Description
Graphs part 1
Problems
- (15 pts) Exercise 22.1-5.
- (15 pts) Exercise 22.2-6.
- (15 pts) Exercise 22.2-7.
- (10 pts) Exercise 22.3-7.
- (10 pts) Exercise 22.3-10.
- (15 pts) Exercise 22.3-12.
- (20 pts) Exercise 22.4-5.
- (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 + |V |/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 find such a node v.
- (Extra credit 25) Problem 22-3.
- (Extra credit 25) Problem 22-4.
- (25 pts) Exercise 23.1-3.
- (25 pts) Exercise 23.2-2.
- (25 pts) Exercise 23.2-4.
- (25 pts) Exercise 23.2-5.
- (Extra credit 40 pts) Problem 23-1.
- (Extra credit 30 pts) Exercise 23.1-11.
- (Extra credit 30 pts) Write the code for Kruskal algorithm in a language of your choice. You will first have to read on the disjoint sets datastructures and operations (Chapter 21 in the book) for an efficient implementation of Kruskal trees.
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