1
CS231 Algorithms Handout #29
Prof Lyn Turbak April 26, 2001
Wellesley College
PROBLEM SET 9
Due: Monday, May 7
Reading: Handouts 28 (Depth-First Search), 30 (P&NP), 31 (NP-Completeness); CLR
Sections 23.3--23.5 (Depth-First Search, Toplogical Sort, Strongly Connected
Components); CLR Chapter 36;
Suggested Problems: ; 23.3-9; 23.4-2, 23.4-5; 23.5-1, 23..5-3, 23.5-4, 23.5-4; 23-1, 23-
2; 36.1-2, 36.1-7; 36.2-2, 36.2-4;
Problem 1 [30] Consider the following weighted graph G (this is the same graph from
PS8 Problem 1):
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
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 [15] Draw the tree the is induced by performing a depth-first-search starting at node a.
Label each vertex by its discovery and finish times (as on CLR p. 479). Using dotted
lines, draw the edges of G that are not in the depth-first tree and label them as forward
edges (F), back edges (B), or cross edges (C).
b [5] Give a topological sort of the vertices in G.
c [10] Use the strongly connected component algorithm from CLR 23.5 to determine the
strongly connected components of G.
Problem 2 [15]
a [10] CLR 23.4-3 (p. 488).
b [5] Does your algorithm from part a work for directed graphs? Explain.
Problem 3 [15] CLR 23.4-5 (p. 488)
