tldr; Test updating
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You may assume that each input would have exactly one solution, and you may not use the same element twice.
the following are no longer NP-Complete if only considering planar graphs (graphs with no intersecting edges):
4-colourability (3-colourability still is)
i.e. we may get a scalable solution when restricting the search space.
approximation algorithms: not guaranteed to be the best solution but will produce solution within known factor.
heuristics: arise from limitations of application area and are used to cut down the search space.