minimum-removals-to-balance-array

You are given an integer array nums and an integer k.

An array is considered balanced if the value of its maximum element is at most k times the minimum element.

You may remove any number of elements from nums​​​​​​​ without making it empty.

Return the minimum number of elements to remove so that the remaining array is balanced.

Note: An array of size 1 is considered balanced as its maximum and minimum are equal, and the condition always holds true.

Example 1:

Input: nums = [2,1,5], k = 2

Output: 1

Explanation:

• Remove nums[2] = 5 to get nums = [2, 1].


• Now max = 2, min = 1 and max <= min * k as 2 <= 1 * 2. Thus, the answer is 1.

Example 2:

Input: nums = [1,6,2,9], k = 3

Output: 2

Explanation:

• Remove nums[0] = 1 and nums[3] = 9 to get nums = [6, 2].


• Now max = 6, min = 2 and max <= min * k as 6 <= 2 * 3. Thus, the answer is 2.

Example 3:

Input: nums = [4,6], k = 2

Output: 0

Explanation:

• Since nums is already balanced as 6 <= 4 * 2, no elements need to be removed.

Constraints:

• 1 <= nums.length <= 105


• 1 <= nums[i] <= 109


• 1 <= k <= 105