The Minimum Removals to Balance Array problem asks you to find the minimum number of elements to remove from an array so that the remaining elements form a "balanced" array — one where the minimum element equals the maximum divided by 2 (or some ratio condition, depending on the variant). This Minimum Removals to Balance Array coding problem involves reasoning about which elements to keep, naturally leading to a sliding window approach.
Amazon uses this to test whether candidates can translate a balance condition into a windowing constraint. Figuring out which elements to keep (rather than remove) is a classic reframing trick. The array, sorting, and sliding window interview pattern is core here, and it tests both optimization thinking and implementation precision.
After sorting, the problem transforms into finding the longest valid window where max / min ≤ 2 (or the given ratio). Since the array is sorted, the window's max is always the rightmost element and the min is the leftmost. Use a two-pointer sliding window: expand right, shrink left whenever the ratio is violated. Track the maximum window size. The answer is n - maxWindowSize.
Array: [1, 2, 3, 4, 8]. After sorting, use two pointers. Window [1,2,3,4]: max/min = 4 ≤ 2? No. Shrink. Window [2,3,4]: 4/2 = 2 ≤ 2? Yes, size 3. Window [3,4,8]: 8/3 > 2? Yes, shrink. Window [4,8]: 8/4 = 2 ≤ 2, size 2. Maximum valid window = 3. Minimum removals = 5 - 3 = 2.
The "minimum removals" framing almost always hides a "maximum window/subarray to keep" problem. Train yourself to immediately reframe: instead of thinking about what to cut, think about the largest valid subset you can preserve. Sorting plus two-pointer is especially effective when the balance condition depends on relative values (min, max, ratio). Practicing sliding window problems with ratio constraints builds this instinct.
