = [5, 4, 6, 2, 8]
B = [1, 0, 1, 1, 0]
K = 2
N = len(A)
print(maximiseScore(A, B, K, N))

# This code is contributed by avanitrachhadiya2155

// C# program to maximise the
// sum of the given array
using System;
using System.Collections;
using System.Collections.Generic;

class Pairs : IComparable
{
    public int first, second;
    public Pairs(int x, int y)
    {
        first = x;
        second = y;
    }
    public  int CompareTo(object obj) 
    {
        if (obj == null)
            return 1;
        Pairs p = obj as Pairs;
        return p.first - first; 
    }
}

class GFG{

// Function to maximise the sum of
// the given array
static int maximiseScore(int[] A, int[] B,
                         int K, int N)
{

    // Stores {A[i], B[i]} pairs
    List<Pairs> pairs = new List<Pairs>();
    for(int i = 0; i < N; i++)
    {
        pairs.Add(new Pairs(A[i], B[i]));
    }

    // Sort in descending order of the
    // values in the array A[]
    pairs.Sort();

    // Stores the maximum sum
    int sum = 0;
    for(int i = 0; i < N; i++)
    {

        // If B[i] is equal to 0
        if (pairs[i].second == 0)
        {

            // Simply add A[i] to the sum
            sum += pairs[i].first;
        }

        else if (pairs[i].second == 1) 
        {

            // Add the highest K numbers
            if (K > 0)
            {
                sum += pairs[i].first;
                K--;
            }

            // Subtract from the sum
            else 
            {
                sum -= pairs[i].first;
            }
        }
    }

    // Return the sum
    return sum;
}

// Driver Code
public static void Main(string[] args)
{

    int[] A = { 5, 4, 6, 2, 8 };
    int[] B = { 1, 0, 1, 1, 0 };
    int K = 2;
    int N = A.Length;

    Console.Write(maximiseScore(A, B, K, N));
}
}

// This code is contributed by phasing17

JavaScript

<script>

// JavaScript Program to maximize the
// sum of the given array

// Comparator to sort the array
// in ascending order
function compare(p1,p2)
{
    return p2[0] - p1[0];
}

// Function to maximize the sum of
// the given array
function maximizeScore(A, B, K, N)
{

    // Stores {A[i], B[i]} pairs
    let pairs = new Array(N);
    for (let i = 0; i < N; i++) {
        pairs[i] = [A[i], B[i]];
    }

    // Sort in descending order of the
    // values in the array A[]
    pairs.sort(compare);

    // Stores the maximum sum
    let sum = 0;
    for (let i = 0; i < N; i++) {

        // If B[i] is equal to 0
        if (pairs[i][1] == 0) {

            // Simply add A[i] to the sum
            sum += pairs[i][0];
        }

        else if (pairs[i][1] == 1) {

            // Add the highest K numbers
            if (K > 0) {
                sum += pairs[i][0];
                K--;
            }

            // Subtract from the sum
            else {
                sum -= pairs[i][0];
            }
        }
    }

    // Return the sum
    return sum;
}

// Driver Code
let A = [ 5, 4, 6, 2, 8 ];
let B = [ 1, 0, 1, 1, 0 ];
let K = 2;
let N = A.length;
document.write(maximizeScore(A, B, K, N),"</br>");

// This code is contributed by shinjanpatra.
</script>

Output:

Time complexity: O(N*log(N))
Auxiliary Space: O(N)

Maximize the sum of sum of the Array by removing end elements

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