Description

Homework 2: Coding – Search
Please read carefully:
• You must name your file puzzle.py. Any submission that does not follow this naming will not be graded.
• A skeleton of each function has been provided to you in puzzle.py. You are expected to ONLY write code in the functions and blocks specified. In any case, DO NOT modify the function signatures, or any code that is not specified to be modifiable for any reason. This will be run by our autograder, so any unexpected modifications that make it malfunction will receive a zero. You can, however, modify the main function as necessary to make the program run as specified in the assignment Test cases have been provided in the main function in the skeleton code.
• Only Python 3.x versions will be graded.
In this assignment you will create an agent to solve the N-puzzle game. You will implement and compare several search algorithms, and collect some statistics related to their performances. Visit mypuzzle.org/sliding for the game’s rules. Please read all sections carefully:
I. Introduction
II. Algorithm Review
III. What You Need To Submit
IV. What Your Program Outputs
V. Implementation and Testing
VI. Before You Finish
I. Introduction
The N-puzzle game consists of a board holding N = m2 − 1 distinct movable tiles, plus one empty space. There is one tile for each number in the set {0, 1,…, m2− 1}. In this assignment, we will represent the blank space with the number 0 and focus on the m = 3 case (8-puzzle).
In this combinatorial search problem, the aim is to get from any initial board state to the configuration with all tiles arranged in ascending order {0, 1,…, m2−1} – this is your goal state. The search space is the set of all possible states reachable from the initial state. Each move consists of swapping the empty space with a component in one of the four directions {‘Up’, ‘Down’, ‘Left’, ‘Right’}. Give each move a cost of one. Thus, the total cost of a path will be equal to the number of moves made.
II. Algorithm Review
Recall from lecture that search begins by visiting the root node of the search tree, given by the initial state. Three main events occur when visiting a node:
• First, we remove a node from the frontier set.
• Second, we check if this node matches the goal state.
• If not, we then expand the node. To expand a node, we generate all of its immediate successors and add them to the frontier, if they (i) are not yet already in the frontier, and (ii) have not been visited yet.
This describes the life cycle of a visit, and is the basic order of operations for search agents in this assignment–(1) remove, (2) check, and (3) expand. We will implement the assignment algorithms as described here. Please refer to lecture notes for further details, and review the lecture pseudo-code before you begin.
III. What You Need To Submit
Your job in this assignment is to write puzzle.py, which solves any 8-puzzle board when given an arbitrary starting configuration. The program will be executed as follows:
$ python3 puzzle.py <method><board>
The method argument will be one of the following. You must implement all three of them:
bfs (Breadth-First Search) dfs (Depth-First Search) ast (A-Star Search)
The board argument will be a comma-separated list of integers containing no spaces. For example, to use the bread-first search strategy to solve the input board given by the starting configuration {0,8,7,6,5,4,3,2,1}, the program will be executed like so (with no spaces between commas):
$ python3 puzzle.py bfs 0,8,7,6,5,4,3,2,1
IV. What Your Program Outputs
Your program will create and/or write to a file called output.txt, containing the following statistics:
path to goal: the sequence of moves taken to reach the goal cost of path: the number of moves taken to reach the goal nodes expanded: the number of nodes that have been expanded search depth: the depth within the search tree when the goal node is found max search depth: the maximum depth of the search tree in the lifetime of the algorithm running time: the total running time of the search instance, reported in seconds max ram usage: the maximum RAM usage in the lifetime of the process as measured by the ru maxrss attribute
in the resource module, reported in megabytes
Example 1: Breadth-First Search
Suppose the program is executed for breadth-first search as follows:
$ python3 puzzle.py bfs 1,2,5,3,4,0,6,7,8 This should result in the solution path:

The output file will contain exactly the following lines:
path to goal: [‘Up’, ‘Left’, ‘Left’] cost of path: 3 nodes expanded: 10 search depth: 3 max search depth: 4
running time: 0.00188088 max ram usage: 0.07812500
Example 2: Depth-First Search
Suppose the program is executed for depth-first search as follows:
$ python3 puzzle.py dfs 1,2,5,3,4,0,6,7,8 This should result in the solution path:

