How to Solve Put Marbles in Bags Problem
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Put Marbles in Bags
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...
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Understanding the Put Marbles in Bags Problem
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Problem Statement
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.
Put Marbles in Bags
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Examples
weights = [1,3,5,1], k = 2
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.
weights = [1, 3], k = 2
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 <= 105
1 <= weights[i] <= 109
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