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Computer Science 130B
Spring 2012
Homework #2
Due: 4pm, Feb. 3, Friday
Problem 1
Consider the coin change problem. You are at a check out register, and have an unlimited supply of
quarters, dimes, nickels, and pennies. You have to make change for a customer. Design a greedy algorithm to make
out an amount of
x
cents that uses the smallest number of coins. Prove the optimality of your algorithm.
Problem 2
We know that a minimumcost spanning tree links all the vertices in a connected undirected graph together
in such a way that the
total
cost of the tree arcs is minimized. Does this fact imply that given two vertices
i
and
j
in a
graph and a minimumcost spanning tree of that graph, the shortest path from
i
to
j
must contain only the tree arcs in
the minimumcost spanning tree? If you think so, prove it, otherwise, give a counterexample.
Problem 3
Consider the graph shown in figure 1.
a.
Find the shortest path from vertex
a
to vertex
e
using Dijkstra’s algorithm. Show intermediate steps in executing
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This note was uploaded on 02/19/2012 for the course ENGR 361 taught by Professor Drexel during the Spring '12 term at Bloomsburg.
 Spring '12
 Drexel
 Computer Science

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