CS 3346A / CS 3121A Assignment 1 – UWO
Pacman Project: Search
Weight: 15% (Q1 – Q6)
If you need to pick up Python and Unix basis, please learn this
This assignment assumes you use Python 3.6 or above. Please make certain that your
code runs on python3 using only standard imports.
Welcome to Pacman
After downloading the code (search_pacman.zip), unzipping it, and changing to the directory,
you should be able to play a game of Pacman by typing the following at the command line:
Pacman lives in a shiny blue world of twisting corridors and tasty round treats. Navigating this
world efficiently will be Pacman’s first step in mastering his domain.
The simplest agent in searchAgents.py is called the GoWestAgent, which always goes West (a
trivial reflex agent). This agent can occasionally win:
python3 pacman.py –layout testMaze –pacman GoWestAgent
But, things get ugly for this agent when turning is required:
python3 pacman.py –layout tinyMaze –pacman GoWestAgent
If Pacman gets stuck, you can exit the game by typing CTRL-c into your terminal.
Soon, your agent will solve not only tinyMaze, but any maze you want.
Note that pacman.py supports a number of options that can each be expressed in a
long way (e.g., –layout) or a short way (e.g., -l). You can see the list of all options and
their default values via:
python3 pacman.py -h
Also, all of the commands that appear in this project also appear in commands.txt, for easy
copying and pasting. In UNIX/Mac OS X, you can even run all these commands in order with
Question 1 (2.5 points): Finding a Fixed Food Dot using Depth
In searchAgents.py, you’ll find a fully implemented SearchAgent, which plans out a path
through Pacman’s world and then executes that path step-by-step. The search algorithms for
formulating a plan are not implemented – that’s your job. As you work through the following
questions, you might find it useful to refer to the object glossary (the second to last tab in the
navigation bar above).
First, test that the SearchAgent is working correctly by running:
python3 pacman.py -l tinyMaze -p SearchAgent -a fn=tinyMazeSearch
The command above tells the SearchAgent to use tinyMazeSearch as its search algorithm,
which is implemented in search.py. Pacman should navigate the maze successfully.
Now it’s time to write full-fledged generic search functions to help Pacman plan routes!
Pseudocode for the search algorithms you’ll write can be found in the lecture slides. Remember
that a search node must contain not only a state but also the information necessary to
reconstruct the path (plan) which gets to that state.
Important note: All of your search functions need to return a list of actions that will lead the
agent from the start to the goal. These actions all have to be legal moves (valid directions, no
moving through walls).
Important note: Make sure to use the Stack, Queue and PriorityQueue data structures provided
to you in util.py! These data structure implementations have particular properties which are
required for compatibility with the autograder.
Hint: Each algorithm is very similar. Algorithms for DFS, BFS, UCS, and A* differ only in the
details of how the fringe is managed. So, concentrate on getting DFS right and the rest should
be relatively straightforward. Indeed, one possible implementation requires only a single
generic search method which is configured with an algorithm – specific queuing strategy.
Implement the depth-first search (DFS) algorithm in the depthFirstSearch function in search.py.
To make your algorithm complete, write the graph search version of DFS, which avoids
expanding any already visited states.
Your code should quickly find a solution for:
python3 pacman.py -l tinyMaze -p SearchAgent
python3 pacman.py -l mediumMaze -p SearchAgent
python3 pacman.py -l bigMaze -z .5 -p SearchAgent
The Pacman board will show an overlay of the states explored, and the order in which they
were explored (brighter red means earlier exploration). Is the exploration order what you would
have expected? Does Pacman actually go to all the explored squares on his way to the goal?
Hint: If you use a Stack as your data structure, the solution found by your DFS algorithm for
mediumMaze should have a length of 130 (provided you push successors onto the fringe in the
order provided by getSuccessors; you might get 246 if you push them in the reverse order). Is
this a least cost solution? If not, think about what depth-first search is doing wrong.
Question 2 (2.5 points): Breadth First Search
Implement the breadth-first search (BFS) algorithm in the breadthFirstSearch function in
search.py. Again, write a graph search algorithm that avoids expanding any already visited
states. Test your code the same way you did for depth-first search.
python3 pacman.py -l mediumMaze -p SearchAgent -a fn=bfs
python3 pacman.py -l bigMaze -p SearchAgent -a fn=bfs -z .5
Does BFS find a least cost solution? If not, check your implementation.
