Minimum Removals to Balance Array

You are given an integer array arr.
The array is called balanced if:
the largest element is at most twice the smallest element
You may perform the following changes:
Remove any number of elements
Modify at most one remaining element to any positive integer
Your task is to determine the minimum number of elements that must be removed so that the resulting array can be made balanced under these rules.

Function
minimumRemovalsToBalance(arr: int[]) → int

Examples
Example 1
arr = [7, 4, 2, 3, 12, 9]
return = 2
An optimal sequence of operations is:
Change the second element from 4 to 8.
Remove the third and fourth elements, 2 and 3.The modified array is [7, 8, 12, 9]
12 is less than or equal to 2 * 7.
Example 2
arr = [4, 6, 2, 9, 8, 7, 3]
return = 2
An optimal sequence of operations is:
Change the third element from 2 to 11
Remove the first and seventh elements, 4 and 3.The modified array is [6, 11, 9, 8, 7]
11 is less than or equal to 2 * 6.

Sort the array. Any kept set is a contiguous window in sorted order, so the base idea is the longest window where max <= 2 * min. The twist is the single modification. You can change one kept element to any positive integer, which means one outlier can be rewritten to sit inside the range. So a window can be extended by one element past the usual limit, either a too-large element on the right or a too-small one on the left, because you rewrite it into range. Try each left bound with two pointers and allow one skipped violator, then take the max kept size. Answer is n minus that. The pitfall is forgetting a modified element also removes itself as the min or max constraint, and arrays of size 1 or 2 are always fixable with zero removals. StealthCoder is the hedge if the live clock rattles you, but test those tiny cases yourself first.

Memorize the pattern. If you can't, run StealthCoder. The proctor sees the IDE. They don't see what's behind it.