# Select numbers in such way to maximize the amount of money

• Difficulty Level : Medium
• Last Updated : 16 Jun, 2022

Given two arrays A1 and A2 of N numbers. There are two people A and B who select numbers out of N. If A selects i-th number, then he will be paid A1[i] amount of money and if B selects i-th number then he will be paid A2[i] amount of money but A cannot select more than X numbers and B cannot select more than Y numbers. The task is to select N numbers in such a way that the amount of total money is maximized at the end.
Note: X + Y >= N

```Examples:
Input: N = 5, X = 3, Y = 3
A1[] = {1, 2, 3, 4, 5},
A2= {5, 4, 3, 2, 1}
Output: 21
B will take the first 3 orders and A
will take the last two orders.

Input: N = 2, X = 1, Y = 1
A1[] = {10, 10}, A2= {20, 20}
Output: 30 ```

Approach: Let us create a new array C such that C[i] = A2[i] – A1[i]. Now we will sort the array C in decreasing order. Note that the condition X + Y >= N guarantees that we will be able to assign the number to any one of the persons. Assume that for some i, A1[i] > A2[i] and you assigned an order to B, the loss encountered due to this assignment is C[i]. Similarly, for some i, A2[i] > A1[i] and you assigned a number to A, the loss encountered due to this assignment is C[i]. As we want to minimize the loss encountered, it is better to process the numbers having high possible losses, because we can try to reduce the loss in the starting part. There is no point in selecting a number with a high loss after assigning a number with less loss. Hence we initially assign all numbers to A initially, then subtract the loss from them greedily. Once the assigned order number is under X, then we store the maximal of that.
Below is the implementation of the above approach:

## C++

 `// C++ program to maximize profit` `#include ``using` `namespace` `std;` `// Function that maximizes the sum``int` `maximize(``int` `A1[], ``int` `A2[], ``int` `n,``             ``int` `x, ``int` `y)``{``    ``// Array to store the loss``    ``int` `c[n];` `    ``// Initial sum``    ``int` `sum = 0;` `    ``// Generate the array C``    ``for` `(``int` `i = 0; i < n; i++) {``        ``c[i] = A2[i] - A1[i];``        ``sum += A1[i];``    ``}` `    ``// Sort the array elements``    ``// in descending order``    ``sort(c, c + n, greater<``int``>());` `    ``// Variable to store the answer``    ``int` `maxi = -1;` `    ``// Iterate in the array, C``    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// Subtract the loss``        ``sum += c[i];` `        ``// Check if X orders are going``        ``// to be used``        ``if` `(i + 1 >= (n - x))``            ``maxi = max(sum, maxi);``    ``}` `    ``return` `maxi;``}` `// Driver Code``int` `main()``{``    ``int` `A1[] = { 1, 2, 3, 4, 5 };``    ``int` `A2[] = { 5, 4, 3, 2, 1 };` `    ``int` `n = 5;``    ``int` `x = 3, y = 3;` `    ``cout << maximize(A1, A2, n, x, y);` `    ``return` `0;``}`

## Java

 `// Java program to maximize profit``import` `java.util.*;` `class` `GFG``{` `// Function that maximizes the sum``static` `int` `maximize(``int` `A1[], ``int` `A2[], ``int` `n,``            ``int` `x, ``int` `y)``{``    ``// Array to store the loss``    ``int``[] c = ``new` `int``[n];` `    ``// Initial sum``    ``int` `sum = ``0``;` `    ``// Generate the array C``    ``for` `(``int` `i = ``0``; i < n; i++)``    ``{``        ``c[i] = A2[i] - A1[i];``        ``sum += A1[i];``    ``}` `    ``// Sort the array elements``    ``// in descending order``int` `temp;``for``(``int` `i = ``0``; i < n - ``1``; i++)``{``    ``if``(c[i] < c[i+``1``])``    ``{``        ``temp = c[i];``        ``c[i] = c[i + ``1``];``        ``c[i + ``1``] = temp;``    ``}``}` `    ``// Variable to store the answer``    ``int` `maxi = -``1``;` `    ``// Iterate in the array, C``    ``for` `(``int` `i = ``0``; i < n; i++)``    ``{` `        ``// Subtract the loss``        ``sum += c[i];` `        ``// Check if X orders are going``        ``// to be used``        ``if` `(i + ``1` `>= (n - x))``            ``maxi = Math.max(sum, maxi);``    ``}` `    ``return` `maxi;``}` `// Driver Code``public` `static` `void` `main(String args[])``{``    ``int` `A1[] = { ``1``, ``2``, ``3``, ``4``, ``5` `};``    ``int` `A2[] = { ``5``, ``4``, ``3``, ``2``, ``1` `};` `    ``int` `n = ``5``;``    ``int` `x = ``3``, y = ``3``;` `    ``System.out.println(maximize(A1, A2, n, x, y));``}``}` `// This code is contributed by``// Surendra_Gangwar`

