Solution Found!
Squares. Design and analyze an algorithm that takes as input an undirected graph G = (V
Chapter 4, Problem 4.3(choose chapter or problem)
Design and analyze an algorithm that takes as input an undirected graph \(G=(V, E)\) and determines whether \(G\) contains a simple cycle (that is, a cycle which doesn’t intersect itself) of length four. Its running time should be at most \(O\left(|V|^{3}\right)\).
You may assume that the input graph is represented either as an adjacency matrix or with adjacency lists, whichever makes your algorithm simpler.
Questions & Answers
QUESTION:
Design and analyze an algorithm that takes as input an undirected graph \(G=(V, E)\) and determines whether \(G\) contains a simple cycle (that is, a cycle which doesn’t intersect itself) of length four. Its running time should be at most \(O\left(|V|^{3}\right)\).
You may assume that the input graph is represented either as an adjacency matrix or with adjacency lists, whichever makes your algorithm simpler.
ANSWER:Step 1 of 3
Consider an undirected graph, \(G=(V, E)\) with the cycle of length four. An adjacency matrix is a square matrix which represents the vertices and edges of the graph. To determine whether the graph contains a cycle of length four by using the adjacency matrix method of the graph. Since the adjacency matrix is a square matrix, and the four edges of the square does not intersect each other, it is simple to develop an algorithm that runs in at most \(O\left(|V|^{3}\right)\) , where \(V\) is the number of vertices in the graph.