396. Rotate Function

Difficulty: Medium

Topics: Junior , Array , Math , Dynamic Programming

You are given an integer array nums of length n .

Assume arrₖ to be an array obtained by rotating nums by k positions clock-wise. We define the rotation function F on nums as follow:

F(k) = 0 * arrₖ[0] + 1 * arrₖ[1] + ... + (n - 1) * arrₖ[n - 1].

Return the maximum value of F(0), F(1), ..., F(n-1) .

The test cases are generated so that the answer fits in a 32-bit integer.

Example 1:

Input: nums = [4,3,2,6]

Output: 26

Explanation:

F(0) = (0 * 4) + (1 * 3) + (2 * 2) + (3 * 6) = 0 + 3 + 4 + 18 = 25

F(1) = (0 * 6) + (1 * 4) + (2 * 3) + (3 * 2) = 0 + 4 + 6 + 6 = 16

F(2) = (0 * 2) + (1 * 6) + (2 * 4) + (3 * 3) = 0 + 6 + 8 + 9 = 23

F(3) = (0 * 3) + (1 * 2) + (2 * 6) + (3 * 4) = 0 + 2 + 12 + 12 = 26

So the maximum value of F(0), F(1), F(2), F(3) is F(3) = 26.

Example 2:

Input: nums = [100]

Output: 0

Example 3:

Input: nums = [0,0,0,0]

Output: 0

Constraints:

n == nums.length

1 <= n <= 10⁵

-100 <=…