Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 22.3, Problem 10E
Program Plan Intro
To modify the pseudocode for depth-first search so that it prints out every edge in the directed graph and also for undirected graph.
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The reverse of a directed graph G = (V,E) is another directed graph G^R = (V,E^R) on the same
vertex set, but with all edges reversed; that is, E^R = {(v, u) : (u, v) ∈ E}.Give a linear-time algorithm for computing the reverse of a graph in adjacency list format.
Prove that when doing depth-first search on undirected graphs there are never any forward or cross edges.
In a directed graph represented by adjacency lists, write a function that returns true (1) if there is an edge between two given vertices u and v and false (0) otherwise.
Chapter 22 Solutions
Introduction to Algorithms
Ch. 22.1 - Prob. 1ECh. 22.1 - Prob. 2ECh. 22.1 - Prob. 3ECh. 22.1 - Prob. 4ECh. 22.1 - Prob. 5ECh. 22.1 - Prob. 6ECh. 22.1 - Prob. 7ECh. 22.1 - Prob. 8ECh. 22.2 - Prob. 1ECh. 22.2 - Prob. 2E
Ch. 22.2 - Prob. 3ECh. 22.2 - Prob. 4ECh. 22.2 - Prob. 5ECh. 22.2 - Prob. 6ECh. 22.2 - Prob. 7ECh. 22.2 - Prob. 8ECh. 22.2 - Prob. 9ECh. 22.3 - Prob. 1ECh. 22.3 - Prob. 2ECh. 22.3 - Prob. 3ECh. 22.3 - Prob. 4ECh. 22.3 - Prob. 5ECh. 22.3 - Prob. 6ECh. 22.3 - Prob. 7ECh. 22.3 - Prob. 8ECh. 22.3 - Prob. 9ECh. 22.3 - Prob. 10ECh. 22.3 - Prob. 11ECh. 22.3 - Prob. 12ECh. 22.3 - Prob. 13ECh. 22.4 - Prob. 1ECh. 22.4 - Prob. 2ECh. 22.4 - Prob. 3ECh. 22.4 - Prob. 4ECh. 22.4 - Prob. 5ECh. 22.5 - Prob. 1ECh. 22.5 - Prob. 2ECh. 22.5 - Prob. 3ECh. 22.5 - Prob. 4ECh. 22.5 - Prob. 5ECh. 22.5 - Prob. 6ECh. 22.5 - Prob. 7ECh. 22 - Prob. 1PCh. 22 - Prob. 2PCh. 22 - Prob. 3PCh. 22 - Prob. 4P
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- Prove that in a breadth-first search on a undirected graph G, every edge iseither a tree edge or a cross edge, where x is neither an ancestor nor descendant of y, in cross edge (x, y).arrow_forward. Show the result of topological sorting of the graph. There will be multiple of them. Just list one of them.arrow_forwardWrite code for Iterative Depth First Search of a Graph and explain?arrow_forward
- Give a high-level analysis of the running time of depth-first-search, assuming that the graph G has n nodes and m edges.arrow_forwardIs it necessary for every cut edge e in an undirected graph G to be an edge in G's depth-first search tree? Give at least two examples to back up your point. A cut edge is defined as any edge that cuts the graph.)arrow_forwardThe graph with edges AB, BC, CD and DA is a complete graph. True or Falsearrow_forward
- Given a directed graph G(V, E), find an O(|V | + |E|) algorithm that deletes at most half of its edges so that the resulting graph doesn’t contain any directed cycles. Also follow up with proof of correctness.arrow_forwardFor a directed graph, find if there is a path between two vertices or not. Write the algorithm and C++ code for it. Represent the example diagrammatically. Calculate the time and space complexity for it too.arrow_forwardIt is stated that K6 is not a planar graph (because K5 is one of the subgraphs of K6), but there is a subgraph of K6 which is a planar graph. If G' is a subgraph of K6, then find G' which has the maximum number of vertices and edges. Hint: Answers are expressed in sets and pictures.arrow_forward
- Suppose that the graph G has n nodes and m edges, and that the completion of a depth-first search takes n minutes.arrow_forwarddraw the graph that represents said matrix and find out, using Python, the number of 3-paths that connect the vertices v1 and v3 of the same.arrow_forwardI have a directed graph with N nodes. How can I tell if the graph has a cycle? Your answer should be an algorithm in English. It is nice but not essential for you to give the name of the algorithm. You should describe how the algorithm works.arrow_forward
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