Project 1: Search
The goal of this project is to help you better understand statespace search problems and search algorithms.
Figure 1: All those colored walls, Mazes give Pacman the blues, So teach
him to search.
In this project, your Pacman agent will find paths through his maze world,
both to reach a particular location and to collect food efficiently. You will
build general search algorithms and apply them to Pacman scenarios.
The code for this project consists of several Python files, some of which you
will need to read and understand in order to complete the assignment, and
some of which you can ignore. You can download all the code and supporting
files from P1.zip in the folder Projects on Canvas.
Files you’ll edit:
search.py Where all of your search algorithms will reside.
searchAgents.py Where all of your search-based agents will reside.
Files you might want to look at:
The main file that runs Pacman games. This file
describes a Pacman GameState type, which you
use in this project.
The logic behind how the Pacman world works.
This file describes several supporting types like
AgentState, Agent, Direction, and Grid.
Useful data structures for implementing search
Supporting files you can ignore:
graphicsDisplay.py Graphics for Pacman
graphicsUtils.py Support for Pacman graphics
textDisplay.py ASCII graphics for Pacman
ghostAgents.py Agents to control ghosts
keyboardAgents.py Keyboard interfaces to control Pacman
Code for reading layout files and storing their
Files to Edit and Submit: You will fill in portions of search.py and
searchAgents.py during the assignment. Please do not change the other
files in this distribution or submit any of our original files other than these
Evaluation: Your code will be autograded for technical correctness. Please
do not change the names of any provided functions or classes within the code,
or you will wreak havoc on the autograder. However, the correctness of your
implementation – not the online judge’s judgements – will be the final judge
of your score. If necessary, we will review and grade assignments individually
to ensure that you receive due credit for your work.
Academic Dishonesty: We will be checking your code against other submissions in the class, but also codes found on internet, for logical redundancy.
If you copy someone else’s code and submit it with minor changes, we will
know. These cheat detectors are quite hard to fool, so please don’t try. We
trust you all to submit your own work only; please don’t let us down. If you
do, we will pursue the strongest consequences available to us.
Getting Help: You are not alone! If you find yourself stuck on something,
contact the course staff for help. Office hours and the discussion forum on
Piazza are there for your support; please use them. If you can’t make our
office hours, let us know and we will schedule more. We want these projects
to be rewarding and instructional, not frustrating and demoralizing. But, we
don’t know when or how to help unless you ask.
Discussion: Please be careful not to post spoilers.
Welcome to Pacman
After downloading the code P1.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:
python pacman.py –layout testMaze –pacman GoWestAgent
But, things get ugly for this agent when turning is required:
python pacman.py –layout tinyMaze –pacman GoWestAgent
If Pacman gets stuck, you can exit the game by typing CTRL-c into your
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:
python 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 bash commands.txt.
Question 1: Finding a Fixed Food Dot using
Depth First Search
In searchAgents.py, you’ll find a fully implemented SearchAgent, which
plans out a path through Pacman’s world and then executes that path stepby-step. The search algorithms for formulating a plan are not implemented
– that’s your job.
First, test that the SearchAgent is working correctly by running:
python 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 online judge.
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. (Your implementation need not be of this form to receive full credit).
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:
python pacman.py -l tinyMaze -p SearchAgent
python pacman.py -l mediumMaze -p SearchAgent
python 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: 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.
python pacman.py -l mediumMaze -p SearchAgent -a fn=bfs
python 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: 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
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):
python pacman.py -l mediumMaze -p SearchAgent -a fn=ucs
python pacman.py -l mediumDottedMaze -p StayEastSearchAgent
python 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: 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).
python pacman.py -l bigMaze -z .5 -p SearchAgent\
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: 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
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
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:
python pacman.py -l tinyCorners -p SearchAgent\
python pacman.py -l mediumCorners -p SearchAgent\
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 also wrong).
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
Our implementation of breadthFirstSearch expands just under 2000 search
nodes on mediumCorners. However, heuristics (used with A* search) can
reduce the amount of searching required.
Question 6: 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
python pacman.py -l mediumCorners -p AStarCornersAgent -z 0.5
Note: AStarCornersAgent is a shortcut for
-p SearchAgent -a\
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 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
online judge. You want a heuristic which reduces total compute time, though
for this assignment the online judge 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:
Remember: If your heuristic is inconsistent, you will receive no credit, so be
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
Question 7: Eating All The Dots
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
python pacman.py -l testSearch -p AStarFoodSearchAgent
Note: AStarFoodSearchAgent is a shortcut for
-p SearchAgent -a fn=astar,prob=FoodSearchProblem,heuristic=foodHeuristic
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:
python 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
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)
negative value. Depending on how few nodes your heuristic expands, you’ll
get additional points:
Remember:If your heuristic is inconsistent, you will receive no credit, so be
careful! If your number of nodes expanded is less than 7000, you can get 5%
of bonus point in project 1.
Hint: You can create your own heuristic function with the search method
you have implemented in the previous problems.
Question 8: Suboptimal Search
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. In this section, you’ll write an agent that always greedily
eats the closest dot. ClosestDotSearchAgent is implemented for you in
searchAgents.py, but it’s missing a key function that finds a path to the
Implement the function findPathToClosestDot in searchAgents.py. Our
agent solves this maze (sub-optimally!) in under a second with a path cost
python pacman.py -l bigSearch -p ClosestDotSearchAgent -z .5
Hint:The quickest way to complete findPathToClosestDot is to fill in the
AnyFoodSearchProblem, which is missing its goal test. Then, solve that
problem with an appropriate search function. The solution should be very
Your ClosestDotSearchAgent won’t always find the shortest possible path
through the maze. Make sure you understand why and try to come up with
a small example where repeatedly going to the closest dot does not result in
finding the shortest path for eating all the dots.
Submission and Due Date
Submit it to online judge.