Smallest Rotation with Highest Score

arrayprefix sum

Problem Statement

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 .

Examples

Example 1

Input: nums = [2,3,1,4,0]
Output: 3
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
nums will always have 3 points no matter how it shifts.
So we will choose the smallest k, which is 0.

Constraints

1 <= nums.length <= 10 ^5

0 <= nums[i] < nums.length

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicPrefix Sum