# Maximize

Easy
0/40
Average time to solve is 25m
Contributed by
1 upvote

## Problem statement

You have an integer ‘N’ and an array ‘X’ of ‘N’ integers. You need to maximize the value of the array, which is equal to ⅀ '(X[i] - i)^2' from ‘i’ in the range ‘[0, N-1]’. To do this, you can rearrange the elements of the given array.

Determine the maximum value of the array you can get after rearranging the array ‘X’ elements.

Example:
'N' = 3, ‘X' = [1,2,1]
If we rearrange our array 'X' to '[2, 1, 1]' .
Then our answer will be (0-2)^2 + (1-1)^2 + (1-2)^2 = 4 + 0 + 1 = 5.
For array ‘[1, 1, 2]’ value will be equal to ‘1 + 0 + 0 = 1’.
For array ‘[1, 2, 1]’ value will be equal to ‘1 + 1 + 1 = 3’.
Detailed explanation ( Input/output format, Notes, Images )
Constraints :
1 <= T <= 10
1 <= N <= 10^4
1<= X[i] <= 10^5

Time Limit: 1 sec
2
2
1 2
3
1 1 1
4
2
##### Explanation Of Sample Input 1 :
For test case 1:

From this array, we can have 2 arrays i.e. ‘[1,2]’ and ‘[2,1]’
For ‘[1,2]’ the value will be equal to ‘ (1-0)^2 + (2-1)^2’ which is equal to 2.
For ‘[2,1]’ the value will be equal to ‘ (2-0)^2 + (1-1)^2’ which is equal to 4.

For test case 2:
In this case, there is only one array you can get after rearranging elements of ‘X’.
For array ‘[1,1,1]’ answer will be ‘1+0+1=2’.