leetcode 813. Largest Sum of Averages

leetcode 813. Largest Sum of Averages

---

原题地址：https://leetcode.com/problems/largest-sum-of-averages/

题目

We partition a row of numbers A into at most K adjacent (non-empty) groups, then our score is the sum of the average of each group. What is the largest score we can achieve?

Note that our partition must use every number in A, and that scores are not necessarily integers.

Example:
Input: 
A = [9,1,2,3,9]
K = 3
Output: 20
Explanation: 
The best choice is to partition A into [9], [1, 2, 3], [9]. The answer is 9 + (1 + 2 + 3) / 3 + 9 = 20.
We could have also partitioned A into [9, 1], [2], [3, 9], for example.
That partition would lead to a score of 5 + 2 + 6 = 13, which is worse.

Note:

• 1 <= A.length <= 100.
• 1 <= A[i] <= 10000.
• 1 <= K <= A.length.
• Answers within 10^-6 of the correct answer will be accepted as correct.

python代码

class Solution:
    def largestSumOfAverages(self, A, K):
        """
        :type A: List[int]
        :type K: int
        :rtype: float
        """
        out = dict()

        def dp(length, groups):

            if (length, groups) in out: 
                return out[(length, groups)]

            if groups == 1:
                out[(length, groups)] = sum(A[:length]) / length
                return out[(length, groups)]

            temp = 0
            out[length, groups] = 0

            for i in range(length - 1, 0, -1):
                temp += A[i]
                out[(length, groups)] = max(out[(length, groups)], dp(i, groups - 1) + temp / (length - i))

            return out[(length, groups)]

        return dp(len(A), K)

版权声明：转载注明 http://blog.csdn.net/birdreamer/article/details/79850052