Introduction to Algorithms
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 22.2, Problem 5E
Program Plan Intro

To argue the value of v.d assigned to a vertex v is independent of the order in which the vertices appeared in each adjacency list.

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Consider the following undirected binary tree T with 17 vertices. a lo Starting with the root vertex a, we can use Breadth-First Search (BFS) or Depth-First Search (DFS) to pass through all of the vertices in this tree. Whenever we have more than one option, we always pick the vertex that appears earlier in the alphabet. For example, from vertex a, we go to b instead of c. Clearly explain the difference between Breadth-First Search and Depth-First Search, and deter- mine the order in which the 17 vertices are reached using each algorithm.
In the following G, each adjacency list is sorted in increasing alphabetical order. B H G Do depth-first search in G, considering vertices in increasing alphabetical or- der. Show the final result, with vertices labeled with their starting and finishing times, and edges labeled with their type (T/B/F/C). Here T, B, F and C refer to tree, back, forward, and cross edges, respectively. For your convenience, the graph is reproduced enlarged below. B D E H G F
4. Consider the graph G, shown below, which is simply a copy of K5. 02 V3 5 V1 24 V5 How many distinct spanning trees does G have? (Hint: Break up your search by the isomorphism type of the tree, as discovered on the previous page. So for example, start by counting the paths of length 5 in G. Then proceed to the next type of tree with 5 vertices. The total number of trees is 125, but please use this answer only to check that your solution is complete!)
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