# Maximize the Sum of the given array using given operations

• Last Updated : 10 Nov, 2021

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:

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Input: A[] = {5, 4, 6, 2, 8}, B[] = {1, 0, 1, 1, 0}, K = 2
Output: 21
Explanation:
Add A and A to the sum as B = B = 0
Therefore, sum = 4 + 8 = 12.
Now, add A and A 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 ``using` `namespace` `std;` `// Comparator to sort the array``// in ascending order``bool` `compare(pair<``int``, ``int``> p1,``             ``pair<``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(N);``    ``for` `(``int` `i = 0; i < N; i++) {``        ``pairs[i] = make_pair(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` `Pair ``implements` `Comparable``{``    ``int` `first, second;``    ``Pair(``int` `x, ``int` `y)``    ``{``        ``first = x;``        ``second = y;``    ``}``    ``public` `int` `compareTo(Pair 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 = ``new` `ArrayList<>();``    ``for``(``int` `i = ``0``; i < N; i++)``    ``{``        ``pairs.add(``new` `Pair(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`
Output:
`21`

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

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