Hint: If Pacman moves too slowly for you, try the option –frameTime 0.
Note: If you’ve written your search code generically, your code should work equally well for the
eight-puzzle search problem without any changes.
Question 3 (2.5 points): Varying the Cost Function
While BFS will find a fewest-actions path to the goal, we might want to find paths that are
“best” in other senses. Consider mediumDottedMaze and mediumScaryMaze.
By changing the cost function, we can encourage Pacman to find different paths. For example,
we can charge more for dangerous steps in ghost-ridden areas or less for steps in food-rich
areas, and a rational Pacman agent should adjust its behavior in response.
Implement the uniform-cost graph search algorithm in the uniformCostSearch function in
search.py. We encourage you to look through util.py for some data structures that may be
useful in your implementation. You should now observe successful behavior in all three of the
following layouts, where the agents below are all UCS agents that differ only in the cost
function they use (the agents and cost functions are written for you):
python3 pacman.py -l mediumMaze -p SearchAgent -a fn=ucs
python3 pacman.py -l mediumDottedMaze -p StayEastSearchAgent
python3 pacman.py -l mediumScaryMaze -p StayWestSearchAgent
Note: You should get very low and very high path costs for the StayEastSearchAgent and
StayWestSearchAgent respectively, due to their exponential cost functions (see
searchAgents.py for details).
Question 4 (2.5 points): A* search
Implement A* graph search in the empty function aStarSearch in search.py. A* takes a
heuristic function as an argument. Heuristics take two arguments: a state in the search problem
(the main argument), and the problem itself (for reference information). The nullHeuristic
heuristic function in search.py is a trivial example.
You can test your A* implementation on the original problem of finding a path through a maze
to a fixed position using the Manhattan distance heuristic (implemented already as
manhattanHeuristic in searchAgents.py).
python3 pacman.py -l bigMaze -z .5 -p SearchAgent -a fn=astar,heuristic=manhattanHeuristic
You should see that A* finds the optimal solution slightly faster than uniform cost search (about
549 vs. 620 search nodes expanded in our implementation, but ties in priority may make your
numbers differ slightly). What happens on openMaze for the various search strategies?
Question 5 (2.5 points): Finding All the Corners
The real power of A* will only be apparent with a more challenging search problem. Now, it’s
time to formulate a new problem and design a heuristic for it.
In corner mazes, there are four dots, one in each corner. Our new search problem is to find the
shortest path through the maze that touches all four corners (whether the maze actually has
food there or not). Note that for some mazes like tinyCorners, the shortest path does not
always go to the closest food first! Hint: the shortest path through tinyCorners takes 28 steps.
Note: Make sure to complete Question 2 before working on Question 5, because Question 5
builds upon your answer for Question 2.
Implement the CornersProblem search problem in searchAgents.py. You will need to choose a
state representation that encodes all the information necessary to detect whether all four
corners have been reached. Now, your search agent should solve:
python3 pacman.py -l tinyCorners -p SearchAgent -a fn=bfs,prob=CornersProblem
python3 pacman.py -l mediumCorners -p SearchAgent -a fn=bfs,prob=CornersProblem
To receive full credit, you need to define an abstract state representation that does not encode
irrelevant information (like the position of ghosts, where extra food is, etc.). In particular, do
not use a Pacman GameState as a search state. Your code will be very, very slow if you do (and
Hint: The only parts of the game state you need to reference in your implementation are the
starting Pacman position and the location of the four corners.
Our implementation of breadthFirstSearch expands just under 2000 search nodes on
mediumCorners. However, heuristics (used with A* search) can reduce the amount of searching
Question 6 (2.5 points): Corners Problem: Heuristic
Note: Make sure to complete Question 4 before working on Question 6, because Question 6
builds upon your answer for Question 4.
Implement a non-trivial, consistent heuristic for the CornersProblem in cornersHeuristic.
python3 pacman.py -l mediumCorners -p AStarCornersAgent -z 0.5
Note: AStarCornersAgent is a shortcut for
-p SearchAgent -a fn=aStarSearch,prob=CornersProblem,heuristic=cornersHeuristic.
