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g2501_2600.s2551_put_marbles_in_bags.readme.md Maven / Gradle / Ivy

2551\. Put Marbles in Bags

Hard

You have `k` bags. You are given a **0-indexed** integer array `weights` where `weights[i]` is the weight of the ith 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 ith marble and jth marble are in a bag, then all marbles with an index between the ith and jth 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_.

**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