The output file will contain exactly the following lines:
path to goal: [‘Up’, ‘Left’, ‘Left’] cost of path: 3 nodes expanded: 181437 search depth: 3
max search depth: 66125 running time: 5.01608433 max ram usage: 4.23940217
More test cases are provided in the FAQs.
Note on Correctness
All variables, except running time and max ram usage, have one and only one correct answer when running BFS and DFS. A* nodes expanded might vary depending on implementation details. You’ll be fine as long as your algorithm follows all specifications listed in these instructions.
As running time and max ram usage values vary greatly depending on your machine and implementation details, there is no “correct” value to look for. They are for you to monitor time and space complexity of your code, which we highly recommend. A good way to check the correctness of your program is to walk through small examples by hand, like the ones above.
V. Implementation and Testing
For your first programming project, we are providing hints and explicit instructions. Before posting a question on the discussion board, make sure your question is not already answered here or in the FAQs.
1. Implementation
You will implement the following three algorithms as demonstrated in lecture. In particular:
• Breadth-First Search. Use an explicit queue, as shown in lecture.
• Depth-First Search. Use an explicit stack, as shown in lecture.
• A-Star Search. Use a priority queue, as shown in lecture. For the choice of heuristic, use the Manhattan priority function;

that is, the sum of the distances of the tiles from their goal positions. Note that the blanks space is not considered an actual tile here.
2. Order of Visits
In this assignment, where an arbitrary choice must be made, we always visit child nodes in the “UDLR” order; that is, [‘Up’, ‘Down’, ‘Left’, ‘Right’] in that exact order. Specifically:
• Breadth-First Search. Enqueue in UDLR order; de-queuing results in UDLR order.
• Depth-First Search. Push onto the stack in reverse-UDLR order; popping off results in UDLR order.
• A-Star Search. Since you are using a priority queue, what happens with duplicate keys? How do you ensure nodes are retrieved from the priority queue in the desired order?
3. Submission Test Cases
Run all three of your algorithms on the following test cases:
Test Case 1
$python3 puzzle.py bfs 3,1,2,0,4,5,6,7,8
$python3 puzzle.py dfs 3,1,2,0,4,5,6,7,8
$python3 puzzle.py ast 3,1,2,0,4,5,6,7,8
Test Case 2
$python3 puzzle.py bfs 1,2,5,3,4,0,6,7,8
$python3 puzzle.py dfs 1,2,5,3,4,0,6,7,8
$python3 puzzle.py ast 1,2,5,3,4,0,6,7,8
Make sure your code passes at least these test cases and follows our formatting exactly. The results of each test are assessed by 8 items: 7 are listed in Section IV. What Your Program Outputs. The last point is for code that executes and produces any output at all. Each item is worth 0.75 point.
4. Grading and Stress Tests
We will grade your project by running additional test cases on your code. In particular, there will be five test cases in total, each tested on all three of your algorithms, for a total of 15 distinct tests. Similar to the submission test cases, each test will be graded by 8 items, for a total of 90 points. Plus, we give 10 points for code completing all 15 test cases within 10 minutes. If you implement your code with reasonable designs of data structures, your code will solve all 15 test cases within a minute in total. We will be using a wide variety of inputs to stress-test your algorithms to check for correctness of implementation. So, we recommend that you test your own code extensively.
Don’t worry about checking for malformed input boards, including boards of non-square dimensions, other sizes, or unsolvable boards.
You will not be graded on the absolute values of your running time or RAM usage statistics. The values of these statistics can vary widely depending on the machine. However, we recommend that you take advantage of them in testing your code. Try batch-running your algorithms on various inputs, and plotting your results on a graph to learn more about the space and time complexity characteristics of your code. Just because an algorithm provides the correct path to goal does not mean it has been implemented correctly.
5. Tips on Getting Started
Begin by writing a class to represent the state of the game at a given turn, including parent and child nodes. We suggest writing a separate solver class to work with the state class. Feel free to experiment with your design, for example including a board class to represent the low-level physical configuration of the tiles, delegating the high-level functionality to the state class.
You will not be graded on your design, so you are at a liberty to choose among your favorite programming paradigms. Students have successfully completed this project using an entirely object-oriented approach, and others have done so with a purely functional approach. Your submission will receive full credit as long as your puzzle program outputs the correct information.
VI. Before You Finish
• Make sure your code passes at least the submission test cases.
• Make sure your algorithms generate the correct solution for an arbitrary solvable problem instance of 8-puzzle.
• Make sure your program output follows the specified format exactly. In particular, for the path to goal, use

square brackets to surround the list of items, use single quotes around each item, and capitalize the first letter of each item. Round floating-point numbers to 8 places after the decimal. You will not receive proper credit from the grader if your format differs from the provided examples above.