Admissibility vs. Consistency: Remember, heuristics are just functions that take search states
and return numbers that estimate the cost to a nearest goal. More effective heuristics will
return values closer to the actual goal costs. To be admissible, the heuristic values must be
lower bounds on the actual shortest path cost to the nearest goal (and non-negative). To be
consistent, it must additionally hold that if an action has cost c, then taking that action can only
cause a drop in heuristic of at most c.
Remember that admissibility isn’t enough to guarantee correctness in graph search — you need
the stronger condition of consistency. However, admissible heuristics are usually also
consistent, especially if they are derived from problem relaxations. Therefore it is usually
easiest to start out by brainstorming admissible heuristics. Once you have an admissible
heuristic that works well, you can check whether it is indeed consistent, too. The only way to
guarantee consistency is with a proof. However, inconsistency can often be detected by
verifying that for each node you expand, its successor nodes are equal or higher in in f-value.
Moreover, if UCS and A* ever return paths of different lengths, your heuristic is inconsistent.
This stuff is tricky!
Non-Trivial Heuristics: The trivial heuristics are the ones that return zero everywhere (UCS) and
the heuristic which computes the true completion cost. The former won’t save you any time,
while the latter will timeout the autograder. You want a heuristic which reduces total compute
time, though for this assignment the autograder will only check node counts (aside from
enforcing a reasonable time limit).
Grading: Your heuristic must be a non-trivial non-negative consistent heuristic to receive any
points. Make sure that your heuristic returns 0 at every goal state and never returns a negative
value. Depending on how few nodes your heuristic expands, you’ll be graded:
Number of nodes expanded Grade
more than 2000 0/3
at most 2000 1/3
at most 1600 2/3
at most 1200 3/3
Remember: If your heuristic is inconsistent, you will receive no credit, so be careful!
Question 7 (2 points): Eating All The Dots
This question will be one question of your second assignment. You can start in advance if you
are interested. Submit it with Assignment 2 even if you have finished it.
Now we’ll solve a hard search problem: eating all the Pacman food in as few steps as possible.
For this, we’ll need a new search problem definition which formalizes the food-clearing problem:
FoodSearchProblem in searchAgents.py (implemented for you). A solution is defined to be a
path that collects all of the food in the Pacman world. For the present project, solutions do not
take into account any ghosts or power pellets; solutions only depend on the placement of walls,
regular food and Pacman. (Of course ghosts can ruin the execution of a solution! We’ll get to
that in the next project.) If you have written your general search methods correctly, A* with a
null heuristic (equivalent to uniform-cost search) should quickly find an optimal solution to
testSearch with no code change on your part (total cost of 7).
python3 pacman.py -l testSearch -p AStarFoodSearchAgent
Note: AStarFoodSearchAgent is a shortcut for -p SearchAgent -a
You should find that UCS starts to slow down even for the seemingly simple tinySearch. As a
reference, our implementation takes 2.5 seconds to find a path of length 27 after expanding
5057 search nodes.
Note: Make sure to complete Question 4 before working on Question 7, because Question 7
builds upon your answer for Question 4.
Fill in foodHeuristic in searchAgents.py with a consistent heuristic for the FoodSearchProblem.
Try your agent on the trickySearch board:
python3 pacman.py -l trickySearch -p AStarFoodSearchAgent
Our UCS agent finds the optimal solution in about 13 seconds, exploring over 16,000 nodes.
Any non-trivial non-negative consistent heuristic will receive 1 point. Make sure that your
heuristic returns 0 at every goal state and never returns a negative value. Depending on how
few nodes your heuristic expands, you’ll get additional points:
Number of nodes expanded Grade
more than 15000 1/4
at most 15000 2/4
at most 12000 3/4
at most 9000 4/4 (full credit; medium)
at most 7000 5/4 (optional extra credit; hard)
Remember: If your heuristic is inconsistent, you will receive no credit, so be careful! Can you
solve mediumSearch in a short time? If so, we’re either very, very impressed, or your heuristic
Please submit your final implementation python files: search.py and
searchAgents.py through OWL.
Please do not change the other files in this distribution or submit any of our original files
other than these files.