Rohan and his friends kept track of which cities they visited on their Euro trip on a map with 2k cities and k edges, where 2 cities have an edge between them if the group took a direct mode of transportation between them. Rohan noticed that their map had no isolated cities. Show that their map has exactly k connected components (groups of cities all connected via direct mode of transportation)

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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”.