Rotate Function

Problem Description

You are given an integer array nums of length n. Assume arr_k to be an array obtained by rotating nums by k positions clock-wise. We define the rotation function F on nums as follows:
F(k) = 0 * arr_k[0] + 1 * arr_k[1] + ... + (n - 1) * arr_k[n - 1].
Return the maximum value of F(0), F(1), ..., F(n-1).

Key Insights

• The rotation function calculates a weighted sum of the elements in the array based on their indices after rotation.
• Instead of calculating each F(k) from scratch, we can derive F(k) from F(k-1) by recognizing how the rotation affects the sum.
• The relationship between F(k) and F(k-1) can be expressed as: F(k) = F(k-1) + sum(nums) - n * nums[n-k], where sum(nums) is the sum of all elements in the array and n is the length of the array.
• This allows us to compute all values of F(k) in linear time.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we will use an iterative approach to calculate the value of F(k) starting from F(0). We will maintain a running sum of the array elements and update the value of F based on the derived formula mentioned in the key insights.

Code Solutions