## Python3

 `# Python3 program to maximize profit` `# Function that maximizes the Sum``def` `maximize(A1, A2, n, x, y):` `    ``# Array to store the loss``    ``c ``=` `[``0` `for` `i ``in` `range``(n)]` `    ``# Initial Sum``    ``Sum` `=` `0` `    ``# Generate the array C``    ``for` `i ``in` `range``(n):``        ``c[i] ``=` `A2[i] ``-` `A1[i]``        ``Sum` `+``=` `A1[i]``    ` `    ``# Sort the array elements``    ``# in descending order``    ``c.sort()``    ``c ``=` `c[::``-``1``]` `    ``# Variable to store the answer``    ``maxi ``=` `-``1` `    ``# Iterate in the array, C``    ``for` `i ``in` `range``(n):` `        ``# Subtract the loss``        ``Sum` `+``=` `c[i]` `        ``# Check if X orders are going``        ``# to be used``        ``if` `(i ``+` `1` `>``=` `(n ``-` `x)):``            ``maxi ``=` `max``(``Sum``, maxi)` `    ``return` `maxi``    ` `# Driver Code``A1 ``=` `[ ``1``, ``2``, ``3``, ``4``, ``5` `]``A2 ``=` `[ ``5``, ``4``, ``3``, ``2``, ``1` `]` `n ``=` `5``x, y ``=` `3``, ``3` `print``(maximize(A1, A2, n, x, y))` `# This code is contributed``# by Mohit Kumar`

## C#

 `// C# program to maximize profit``using` `System;` `class` `GFG``{``    ` `    ``// Function that maximizes the sum``    ``static` `int` `maximize(``int` `[] A1, ``int` `[] A2, ``int` `n,``                                    ``int` `x, ``int` `y)``    ``{``        ``// Array to store the loss``        ``int` `[] c = ``new` `int``[n];``    ` `        ``// Initial sum``        ``int` `sum = 0;``    ` `        ``// Generate the array C``        ``for` `(``int` `i = 0; i < n; i++)``        ``{``            ``c[i] = A2[i] - A1[i];``            ``sum += A1[i];``        ``}``    ` `        ``// Sort the array elements``        ``// in descending order``            ``int` `temp;``        ``for``(``int` `i = 0; i < n - 1; i++)``        ``{``            ``if``(c[i] < c[i+1])``            ``{``                ``temp = c[i];``                ``c[i] = c[i + 1];``                ``c[i + 1] = temp;``            ``}``        ``}``    ` `        ``// Variable to store the answer``        ``int` `maxi = -1;``    ` `        ``// Iterate in the array, C``        ``for` `(``int` `i = 0; i < n; i++)``        ``{``    ` `            ``// Subtract the loss``            ``sum += c[i];``    ` `            ``// Check if X orders are going``            ``// to be used``            ``if` `(i + 1 >= (n - x))``                ``maxi = Math.Max(sum, maxi);``        ``}``    ` `        ``return` `maxi;``    ``}``    ` `    ``// Driver Code``    ``public` `static` `void` `Main()``    ``{``        ``int` `[] A1 = { 1, 2, 3, 4, 5 };``        ``int` `[] A2 = { 5, 4, 3, 2, 1 };``    ` `        ``int` `n = 5;``        ``int` `x = 3, y = 3;``    ` `        ``Console.WriteLine(maximize(A1, A2, n, x, y));``    ``}``}` `// This code is contributed by ihritik`

## PHP

 `= (``\$n` `- ``\$x``))``            ``\$maxi` `= max(``\$sum``, ``\$maxi``);``    ``}` `    ``return` `\$maxi``;``}``    ` `# Driver Code``\$A1` `= ``array``( 1, 2, 3, 4, 5 );``\$A2` `= ``array``( 5, 4, 3, 2, 1 );` `\$n` `= 5;``\$x` `= 3;``\$y` `= 3;` `echo` `maximize(``\$A1``, ``\$A2``, ``\$n``, ``\$x``, ``\$y``);` `// This code is contributed by Ryuga``?>`

## Javascript

 ``

Output:

`21`

Time Complexity: O(N*logN), as we are using an inbuilt sort function that costs N*logN time.

Auxiliary Space: O(N), as we are using extra space of the array c. Where N is the number of elements in the arrays.

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