[396]Rotate Function

Given an array of integers A and let n to be its length.

Assume Bk to be an array obtained by rotating the array A k positions clock-wise, we define a "rotation function" F on A as follow:

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

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

Note: n is 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.

思路

巧妙之处在于每一次右移才相乘可以理解为，除某一个元素导致总和下降外，其他元素都使得总和增加了，以减少运算量。

Code

Python

class Solution(object):
    def maxRotateFunction(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        length = len(A)
        sumA = sum(A)
        s = sum(i*n for i,n in enumerate(A))
        m = s
        i = 1
        while i < length:
            s += sumA-A[-1-i+1]*length
            m = max(m,s)
            i += 1
        return m

Runtime: 52ms