Assignment 1: Search (Individual assignment)


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Programming Assignment One

Programming Assignment 1: Search (Individual
Modified version UC Berkeley CSC188 Project 1 (
Table of Contents.
1. Critical Warning
2. Introduction
3. What to submit
4. Welcome
5. Q1: Depth First Search
6. Q2: Breadth First Search
7. Q3: Uniform Cost Search
8. Q4: A* Search
9. Q5: Corners Problem: Representation
10. Q6: Corners Problem: Heuristic
11. Q7: Eating All The Dots: Heuristic
12. Q8: Suboptimal Search All those colored walls,
Mazes give Pacman the blues,
So teach him to search.
Warning (Please read this)
Also please consider the following points.
You are to implement the search algorithms presented in the course. These algorithms differ in
subtle but important ways from other presentations of this material. If you implement your search
based on other non-course material it might give the wrong answers. If you try to use solutions
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found on the internet the same problem might occur.
Please do not implement your own “improvement” to the search algorithms: it will wreak havoc
with the automarker.
Do not add any non-standard imports in the python files you submit (all imports already in
the starter code must remain). All imports that are available on teach.cs are considered to be
Do not change any of the supplied files except for sseeaarrcchh..ppyy and sseeaarrcchhAAggeennttss..ppyy
Make certain that your code runs on teach.cs using python3. You should all have an account
on teach.cs and you can log in, download all of your code (including all of the supplied code) to a
subdirectory of your home directory, and use the command python3 and test it
there before you submit. Your code will be graded by running it on teach.cs, so the fact that it runs
on your own system but not on teach is not a legitimate reason for a regrade.
No more test cases will be run on your code beyond the test cases used in the autograder. So the
grade shown to you by the autograder will be a good predictor of your final grade on the
assignment. However, we will look for certain things in the assignments (e.g., running them
through code plagiarism checkers, looking at assignments that fail all tests, etc.). If we have good
reasons we will change your grade from that given by the autograder either up or down.
In this assignment, 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.
This assignment includes an autograder for you to check your solutions as you develop them. The
autograder can be run with the command:
Note: the autograder and pacman environment use python3. If you default python is not 3 then
you can try executing. Note that on teach.cs the default is python2.7, so you must use the
command below on teach.cs.
See the autograder tutorial in Assignment 0 for more information about using the autograder.
The code for this assignment 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 as a zip archive. In that zip you will find the following files.
Files you’ll edit and submit on Markus:
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2 of 13 2020-12-06, 14:58 Where all of your search algorithms will reside. Where all of your search-based agents will reside.
Files you might want to look at (look but don’t modify):
The main file that runs Pacman games. This file describes a Pacman
GameState type, which you use in this assignment.
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 algorithms.
Supporting files you can ignore: Graphics for Pacman Support for Pacman graphics ASCII graphics for Pacman Agents to control ghosts Keyboard interfaces to control Pacman Code for reading layout files and storing their contents Assignment autograder Parses autograder test and solution files General autograding test classes
test_cases/ Directory containing some test cases for each question Assignment 1 specific autograding test classes
Files to Edit and Submit: You will fill in portions of and during the
assignment. You may also add other functions and code to these files so as to create a modular
implementation. You will submit these files with your modifications. Do not put your modifications in
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other files as those other files will not be uploadable to Markus. Do not change the other files in this
distribution. Note that all of the code that your implementation depends on must reside inside of one
of the two submitted files. You may use standard python imports (test these on teach.cs!) .
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. The
grade given by the autograder will be a good indication of your actual grade. But we if we find some
other issues with your program you actual grade can differ from the autograder grade.
Getting Help: There will be scheduled help sessions (to be announced), the piazza discussion forum
will be monitored and questions answered, and you can also ask questions about the assignment
during office hours or tutorials. These things are for your support; please take advantage of them. If
you can’t make our office hours, let us know and we will arrange a different appointment. We want the
assignment to be rewarding and instructional, not frustrating and demoralizing. But, we don’t know
when or how to help unless you ask.
Piazza Discussion: Do not post spoilers! Students posting information on piazza that hinders
the learning process of other students will be in violation of class policy.
What to Submit
You will be using MarkUs to submit your assignment. MarkUs accounts for the course will be set up
on Sept 24th. You will submit two files:
1. Your modified
2. Your modified
Note: In the various parts below we ask a number of questions. You do not have to hand in answers
to these questions, rather these questions are designed to help you understand what is going on with
Welcome to Pacman
After downloading the code ( sseeaarrcchh..zziipp ), unzipping it, and changing to the directory created, you
should be able to play a game of Pacman by typing the following at the command line:
Note: if python3 is not the default python on the machine you are using you will have to
change ppyytthhoonn to the command that invokes python3 (typically by using ppyytthhoonn33 rather than
plain ppyytthhoonn ).
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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 is called the GoWestAgent , which always goes West (a trivial
reflex agent). This agent can occasionally win:
python –layout testMaze –pacman GoWestAgent
But, things get ugly for this agent when turning is required:
python –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 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 -h
Note: if you have a non-graphics connection you can run the code with the -t argument.
If you install python on your personal machine it should come with the correct graphics support, and
the graphics should also work if you are connected to the teaching labs with an X-windows
Question 1 (4 points): Finding a Fixed Food Dot using Depth First
In , 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.
First, test that the SearchAgent is working correctly by running:
python -l tinyMaze -p SearchAgent -a fn=tinyMazeSearch
The command above tells the SearchAgent to use tinyMazeSearch as its search algorithm, which is
implemented in . 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
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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: You might find the Stack , Queue and PriorityQueue data structures provided in useful. If you create your own data structures for OPEN and have autograder errors check
your data structures against these predefined data structures to ensure that you are implementing the
same functionality.
