Assignment 1 Problem A Solution

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Please refer to main Assignment 1 document for all submission instructions and dates


In this homework, your Pacman agent will nd paths through his maze world, both to reach a particular location and to collect food e ciently.

On Canvas there is a zip le with the contents of the Pacman game around which you will be developing code to implement various search techniques. You should unzip the le and run it to get an idea of how it works. For instance, to play a game of classic Pacman, run:


Pacman lives in a shiny blue world of twisting corridors and tasty round treats. Navigating this world e ciently will be Pacman’s rst step in mastering his domain.

Note: A description of the les involved in this project can be found in Appendix A at the end of this document.


The simplest agent in is called the GoWestAgent, which always goes West (a trivial re ex 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 (or equivalent) 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

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.


Useful Information

Checking Your Work, you can check your code by running


This will run your functions through a series of test cases, similar to those used on gradescope. Questions 4b and 5 are not autograded, so the autograder will only give you a score out of 7, the remaining 3 points will be manually graded.

Note. Gradescope is slow and will not give you as detailed feedback as so its a good idea to test o ine rst!

Files to Edit and Submit: You will ll in portions of and You should submit these les with your code and comments, as well as your nal report. Please do not change the other les in this distribution or submit any of our original les other than these les. You may want to review other les in the project, these have been shown in Appendix A

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 autograder’s judgements { will be the nal judge of your score. If necessary, we will review and grade assignments individually to ensure that you receive due credit for your work.

Q1. [2 pts] Depth First

In, you’ll nd 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 nd 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:

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- edged generic search functions to help Pacman plan routes! We have discussed each of these methods in class, please refer to the slides for implementation guidlines. 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! These data structure implementations have particular properties which are required for compatibility with the au-tograder.

Hint: Each algorithm is very similar. Algorithms for DFS, BFS, UCS, and A* di er 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 con gured with an algorithm-speci c queuing strategy. (Your implementation need not be of this form to receive full credit).

Implement the depth- rst search (DFS) algorithm in the depthFirstSearch function in To make your algorithm complete, write the graph search version of DFS, which avoids expanding any already visited states.

Your code should quickly nd 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). 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).

Q2. [1 pt] Breadth First Search

Implement the breadth- rst search (BFS) algorithm in the breadthFirstSearch function in Again, write a graph search algorithm that avoids expanding any already visited states. Test your code the same way you did for depth- rst search.

python -l mediumMaze -p SearchAgent -a fn=bfs

python -l bigMaze -p SearchAgent -a fn=bfs -z .5

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.


Q3. [2 pts] Uniform Cost

While BFS will nd a fewest-actions path to the goal, we might want to nd paths that are “best” in other senses.

Consider mediumDottedMaze and mediumScaryMaze.

By changing the cost function, we can encourage Pacman to nd di erent 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 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 di er 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 details).

Q4. [4 pts] A* Search

  1. [2 pts] Implement A* graph search 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 nding a path through a maze to a xed 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* nds 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 di er slightly). What happens on openMaze for the various search strategies?

  1. [2 pts] Implement two new heuristics in in the empty functions euclideanHeuristic and



euclideanHeuristic should return the euclidian distance to the target. randomHeuristic should return a random integer value between 1 and 10. Use the following commands to test your heuristics:

python -l bigMaze -z .5 -p SearchAgent -a fn=astar,heuristic=manhattanHeuristic python -l bigMaze -z .5 -p SearchAgent -a fn=astar,heuristic=euclideanHeuristic python -l bigMaze -z .5 -p SearchAgent -a fn=astar,heuristic=randomHeuristic

In your report, Discuss your new heuristics, are they both admissible and consistent? Why? Then compare the three heuristics (manhattan, euclidean, and random) in terms of performance and explain the di erences in performance.

Q5. [1 pt] Algorithm Comparison

In your report answer the following questions: What happens on openMaze for the various search strategies? Describe the behaviour seen and explain why it occurs.

  • Files in the project

Files you’ll edit:

Where all of your search algorithms will reside.

Where all of your search-based agents will reside.

Files you might want to look at:

The main le that runs Pacman games. This le describes a Pacman GameState

type, which you use in this project.

The logic behind how the Pacman world works. This le describes several supporting

types like AgentState, Agent, Direction, and Grid.

Useful data structures for implementing search algorithms.

Supporting les 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 les and storing their contents

Project autograder

Parses autograder test and solution les

General autograding test classes

test cases/

Directory containing the test cases for each question

Project 1 speci c autograding test classes

Table 1: Files in Project