159.302 Artificial Intelligence
Assignment #1
The 8-Puzzle: Comparing Search Algorithms
Maximum number of members per group: 3 students
Deadline for submission: May 2, 2012
Instructions
Your task is to write a program that will solve the 8-puzzle problem using four different search
algorithms, one after the other.
An AnimateSolution() function has been provided that you can use to animate the sequence of
moves (i.e. path) calculated by the algorithms. A start-up program (compiles with ScITE) with a
graphics library is available for downloading from our website:
http://www.massey.ac.nz/~nhreyes/Massey/159302.htm.
It is up to you to write any functions , classes or data structures that you may require. You can use
any printf() (or cout) to trace the algorithm execution.
For each implementation of the algorithms below, include codes that will capture the following
information during the algorithm’s execution:
a. Max. Queue length – e.g. 26
b. Path length - e.g. 30
c. Number of state expansions – e.g. 157
d. Sequence of moves – e.g. DDRRULUL
e. Actual running time in seconds (use the clock() function as shown in the sample codes in
slides)
Part 1: Depth-First Search using the Visited List:
Write code that uses the s (initial state) and g (a goal state) and returns the sequence of moves.
Part 2: Breadth-First Search using the Visited List:
Write code that uses the s (initial state) and g (a goal state) and returns the sequence of moves.
Part 3: Progressive Deepening Search
Write code that uses the s (initial state) and g (a goal state) and returns the sequence of moves.
Part 4: A* Search using the Strict Expanded List:
Write a function in the same form as Part 1 to implement the A* algorithm with Strict Expanded
List and using the following heuristic:
A* with Strict Expanded List and using the Sum of Manhattan Distances as heuristic
Part 5: Algorithm Documentation
Write a pseudo code (or flow chart) for each of the algorithm (in Parts 1, 2, 3 & 4) implementation.
Discuss also the data structures and variables you have used.
Part 6: Tests and Results
N.H.Reyes
159.302 Artificial Intelligence
Assignment #1
Test all the algorithms using the given 5 starting states and 1 goal state below.
Include in your documentation the following information for each test case and algorithm
combination:
a. Max. Queue length
b. Path length
c. Number of state expansions
d. Sequence of moves (e.g. d, l, r, etc.)
e. Actual running time in seconds
Accomplish the given table below to summarize your results.
Algorithm
Initial
State
1
DFS using the Visited List
042158367
2
BFS with Visited List
042158367
3
Progressive Deepening Search
042158367
4
042158367
5
A* using the Strict Expanded List
DFS using the Visited List
6
BFS with Visited List
876543210
7
Progressive Deepening Search
876543210
8
A* using the Strict Expanded List
876543210
Max.
Queue
length
Path
length
No. of state
expansions
Sequence
of moves
Actual
Running
Time
(sec.)
876543210
9
DFS using the Visited List
481302675
10
BFS with Visited List
481302675
11
Progressive Deepening Search
481302675
12
481302675
13
A* using the Strict Expanded List
DFS using the Visited List
14
BFS with Visited List
168342750
15
Progressive Deepening Search
168342750
16
A* using the Strict Expanded List
168342750
17
DFS using the Visited List
123804765
18
BFS with Visited List
123804765
19
Progressive Deepening Search
123804765
20
A* using the Strict Expanded List
123804765
168342750
Note: # - blank space
GOAL STATE:
((# 1 2)
(3 4 5)
(6 7 8))
A set of starting states of differing complexity:
START1:
((# 4 2)
(1 5 8)
(3 6 7))
START2:
((8 7 6)
N.H.Reyes
159.302 Artificial Intelligence
Assignment #1
(5 4 3)
(2 1 #))
START3:
((4 8 1)
(3 # 2)
(6 7 5))
START4:
((1 6 8)
(3 4 2)
(7 5 #))
START5:
((1 2 3)
(8 # 4)
(7 6 5))
Marking:
Make sure your program compiles using gcc before handing it in.
Effective comments make it easier to award marks or partial points if the program is not 100%
working properly.
You can work as a group for this assignment. Copied work will be awarded zero marks.
Hints:
Some random combinations of pieces for your initial state are unsolvable.
Refer to the lecture slides for concepts.
You can step through the search by including a getch() function inside your main loop to pause the
program until the user presses any key.
Example Sequence:
Sequence of states and operations.
You may choose to represent states in an array, size 9. You can represent operations with the 'u' 'd'
'l' 'r' characters.
In notation, the sequence s to get to the goal from the initial state could be represented:
s = {d,r,u,u,l,d} You may find it helpful to printf() (or cout) something similar to help debug your
program.
Nothing follows.
N.H.Reyes