Suppose you are given an undirected graph G and a start node s. Your task is to design an algorithm that returns FALSE if G is not a tree and returns TRUE and labels each vertex v with the number of nodes in the subtree rooted at v if G is a tree. Note that the orientation of edges is implicit given the start node. Hint: Modify DFS to solve the problem.

Suppose you are given an undirected graph G and a start node s. Your task is to design an algorithm that returns FALSE if G is not a tree and returns TRUE and labels each vertex v with the number of nodes in the subtree rooted at v if G is a tree. Note that the orientation of edges is implicit given the start node. Hint: Modify DFS to solve the problem.

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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Given a circular linked list, implement an algorithm that returns the node at the beginning of the loop.DEFINITIONCircular linked list: A (corrupt) linked list in which a node's next pointer points to an earlier node, soas to make a loop in the linked list.EXAMPLEInput:Output:A -> B -> C -> D -> E -> C [the same C as earlier]C
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Your second function is called “isTree". Its input is a graph G, which is a dictionary whose keys are the vertices, and whose values are lists of vertices that are adjacent to the given vertex. Its output is True if G is a tree and False if G is not a tree. Hint: You may want to make use of your "connected" function from the last coding assignment.
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