Homework 10: Graphs part 1 Solution

Description

Problems

1. (15 pts) Exercise 22.1-5.

2. (15 pts) Exercise 22.2-6.

3. (15 pts) Exercise 22.2-7.

4. (10 pts) Exercise 22.3-7.

5. (10 pts) Exercise 22.3-10.

6. (15 pts) Exercise 22.3-12.

7. (20 pts) Exercise 22.4-5.

8. (15 pts) Two special vertices s and t in the undirected graph G=(V,E) have the fol-lowing property: any path from s to t has at least 1 + jV j=2 edges. Show that all paths from s to t must have a common vertex v (not equal to either s or t) and give an algorithm with running time O(V+E) to nd such a node v.

9. (Extra credit 25) Problem 22-3.

10. (Extra credit 25) Problem 22-4.

11. (25 pts) Exercise 23.1-3.

12. (25 pts) Exercise 23.2-2.

13. (25 pts) Exercise 23.2-4.

14. (25 pts) Exercise 23.2-5.

15. (Extra credit 40 pts) Problem 23-1.

16. (Extra credit 30 pts) Exercise 23.1-11.

17. (Extra credit 30 pts) Write the code for Kruskal algorithm in a language of your choice. You will rst have to read on the disjoint sets datastructures and operations (Chapter 21 in the book) for an e cient implementation of Kruskal trees.

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