Assignment 1: Search


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Artificial Intelligence
Assignment 1: Search
In this assignment, you will build general-purpose search algorithms and apply them to solving
puzzles. In Part 1, you will be in charge of a “Pacman”-like agent that needs to find a path through
maze to eat a dot or “food pellet.” In Part 2, you will need to find a single path that goes through all
the dots in the maze.
Image courtesy of the ECE448 course lecturer (Prof. Hasegawa-Johnson) at UIUC
Programming language
This MP will be written in Python. If you’ve never used Python before, you should start getting used to
it. A good place to start is the PythonTutorial (also available in hardcopy form). You should install
version 3.6 or 3.7 on your computer, as well as the pygame graphics package.
Your code may import extra modules, but only ones that are part of the standard python
library . Unless otherwise specified in the instructions for a specific MP, the only external library
available during our grading process will be pygame. For example: in mp1, numpy is not allowed.
Part 1: Basic Pathfinding
Consider the problem of finding the shortest path from a given start state while eating one or more dots
or “food pellets.” The image at the top of this page illustrates the simple scenario of a single dot, which
in this case can be viewed as the unique goal state. The maze layout will be given to you in a simple
text format, where ‘%’ stands for walls, ‘P’ for the starting position, and ‘.’ for the dot(s) (see sample
maze.txt). All step costs are equal to one.
Implement the state representation, transition model, and goal test needed for solving the problem in
the general case of multiple dots. For the state representation, besides your current position in the maze,
is there anything else you need to keep track of? For the goal test, keep in mind that in the case of
multiple dots, the Pacman does not necessarily have a unique ending position. Next, implement a
unified top-level search routine that can work with all of the following search strategies, as covered in
class and/or the textbook (Note: you don’t need to find the best solution when using DFS):
• Depth-first search
• Breadth-first search
• Greedy best-first search
• A* search
For this part of the assignment, use the Manhattan distance from the current position to the goal as the
Artificial Intelligence (Spring 2022) Assignment #1
heuristic function for greedy and A* search.
Run each of the four search strategies on the following inputs:
• Medium maze (mediumMaze.txt)
• Big maze (bigMaze.txt)
• Open maze (openMaze.txt)
The provided code will generate a pretty picture of your solution. Your report should include
• The solution pictures.
• The length of the path. Include both the start and goal positions as part of your path and path
• Number of nodes expanded by the search algorithm.
Part 2: Search with multiple dots
Now consider the harder problem of finding the shortest path through a maze while hitting multiple
dots. Once again, the Pacman is initially at P, but now there is no single goal position. Instead, the goal
is achieved whenever the Pacman manages to eat all the dots. Once again, we assume unit step costs.
As instructed in Part 1, your state representation, goal test, and transition model should already be
adapted to deal with this scenario. The next challenge is to solve the following inputs using A* search
using an admissible heuristic designed by you:
• Tiny search (tinySearch.txt)
• Small search (smallSearch.txt)
• Medium search (mediumSearch.txt)
You should be able to handle the tiny search using uninformed BFS. In fact, it is a good idea to try that
first for debugging purposes, to make sure your representation works with multiple dots. However, to
successfully handle all the inputs, it is crucial to come up with a good heuristic. For full credit, your
heuristic should be admissible and should permit you to find the solution for the medium search in a
reasonable amount of time. In your report, explain the heuristic you chose, and discuss why it is
admissible and whether it leads to an optimal solution.
Hints: In the past almost all working solutions to this problem have used a heuristic based on the
minimum spanning tree. The minimum spanning tree of a set of points can be computed easily via
Kruskal’s algorithm or Prim’s algorithm. If T is the total length of the edges in the minimum spanning
tree, then the shortest path connecting all the points must have length between T and 2T. Now, suppose
you are at some location (x,y) with a set of S dots still to reach. Your heuristic function h might be the
sum of the distance from (x,y) to the nearest dot, plus the MST length for the dots in S.
Extra Credit Suggestion
Sometimes, even with A* and a good heuristic, finding the optimal path through all the dots is hard. In
these cases, we’d still like to find a reasonably good path, quickly. Write a suboptimal search algorithm
that will do a good job on this big maze (bigDots.txt). Your algorithm could either be A* with a nonadmissible heuristic, or something different altogether. In your report, discuss your approach and output
the solution cost and number of expanded nodes. Note that the extra credit will be capped to 10% of
what the assignment is worth.
Artificial Intelligence (Spring 2022) Assignment #1
Provided Code Skeleton
We have provided (.tar file or .zip file) all the code to get you started on your MP, which means you
will only have to write the search functions. Do not modify provided code. You will only have to
• getStart() :- Returns a tuple of the starting position, (row, col)
• getObjectives() :- Returns a list of tuples that correspond to the dot positions, [(row1, col1),
(row2, col2)]
• isValidMove(row, col) :- Returns the boolean True if the (row, col) position is valid. Returns
False otherwise.