Hint: Each algorithm is very similar. Algorithms for DFS, BFS, UCS, and A* differ only in the details of
how OPEN 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 . To
ensure that DFS does not run around in circles, implement path checking to prune cyclic paths
during search. Do not use full cycle checking for DFS (we will use full cycle checking for the other
Your code should quickly find a solution for:
python -l tinyMaze -p SearchAgent
python -l mediumMaze -p SearchAgent
python -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). Check that the exploration order is 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 (3 points): Breadth First Search
Implement the breadth-first search (BFS) algorithm in the breadthFirstSearch function in .
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This time you must implement full cycle checking in your search algorithm to avoid the overhead of
cyclic paths. Test your code the same way you did for depth-first search.
python -l mediumMaze -p SearchAgent -a fn=bfs
python -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 eightpuzzle search problem without any changes.
Question 3 (3 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 using -l mediumDottedMaze and
-l mediumScarymaze respectively)
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 search algorithm with full cycle checking in the uniformCostSearch
function in . We encourage you to look through 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 -l mediumMaze -p SearchAgent -a fn=ucs
python -l mediumDottedMaze -p StayEastSearchAgent
python -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 for
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Question 4 (3 points): A* search
Implement A* search with full cycle checking in the empty function aStarSearch in . 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 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 ).
python -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? Try the commands
python -l openMaze -p SearchAgent
python -l openMaze -p SearchAgent -a fn=bfs
python -l openMaze -p SearchAgent -a fn=ucs
python -l openMaze -p SearchAgent -a fn=astar,heuristic=manhattanHeuristic
You will find that DFS will take too long on openMaze maze since it only does path-checking. If you
use full cycle checking with DFS it will find a solution (a very unusual one!). You will also find that A*
finds the same solution as BFS and UCS but it explores far less of the grid.
Question 5 (3 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
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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 . 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 -l tinyCorners -p SearchAgent -a fn=bfs,prob=CornersProblem
python -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 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 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 required.
Question 6 (3 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, admissible heuristic for the CornersProblem in cornersHeuristic .
python -l mediumCorners -p AStarCornersAgent -z 0.5
Note: AStarCornersAgent is a shortcut for
-p SearchAgent -a fn=aStarSearch,prob=CornersProblem,heuristic=cornersHeuristic .
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
Grading: Your heuristic must be a non-trivial non-negative admissible heuristic to receive any points.
Make sure that your heuristic returns 0 at every goal state and never returns a negative value.
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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 1500 2/3
at most 900 3/3
Remember: If your heuristic is inadmissible, you will receive no credit, so be careful!
Question 7 (13 points): 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 (implemented for you). A solution is defined to be a path that
collects all of the food in the Pacman world. For the present assignment, 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
assignment.) 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).
python -l testSearch -p AStarFoodSearchAgent
Note: AStarFoodSearchAgent is a shortcut for -p SearchAgent -a
fn=astar,prob=FoodSearchProblem,heuristic=foodHeuristic .
You should find that UCS ( python -l tinySearch -p SearchAgent -a
fn=ucs,prob=FoodSearchProblem ) starts to slow down even for the seemingly simple tinySearch . As a
reference, our implementation finds a path of length 27 after expanding 5168 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 with an admissible heuristic for the FoodSearchProblem . Try
your agent on the trickySearch board:
python -l trickySearch -p AStarFoodSearchAgent
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Our UCS agent searches over 16,000 nodes before it can find an optimal solution.
Any non-trivial non-negative admissible 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
more than 15000 (and non-trivial) 1/5
at most 15000 2/5
at most 12000 3/5
at most 9000 4/5 (medium)
at most 7000 5/5 (hard)
Also try your agent on the oneDotFocus board:
python -l oneDotFocus -p AStarFoodSearchAgent
On this problem your heuristic must expand no more than 200 nodes to get a mark, and for full marks
you must expand no more than 70 nodes.
Number of nodes expanded
at most 200 (and non-trivial) 1/4
at most 180 2/4
at most 130 3/4
at most 70 4/4
Finally try your agent on the largeGrid board (note the use of the -z 0.25 zoom factor as this grid is to
large to display without shrinking):
python -l largeGrid -z 0.25 -p AStarFoodSearchAgent
On this problem your heuristic must expand no more than 1000 nodes to get a mark, and for full
marks you must expand no more than 360 nodes.
Your implementation must also not take more than 5 mins of CPU time when run on teach.cs to solve
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largeGrid, if it does you will not get any marks for the largeGrid test.
Number of nodes expanded
Takes > 5mins CPU on teach.cs 0/4
at most 1000 (and non-trivial) 1/4
at most 750 2/4
at most 500 3/4
at most 360 4/4
Remember: If your heuristic is inadmissible, 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 is
Question 8 (3 points): Suboptimal Search
Sometimes, even with A* and a good heuristic, finding the optimal path through all the dots is hard
(even the layout mediumSearch is probably too hard for A*). 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 , but it’s missing a key
function that finds a path to the closest dot.
Implement the function findPathToClosestDot in . Our agent solves this maze
(suboptimally!) in under a second with a path cost of 350:
python -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 (its goal should get to any food location). Then, solve that problem with an
appropriate search function. The solution should be very short!
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.
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You’re not done yet! You will also need to submit your code, answers to the written questions and
your signed acknowledgment form to MarkUs (which will be available on Sept 24th).
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