Help with a 2SAT? Problem

Revision en2, by MVB, 2023-12-05 00:42:54

Hello! I have been stuck on this problem for a while. Here is what it asks:

Given an array, determine if it is possible to choose a set of distinct subarrays of length $$$2$$$ such that every index is taken at least once. A set of subarrays is considered distinct if no two subarrays have equal elements. For example, $$$[1,2],[1,2]$$$ is not a valid set, while $$$[1,3],[1,2]$$$ is.

As an example, let's consider the array $$$[1,2,1,2,3]$$$. We can choose $$$[1,2],[2,1],[2,3]$$$, corresponding to the indices $$$[1,2],[2,3],[4,5]$$$ (indexed from $$$1$$$).

The problem can be found here.

I have heard that this can be solved with 2SAT, but I have no idea how. I have never solved a 2SAT problem similar to this one, and I don't know what I am missing. Basically, I don't understand how to construct a graph that solves this task (or if it can be solved in another way).

Any help, similar problem(s), or hints would be much appreciated. Thanks!

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en2 English MVB 2023-12-05 00:42:54 347 Tiny change: ' are equal $[1, 2], ' -> ' are equal. $[1, 2], ' (published)
en1 English MVB 2023-12-05 00:33:07 776 Initial revision (saved to drafts)