Put Marbles in Bags

arraygreedysorting

Problem Statement

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 .

Examples

Example 1

Input: weights = [1,3,5,1], k = 2
Output: 4
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
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 <= 10 ^5

1 <= weights[i] <= 10 ^9

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicGreedy