1
CS231 Algorithms Handout #27
Prof Lyn Turbak April 19, 2001
Wellesley College
PROBLEM SET 8
Due: Thursday, April 26
Reading: Handouts 25--26; CLR Section 5.4 (Graphs); Sections 23.1--23.2 (Bread-First
Search); Chapter 24 (Minimum Spanning Trees); Sections 25.1 -- 25.2 (Relaxation +
Dijkstra’s algorithm). I suggest you skim all the sections and look at the figures but avoid
reading the proofs. Note that some of the graph algorithms I presented in class are
somewhat different than the ones presented in the book.
Suggested Problems: 23.1-1; 24.1-7, 24.2-4, 24.2-5, 25.2-1, 25.2-3, 25.2-5, 25.2-6
Problem 1 [50] Consider the following weighted graph G:
a b c
def g h
ijk
3
4
5
6
7
1
2
4
8
2
7
9
2
6
15
3
10
1
Although edges in the graph are directed (draw with arrows), for this problem you should
ignore the arrows and treat G as an undirected graph. (Sorry, but the latest version of
Microsoft Word prevents me from conveniently editing the graph, which was created in a
previous version.)
In the following problems, you should assume that G is represented as a collection of
adjacency lists, and that vertices are ordered alphabetically within each adjacency list.
a [10] Use Prim's algorithm to derive a minimum spanning tree of G.
b [10] Use Kruskal's algorithm to derive a minimum spanning tree of G.
c [10] Draw the tree that is induced by performing breadth-first search starting at node d.
d [20] Use Dijkstra’s algorithm to determine the shortest paths from d to each of the
other vertices. Draw the shortest path tree that is induced by running Dijkstra's algorithm,
and annotate each vertex by its shortest path distance from d.
