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3634. Minimum Removals to Balance Array

MediumArray Preparing judge… LeetCode

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
ArrayBinary SearchSliding WindowSorting

Hints

Hint 1
Sort nums and use two pointers i and j so that the window's minimum is nums[i] and maximum is nums[j].
Hint 2
Expand j while nums[j] <= k * nums[i] to maximize the balanced window; answer = n - (j - i + 1).