(a) Adjacency list and adjacency matrix are two standard ways to represent graphs. Show the space consumption, the cost to count the number of edges in the graph and the cost to check the existence of an edge with adjacency list and adjacency matrix respectively. (b) In Fig. 1 is an undirected graph ?1. Show the sequence of nodes in the breadth-first traversal starting from node ?1, assuming that the neighbor nodes in the adjacency list of each node are in increasing order.

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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”.