396 Rotate Function

Given an array of integersAand letnto be its length.

AssumeBkto be an array obtained by rotating the arrayAkpositions clock-wise, we define a "rotation function"FonAas follow:

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

Calculate the maximum value ofF(0), F(1), ..., F(n-1).

Note: nis guaranteed to be less than 105.

Example:

A = [4, 3, 2, 6]

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.

Brute Force: (time limit exceeded)

def maxRotateFunction(self, A):
    """
    :type A: List[int]
    :rtype: int
    """

    if not any(A): return 0
    my_max = float('-inf')
    adder = 0
    for i in range(0, len(A)):
        my_max = max(my_max, sum(A[(mult + adder) % len(A)] * mult for mult in range(0, len(A))))
        adder += len(A) - 1

    return my_max