2551. Put Marbles in Bags

題目描述

You have k bags. You are given a 0-indexed integer array weights where weights[i] is the weight of the i^th marble. You are also given the integer k.

Divide the marbles into the k bags according to the following rules:

• No bag is empty.
• If the i^th marble and j^th marble are in a bag, then all marbles with an index between the i^th and j^th indices should also be in that same bag.
• If a bag consists of all the marbles with an index from i to j inclusively, then the cost of the bag is weights[i] + weights[j].

The score after distributing the marbles is the sum of the costs of all the k bags.

Return the difference between the maximum and minimum scores among marble distributions.

範例

Example 1:

Input: weights = [1,3,5,1], k = 2
Output: 4
Explanation: 
The distribution [1],[3,5,1] results in the minimal score of (1+1) + (3+1) = 6. 
The distribution [1,3],[5,1], results in the maximal score of (1+3) + (5+1) = 10. 
Thus, we return their difference 10 - 6 = 4.

Example 2:

Input: weights = [1, 3], k = 2
Output: 0
Explanation: The only distribution possible is [1],[3]. 
Since both the maximal and minimal score are the same, we return 0.

Constraints:

• 1 <= k <= weights.length <= 10⁵
• 1 <= weights[i] <= 10⁹

解答

Python

class Solution:
    def putMarbles(self, weights: List[int], k: int) -> int:
        arr = sorted(map(sum, pairwise(weights)))
        return sum(arr[len(arr)-k+1:]) - sum(arr[:k-1])

Yen-Chi ChenSun, Jul 9, 2023

Reference

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