396. Rotate Function

Medium

30 Points

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: 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.

Examples

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

Constraints

n == nums.length
1 <= n <= 105
-100 <= nums[i] <= 100