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1. (a) (b) DFS of an undirected graph G can be used to identify the connected com- ponents of G, and that the depth-first forest contains as many trees as G has connected components. Modify DFS so that it assigns each vertex v an integer label v.cc between 1 and k, where k is the number of connected components of G such that u.cc = v.cc if and only if u and v are in the same connected component. s] Prove that your algorithm in part (a) is correct.

1. (a) (b) DFS of an undirected graph G can be used to identify the connected com- ponents of G, and that the depth-first forest contains as many trees as G has connected components. Modify DFS so that it assigns each vertex v an integer label v.cc between 1 and k, where k is the number of connected components of G such that u.cc = v.cc if and only if u and v are in the same connected component. s] Prove that your algorithm in part (a) is correct.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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DFS of an undirected graph G can be used to identify the connected com- ponents of G, and that the depth-first forest contains as many trees as G has connected components. Modify DFS so that it assigns each vertex v an integer label v.cc between 1 and k, where k is the number of connected components of G such that u.cc = v.cc if and only if u and u are in the same connected component. (b) s] Prove that your algorithm in part (a) is correct. 1. (a)
Transcribed Image Text:DFS of an undirected graph G can be used to identify the connected com- ponents of G, and that the depth-first forest contains as many trees as G has connected components. Modify DFS so that it assigns each vertex v an integer label v.cc between 1 and k, where k is the number of connected components of G such that u.cc = v.cc if and only if u and u are in the same connected component. (b) s] Prove that your algorithm in part (a) is correct. 1. (a)
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