3.
[20 points]
A* Search
.
You have 5 errands that you need to do on Monday. You need to:
1. Drop off clothes at the dry cleaners
2. Pick up a birthday present for your roommate from Hollister's.
3. Drop off your paper that is due for
your French class at the French department office.
4. Pick up a new book on Artificial Intelligence at the bookstore
5. Buy some stamps from the post office.
You are leaving from your dorm room and following completion of your errands, you
w
ant
to end up at the bookstore which not only is furthest from your dorm, but is closest to where
your midterm study group will meet
. You want to order the errands so that you
have to walk
the least distance. The distance between each pair of locations
is
given below in Table 1.
You decide to solve this problem using A* search.
A.
(5 points)
What is the state space
and goal
that you will use?
B.
(5 points)
What is the successor function?
C
.
(5 points)
What is an admissable heuristic that you can use f
or this problem? State
why it
is admissable (in 2 sentences or less).
D
.
(5 points)
Trace the solution of A* on the problem, showing the search tree that is
constructed, g(n)
(i.e., cost)
and h(n)
(i.e., heuristic estimate)
at each node. You need only
sh
ow the trace for 5 states through the search tree.
Dorm
Cleaners
Hollister
French
bookstore
Postoffice
Dorm
0
4
3
8
9
5
Cleaners
4
0
5
5
7
5
Hollister
3
5
0
7
7
2
French
8
5
7
0
3
5
Bookstore
9
7
7
3
0
5
Postoffice
5
5
2
5
5
0
1.
[20 points]
Sol
ve the cryptarithmetic problem below by hand, using backtracking,
forward checking, and the minimum remaining values and the least

constraining

value heuristics. Show your work, indicating where forward checking and each of the
heuristics comes into play.
PIN
+ PIN
KNOT
1. [12 points] Bayesian Networks
Consider the following Bayesian Network, where variables
H,G,R,
and
J
are all Boolean

valued:
You are given the simple belief network above with Boolean variables, H=Hardworking,
G=Good Grades, R = exc
ellent Recommendation, J = landed a good Job. For each
problem below, show your work.
a.
Which, if any, of the following are asserted by the network structure (ignoring the
CPTs for now)?
[Note: any subset of these may be correct]
i.
P(H,G) = P(H)P(G)
ii.
P(JR,H)
= P(JR)
iii.
P(J)
P(JH)
b.
Calculate the value of P(H,G,
R,
J). It is sufficient to show how you would
calculate it without actually doing the arithmetic.
c.
Suppose we want to add the variable C = HasTheRightConnections to the network;
describe, with justi
fications, all the changes you would make to the network.
H
P(G=true  H)
T
.4
F
.8
H
G
P(R =true  H, G)
false
false
0.2
false
true
0.9
true
false
0.3
true
true
0.8
R
P(J=true  R)
false
0.2
true
0.7
P(H=true)
= 0.1
0.20.20.2
G
H
R
J
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