Given an array consisting of n integers, find the contiguous subarray of given length k that has the maximum average value. And you need to output the maximum average value.

Example 1:

Input: [1,12,-5,-6,50,3], k = 4

Output: 12.75

Explanation: Maximum average is (12-5-6+50)/4 = 51/4 = 12.75

Note:

1. 1 <= k <= n <= 30,000.
2. Elements of the given array will be in the range [-10,000, 10,000].

思路就是sliding windows, A[i] = A[i-1] - nums[i-1] + nums[i+k-1], init: A[0] = sum(nums[:k])

Code:  T: O(n)  S; O(1)  using rolling arry to  O(1)

class Solution(object):

    def findMaxAverage(self, nums, k):

        ans, n = sum(nums[:k]), len(nums)

        dp = [ans] + [0]

        for i in range(1, n-k+1):

            dp[i%2] = dp[i%2-1] - nums[i-1] + nums[i+k-1]

            ans = max(ans, dp[i%2])

        return ans*1.0/k