IELM202
Tutorial 5
1/6/11
1. You need to take a trip by car to another town that you have never visited before.
Therefore, you are studying a map to determine the shortest route to your destination.
Depending on which route you choose, there are five other towns (call them A, B, C, D,
E) that you might pass through on the way. The map shows the mileage along each road
that directly connects two towns without any intervening towns. These numbers are
summarized in the following table, where a dash indicates that there is no road directly
connecting these two towns without going through any other towns.
Town
Miles between Adjacent Towns
A
B
C
D
E
Destination
Origin
40
60
50



A
10

70


B
20
55
40

C

50

D
10
60
E
80
(a) Formulate this problem as a shortestpath problem by drawing a network where
nodes represent towns, links represent roads, and number indicate the length of
each link in miles.
(b) Use Dijkstra algorithm to solve this shortestpath problem.
Ans:
Remove the direction >
(a)
A
B
D
T
O
C
E
70
10
40
50
50
80
60
55
60
20
40
10
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Tutorial 5
1/6/11
(b)
n
Solved
nodes
connected
to unsolved
nodes
Closest
connected
unsolved
odes
Total
distance
involved
Nth
Nearest
node
Minimum
distance
Last
connection
1
O
A
40
A
40
OA
2,3
O
A
C
B
50
40+10=50
C
B
50
50
OC
AB
4
A
B
C
D
E
E
40+70=110
50+40=90
50+50=100
E
90
BE
5
A
B
E
D
D
D
40+70=110
50+55=105
90+10=100
D
100
ED
6
D
E
T
T
100+60=160
90+80=170
T
160
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 Fall '10
 D
 Car, Shortest path problem, Total net cost, Sarah trade

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