• getNeighbors(row, col) :- Given a position, returns the list of tuples that correspond to valid
neighbor positions. This will return at most 4 neighbors but may return less.
There are 4 methods to implement in this file, namely bfs(maze), dfs(maze), greedy(maze), and
astar(maze). (You may need to add another named search method if you implement an additional
search method for extra credit.) Each of these functions takes in a maze instance and should return both
the path taken (as a list of tuples) and the number of states explored. The maze instance provided will
already be instantiated, and the above methods will be accessible.
To understand how to run the MP, read the provided or run python3 -h into
your terminal. The following command will display a maze and let you create a path manually
using the arrow keys.
python –human maps/maze.txt
The following command will run your astar search method on the maze.
python –method astar maps/maze.txt
You can also save your output picture as a file in tga format. If your favorite document formatter
doesn’t handle tga, tools such as gimp can convert it to other formats (e.g. jpg).
• In your implementation, make sure you get all the bookkeeping right. This includes handling of
repeated states (in particular, what happens when you find a better path to a state already on the
frontier) and saving the optimal solution path.
• Pay attention to tie breaking. If you have multiple nodes on the frontier with the same minimum
value of the evaluation function, the speed of your search and the quality of the solution may depend
on which one you select for expansion.
• Implement all four strategies using a similar approach and coding style. In particular, while
DFS can be implemented very compactly using recursion, you must store the frontier in an explicit
stack, queue or priority queue (depending on the search algorithm) for this assignment. Among other
things, limits on recursion depth can be (depending on your installation) much lower than the number
of objects that you can pack into an explicit stack.
• You will be graded primarily on the correctness of your solution, not on the efficiency and
elegance of your data structures. For example, we don’t care whether your priority queue or repeated
state detection uses brute-force search, as long as you end up expanding exactly the correct number of
Artificial Intelligence (Spring 2022) Assignment #1
nodes (except for small differences caused by differences among tie-breaking strategies) and find the
optimal solution. So, feel free to use “dumb” data structures as long as it makes your life easier and still
enables you to find the solutions to all the inputs in a reasonable amount of time.
This MP will be submitted via blackboard.
Please upload only the following files to blackboard.
1. – your solution python file
2. report.pdf – your project report in pdf format
Report Checklist
Your report should briefly describe your implemented solution and fully answer the questions for every part
of the assignment. Your description should focus on the most “interesting” aspects of your solution, i.e., any
non-obvious implementation choices and parameter settings, and what you have found to be especially
important for getting good performance. Feel free to include pseudocode or figures if they are needed to
clarify your approach. Your report should be self-contained, and it should (ideally) make it possible for us
to understand your solution without having to run your source code.
Kindly structure the report as follows:
1. Title Page:
List of all team members, course number and section for which each member is registered, date on which
the report was written
2. Section I:
Algorithms (Search). This section should describe algorithms and data structures used for all four
search strategies. Answer questions like: what is a state? What is the frontier? Do you maintain an
explored states list? How are repeated states detected and managed?
3. Section II:
Algorithms (A* and Greedy BFS). This section should describe the heuristic(s) used for A* and Greedy
BFS, for both the single dot and multiple-dot situations Provide proof that the heuristics for A* are
4. Section III:
Results (Basic Pathfinding). For every algorithm in part 1, (DFS, BFS, Greedy, A*), and every one of
the mazes, (medium, big, open), give the maze screenshot with the computed path, the solution cost and
the number of expanded nodes (12 cases total)
5. Section IV:
Results (Search with multiple dots). For part 2, for each of three mazes (tiny, small, medium), give the
solution screenshot, solution cost, and number of expanded nodes for your A* algorithm.
6. Extra Credit:
If you have done any work which you think should get extra credit, describe it here.
7. Statement of Contribution:
Specify which team-member performed which task. You are encouraged to make this a many-to-many
mapping, if applicable. e.g., You can say that “Rahul and Jason both implemented the BFS function,
their results were compared for debugging and Rahul’s code was submitted. Jason and Mark both
implemented the DFS function, Mark’s code never ran successfully, so Jason’s code was submitted.
Section I of the report was written by all 3 team members. Section II by Mark and Jason, Section III by
Rahul and Jason.”… and so on.
Artificial Intelligence (Spring 2022) Assignment #1
WARNING: You will not get credit for any solutions that you have obtained, but not included in your
report! Make only ONE submission per team.
Only attach files that are the required deliverables in blackboard. Your report must be a formatted pdf
document. Pictures and example outputs should be incorporated into the document. Exception: items which
are very large or unsuitable for inclusion in a pdf document (e.g. videos or animated gifs) may be put on the
web and a URL included in your report.
Extra credit:
We reserve the right to give bonus points for any advanced exploration or especially challenging or creative
solutions that you implement. This includes, but is not restricted to, the extra credit suggestion given above.

Assignment 1: Search
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