3904. Smallest Stable Index II

Solution →

You are given an integer array nums of length n and an integer k.

For each index i, define its instability score as max(nums[0..i]) - min(nums[i..n - 1]).

In other words:

• max(nums[0..i]) is the largest value among the elements from index 0 to index i.
• min(nums[i..n - 1]) is the smallest value among the elements from index i to index n - 1.

An index i is called stable if its instability score is less than or equal to k.

Return the smallest stable index. If no such index exists, return -1.

Example 1

Input: nums = [5,0,1,4], k = 3
Output: 3
Explanation:
- At index 0: The maximum in [5] is 5, and the minimum in [5, 0, 1, 4] is 0,
  so the instability score is 5 - 0 = 5.
- At index 1: The maximum in [5, 0] is 5, and the minimum in [0, 1, 4] is 0,
  so the instability score is 5 - 0 = 5.
- At index 2: The maximum in [5, 0, 1] is 5, and the minimum in [1, 4] is 1,
  so the instability score is 5 - 1 = 4.
- At index 3: The maximum in [5, 0, 1, 4] is 5, and the minimum in [4] is 4,
  so the instability score is 5 - 4 = 1.
- This is the first index with an instability score less than or equal to k = 3.
  Thus, the answer is 3.

Example 2

Input: nums = [3,2,1], k = 1
Output: -1
Explanation:
- At index 0, the instability score is 3 - 1 = 2.
- At index 1, the instability score is 3 - 1 = 2.
- At index 2, the instability score is 3 - 1 = 2.
- None of these values is less than or equal to k = 1, so the answer is -1.

Example 3

Input: nums = [0], k = 0
Output: 0
Explanation:
At index 0, the instability score is 0 - 0 = 0, which is less than or equal to
k = 0. Therefore, the answer is 0.

Constraints

• 1 <= nums.length <= 10^5
• 0 <= nums[i] <= 10^9
• 0 <= k <= 10^9