This problem is based on the Gale-Shapley Algorithm. In each iteration of the while loop, choose an arbitrary unmatched teacher j. Next, j makes an offer to the highest teacher on thier list whom j has not yet made an offer to yet. Statement: If some teacher j makes an offer to j0 and they match forming (j, j0 ), then j will reject any future offers while still matched to j0 Proof. This is true because j has already previously made offers to every teacher they prefer over j0 . (This is false)   Briefly explain why the above Statement is false by explaining a circumstance that would lead to j accepting another proposal while matched to j0.

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Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.