**CS 332:
Algorithms**

**Homework #5**

**Assigned: **

**Due: **

1. Exercise 14.3-7 (15-3.7 in
old book). Additional (perhaps obvious)
hint: use an interval tree. This is a
good example of a problem in the field of *computational geometry*.

2. Exercise 23.2-4 (24.2-4) and
Exercise 23.2-5 (24.2-5). For the second
problem (Prim’s algorithm), ignore the case where
edge weights range from 1 to |V|; just focus on the case when edge weights run
from 1 to a constant W.

3. Exercise 23.4-5 (22.4-5). Give a detailed answer, with pseudocode and
analysis of running time, and sketch a proof that all vertices are output when
there are no cycles, and a description and sketch of a proof of what happens
when a cycle exists.