7. Consider the following graph: A 9 14 D E C 12 10 17 B Apply Kruskal's algorithm to find the minimum spanning tree. Edges are sorted first by length, and in the event of a tie, by name, where the two letters are in alphabetical order. Use makeset (x), find (x), and union (x, y) to determine if there are cycles. a) Circle the edges that are part of the minimum spanning tree. AC, AD, AE, BC, BD, BE, DE b) What is the weight of the minimum spanning tree? c) Draw the tree that results from applying the union-find algorithm for cycle detection. When drawing the tree, put vertices with lower letters in the left subtrees so that all the vertices in a level are sorted alphabetically from left to right

7. Consider the following graph: A 9 14 D E C 12 10 17 B Apply Kruskal's algorithm to find the minimum spanning tree. Edges are sorted first by length, and in the event of a tie, by name, where the two letters are in alphabetical order. Use makeset (x), find (x), and union (x, y) to determine if there are cycles. a) Circle the edges that are part of the minimum spanning tree. AC, AD, AE, BC, BD, BE, DE b) What is the weight of the minimum spanning tree? c) Draw the tree that results from applying the union-find algorithm for cycle detection. When drawing the tree, put vertices with lower letters in the left subtrees so that all the vertices in a level are sorted alphabetically from left to right

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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Concept explainers

Heuristic System

The term heuristic is derived from the Greek word heurisko, which means “I find, discover”. Heuristics can be mental shortcuts or approaches designed from previous experiences. The main aim of the heuristic approach is to find a good enough solution to solve the problem. Test and mistake, rule of thumb, or an educated estimate are all examples of heuristics. These methods are sufficient for achieving an immediate, brief aim. When a heuristic is used in practice, it works as predicted. It can, however, produce systematic errors. Trial and error is an important heuristic that may be used in a variety of situations, from cross-linking nuts and bolts to determining the values of given input variables in mathematical puzzles. Additional hypotheses, visual illustrations, simplification, and forward or backward reasoning are all common heuristics in mathematics.

Question

7. Consider the following graph:
A
14
CO
D
9
E
C
12
10
17
b) What is the weight of the minimum spanning tree?
B
Apply Kruskal's algorithm to find the minimum spanning tree. Edges are sorted first by length, and in
the event of a tie, by name, where the two letters are in alphabetical order. Use makeset (x),
find (x), and union (x, y) to determine if there are cycles.
a) Circle the edges that are part of the minimum spanning tree.
AC, AD, AE, BC, BD, BE, DE
c) Draw the tree that results from applying the union-find algorithm for cycle detection. When
drawing the tree, put vertices with lower letters in the left subtrees so that all the vertices in a
level are sorted alphabetically from left to right

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a) write the algorithm b) Briefly explain why the algorithm solves the problem, and the correctness c ) State and briefly explain the running time of your algorithm
A B. D H Suppose you run the topological sort algorithm on the graph above starting at vertex C. Use the rule that when there is a choice of vertices for the algorithm to visit, it visits them in alphabetic order. Which vertex would end up first in the eventual topologically sorted order? Which would end up being second? Which would end up being third? Which would end up being fourth? Which would end up being fifth? Which would end up being sixth?
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Suppose you have a graph with 100 nodes and 500 edges and you want to find the shortest path between two nodes using Dijkstra's algorithm. What is the time complexity of this operation?
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