https://leetcode.com/problems/rotate-function?envType=daily-question&envId=2026-05-01
瞪眼看一下，很快就能發現規律了：
from typing import List
class Solution:
def maxRotateFunction(self, nums: List[int]) -> int:
# Calculate initial F(0) and the total sum of elements.
# F(0) = 0 * nums[0] + 1 * nums[1] + ... + (n-1) * nums[n-1]
# F(k) = F(k-1) + sum(nums) - n * nums[n-k]
n = len(nums)
if n == 0:
return 0
total_sum = sum(nums)
f = sum(i * val for i, val in enumerate(nums))
max_f = f
for k in range(1, n):
# Update F(k) based on F(k-1)
# The last element in the previous rotation moves to the first position,
# its coefficient changes from (n-1) to 0. All other elements' coefficients increase by 1.
f += total_sum - n * nums[n - k]
max_f = max(max_f, f)
return max_f