798 - Smallest Rotation with Highest Score.

Hard

You are given an array nums. You can rotate it by a non-negative integer k so that the array becomes [nums[k], nums[k + 1], ... nums[nums.length - 1], nums[0], nums[1], ..., nums[k-1]]. Afterward, any entries that are less than or equal to their index are worth one point.

• For example, if we have nums = [2,4,1,3,0], and we rotate by k = 2, it becomes [1,3,0,2,4]. This is worth 3 points because 1 > 0 no points, 3 > 1 no points, 0 <= 2 one point, 2 <= 3 one point, 4 <= 4 one point.

Return the rotation index k that corresponds to the highest score we can achieve if we rotated nums by it. If there are multiple answers, return the smallest such index k.

Example 1:

Input: nums = 2,3,1,4,0

Output: 3

Explanation: Scores for each k are listed below:

k = 0, nums = 2,3,1,4,0, score 2

k = 1, nums = 3,1,4,0,2, score 3

k = 2, nums = 1,4,0,2,3, score 3

k = 3, nums = 4,0,2,3,1, score 4

k = 4, nums = 0,2,3,1,4, score 3 So we should choose

k = 3, which has the highest score.

Example 2:

Input: nums = 1,3,0,2,4

Output: 0

Explanation: nums will always have 3 points no matter how it shifts. So we will choose the smallest k, which is 0.

Constraints:

• <code>1 <= nums.length <= 10⁵</code>

• 0 <= nums[i] < nums.length