# CSI4106 Assignment 1 solution

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## Description

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Learning objective: Program blind and informed search in the eight puzzle problem
Requirements:
a) The assignment must be done in a group of two. Individual assignments will not
be accepted.
b) You must be a regular registered student in the course
1. Description
The 8-puzzle problem is a puzzle played on a 3-by-3 grid with 8 square blocks labeled 1
through 8 and a blank square. Your goal is to rearrange the blocks so that they are in
order, using as few moves as possible. The legal actions include sliding blocks
horizontally or vertically into the blank square.
The initial state can be any arrangement of the blocks.
In this assignment, the final state is always:
———–
| | 1 | 2 |
———–
| 3 | 4 | 5 |
———–
| 6 | 7 | 8 |
———–
The following shows a sequence of legal moves from an easy start board (left) to
the goal board (right).

The Solution is: ‘left’.
The solution must be a sequence of moves/actions. You must display it both visually and
textually as a set of states and actions respectively (see above). Note also that your point
of reference must be the blank node, which is why the solution above indicates “left”
rather than “right”.
————-
| 1 | | 2 |
————-
| 3 | 4 | 5 |
————-
| 6 | 7 | 8 |
———–
| | 1 | 2 |
———–
| 3 | 4 | 5 |
———–
| 6 | 7 | 8 |
Prof. Amal Zouaq, CSI4106, F2017
2
Your program must also display the following information: the solution depth, the path
cost, the number of visited nodes to reach the solution, and the time taken to obtain it.
The method printResults is provided in util.py.
Example:
The Solution is at depth 1
The path cost is 1
Number of visited nodes: 3
The execution time is 0.0004117325215004907 seconds.
Note that not all puzzles are solvable, which means that not all initial configurations can
lead to the goal by a sequence of legal moves.
You will be provided with:
1- Some python code that you must complete
2- Examples of solvable and unsolvable configurations
Your code will be tested with any random configuration so you must make sure that it is
generic and that it can handle all possible cases.
2. Python code
You must use Python 3.6.2: https://www.python.org/downloads/
You will be provided with the following classes and packages:
Class State: to solve a problem, you must define a sub-class of the
class State that redefines the methods in the state class. (COMPLETE)
Class Node: This class represents a node in a search tree. (COMPLETE)
Class EightPuzzleState: you will implement the class EightPuzzleState
as a subclass of State. The skeleton is available in
problems.eightpuzzle. This class must contain the successor function,
the heuristics and all the methods that are dependent on the problem
you are trying to solve(TO BE COMPLETED BY YOUR CODE).
Class Util: The class contains an implementation of the data structures
Queue, Stack and PriorityQueue and utility methods. (TO BE COMPLETED BY
YOUR CODE)
Search algorithms – Folder searchdir: this folder contains sub-folders
with the following files (TO BE COMPLETED BY YOUR CODE):
 breadthfirst_search.py: You must use the queue implemented in
util.py
 depthfirst_search.py: You must use the stack implemented in
util.py
 astar_search.py: You must use the priority queue implemented in
util.py
Note that your search algorithms must remain independent of the
particular problem to solve. Each search algorithm must take as input
an initial state and return a solution node and the number of explored
nodes. The class EightPuzzleState contains examples of calls to the
search algorithms. This must not be modified.
Prof. Amal Zouaq, CSI4106, F2017
3
Several configurations/puzzles are available in EIGHT_PUZZLE_DATA. Some
are solvable and others are not. The code that tests the solvability of
a puzzle is provided.
After testing the available EIGHT_PUZZLE_DATA configurations, make
sure to un-comment the randomization of the puzzles. Test your
algorithms extensively.
Your code must handle exceptions such as for example an out of memory
exception
Note that you do not need any additional python file to solve the
problem and you must not add any other file.
3. To Do List
You must submit on Brighspace a zip file named yourname1_yourname2_A1.zip
containing your complete code and a report.
Code
You must write programs in Python that solve the problem described above using the
following search methods:
a. Depth-first search
b. Breadth-first search
c. A* search with two admissible heuristics H1 and H2
Report
The report must have a front page with your names, the course and the assignment
number. It must contain the following sections:
1. A description of the environment properties. Justify your answers.
2. A table that summarizes the performance of each algorithm (depth of solution,
solution path cost, time, number of visited nodes, and whether it is complete and
optimal) on the three same puzzles. These puzzles are: EIGHT_PUZZLE_DATA
[1](trivial), EIGHT_PUZZLE_DATA [6] (medium) and
EIGHT_PUZZLE_DATA [3] (harder). EIGHT_PUZZLE_DATA is defined in
EightPuzzleState.py
Note that A* must have a separate column for H1 and H2 and that you must
obtain the details of an execution with each heuristic.
3. Heuristics
a. A description of the two admissible heuristics used with A*
b. A clear explanation of their admissibility
c. Does one of the heuristics dominate the other? Why?
4. What is your conclusion regarding the performance of the algorithms?
Marking guidelines
1- Working and correct implementation following the guidelines
2- Good programming practices (appropriate use of classes, methods, parameters,
comments, etc.)
3- Correct answers to questions and correct expected solutions
Prof. Amal Zouaq, CSI4106, F2017
4
Mark Distribution
Code
Problem representation (successor
function, legal moves, cost, etc.)
20
DFS 15
BFS 15
A* 10
Heuristic1 5
Heuristic 2 5
Data structures in util.py 15
Report
Q1 2.5
Q2 5
Q3 5
Q4 2.5
total 100
ACADEMIC HONESTY: You must compose all programs and written material yourself.
All material taken or used as inspiration from outside sources must be appropriately cited.
Solution: The best project will be shared as an indicative solution for the class.