Editorial for CPC '19 Contest 1 P2 - Luggage

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Author: Plasmatic

Subtask 1

For this subtask, you can simply brute force all subsets of the items and pick the largest subset with a height range $\le K$ ~\le K~.

Time Complexity: $\mathcal O(2^N \cdot N)$ ~\mathcal O(2^N \cdot N)~

Subtask 2

Note that it is always advantageous to pick items with as close of a height as possible. Therefore, if you sort the items the question simply becomes finding the largest subarray with a height range $\le K$ ~\le K~. Brute forcing all subarrays and picking the largest one with a height range $\le K$ ~\le K~ is fast enough for the second subtask. Finding the height range of a subarray from indices $i$ ~i~ to $j$ ~j~ is simply $arr[j]-arr[i]$ ~arr[j]-arr[i]~ since the array is sorted.

Time Complexity: $\mathcal O(N^2)$ ~\mathcal O(N^2)~

Subtask 3

To get full points, you have to optimize the brute force from subtask 2 to either binary search or a two-pointer method.

Time Complexity: $\mathcal O(N \log N)$ ~\mathcal O(N \log N)~

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