Leetcode 396. Rotate Function

Given an array, maximize the rotation function F(k) = sum_{i=0}^{n-1} i * arr_k[i] over all k (rotating the array by k positions), with n up to 1e5. The core challenge is to avoid O(n^2) recomputation by using a mathematical recurrence to update F for each rotation in O(1), achieving an overall O(n) solution.