CMPT 310 Assignment 1

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1 CMPT 310 Assignment 1 October 16, points total, worth 10% of the course grade. Turn in on CourSys. Submit a compressed directory (.zip or.tar.gz) with your solutions. Code should be submitted as a single.py file, one file per question. Free-answer questions should be submitted as PDF file. You may write your solution using LaTeX, Microsoft Word (print to PDF, do not submit a.doc file), or write on paper and scan it. If you write on paper, please use a scanner or a scanner app (such as TinyScanner for ios) that removes the background; do not submit a photo. You are encouraged to work in a group. Feel free to discuss solution strategies and check each other s work. However, you must write all the text and code you submit on your own. Joint submissions are not allowed, nor is copying someone elses text or code. Plagiarism is not okay, and will be taken very seriously. If you re not sure whether something is okay, please ask. If you are having trouble, please take advantage of office hours and the discussion forum. 1

2 1 How does the TA mark your assignment? For free-answer questions, please justify your answer with a few sentences explaining the factors that have influenced your answer. If you give justifications of your answers that make sense then the TA will mark according to your assumptions. Otherwise, the TA will just stick to the solution. Programming assignments will be graded with respect to the following criteria: Correctness does your solution satisfy all of the assigned requirements? Code readability and commenting your code should be formatted in a readable fashion, with appropriately named variables, and your own helper functions defined whenever appropriate. You should provide comments to explain the more intricate parts of your code. If a program is written in a way that is hard to understand, it gets a maximum of 50/100 points. 2 PEAS model (10 points) For each of the following problems, develop a PEAS model and characterize the environment along the dimensions: observable, deterministic, episodic, static, discrete, single-agent. 1. Google Maps search for directions using public transit in Vancouver. Performance measure: transit time of route. Environment: roads, transit routes, current traffic. Actuators: Display to user. Sensors: Route database. Partially observable, stochastic, episodic, dynamic, continuous, single-agent. 2. The game show Jeopardy, as played by IBM s Watson. Performance measure: score. Environment: questions, show host. Actuators: press button, answer question. Sensors: knowledge database. Partially observable, deterministic, episodic, dynamic, discrete, multi-agent. 3 Problem formulation (10 points) Give a complete problem formulation for each of the following. Choose a formulation that is precise enough to be implemented. 2

3 1. Using only four colors, you have to color a planar map in such a way that no two adjacent regions have the same color. Initial state: No regions colored. Goal test: All regions colored, and no two adjacent regions have the same color. Successor function: Assign a color to a region. Cost function: Number of assignments. 2. You have three jugs, measuring 12 gallons, 8 gallons, and 3 gallons, and a water faucet. You can fill the jugs up or empty them out from on to another or onto the ground. You need to measure out exactly one gallon. Initial state: jugs have values [0, 0, 0]. Successor function: given values [x, y, z], generate [12, y, z], [x, 8, z], [x, y, 3] (by filling); [0, y, z], [x, 0, z], [x, y, 0] (by emptying); or for any two jugs with current values x and y, pour y into x; this changes the jug with x to the minimum of x + y and the capacity of the jug, and decrements the jug with y by by the amount gained by the first jug. Cost function: Number of actions. 4 Searching using composite actions (10 points) An action such as Go(Sibiu) really consists of a long sequence of finer-grained actions: turn on the car, release the brake, accelerate forward, etc. Having composite actions of this kind reduces the number of steps in a solution sequence, thereby reducing the search time. Suppose we take this to the logical extreme, by making super-composite actions out of every possible sequence of Go actions. Then every problem instance is solved by a single super-composite action, such as Go(Sibiu)Go(Rimnicu Vilcea)Go(Pitesti)Go(Bucharest). Explain how search would work in this formulation. Is this a practical approach for speeding up problem solving? The state space is a tree of depth one, with all states successors of the initial state. There is no distinction between depth-first search and breadth-first search on such a tree. If the sequence length is unbounded the root node will have infinitely many successors, so only algorithms which test for goal nodes as we generate successors can work. What happens next depends on how the composite actions are sorted. If there is no particular ordering, then a random but systematic search of potential solutions occurs. If they are sorted by dictionary order, then this implements 3

4 depth-first search. If they are sorted by length first, then dictionary ordering, this implements breadth-first search. Discarding sequence structure is not a particularly practical approach to search. 5 Lights Out puzzle (60 points total) In this question we will consider the Lights Out puzzle. In this puzzle, there is an n m board of cells, each of which is On or Off. The puzzle starts out with some cells On and some Off. In each move, the player chooses one cell; that cell and all adjacent cells are toggled (i.e. On turns to Off, and Off turns to On). Cells count as adjacent horizontally or vertically, but not diagonally. In other words, targeting a cell in the center of the board toggles a total of five cells; a move on the side toggles four; and a move in the corner toggles three. The goal of the game is to change all cells to the Off position in as few moves as possible. You can try playing Lights Out yourself at: (5 points) Create an implementation of the Lights Out puzzle. It should support the following functions: create puzzle(rows, cols): Create a Lights Out puzzle with all cells initialized to off. perform move(puzzle, row, col): Toggle the appropriate cells corresponding to a move at position (row,col). scramble(puzzle): Scramble the puzzle by, on each cell, randomly with 50% probability, calling perform move(). This ensures that the puzzle is solvable, which might not be the case if cells are flipped individually. is solved(puzzle): Returns True or False depending on whether all cells are off. 4

5 5.2 (10 points) Does the order of moves for a Lights Out puzzle matter? Can an optimal solution ever involve running perform move() twice on the same cell? Explain why or why not. Write a function next cell(rows,cols,row,col) that takes the (row,col) coordinates of a cell on a rows cols grid and outputs the (row,col) coordinates of the next cell in left-right top-bottom order. For example, in a 5 5, zero-indexed grid, next cell(5,5,0,0) = (0,1) and next cell(5,5,3,4) = (4,0). (Any other order is fine, too.) No, the order does not matter. No, an optimal solution cannot run the same move twice, because doing so would undo the first move. This helps us search because we can consider only a sequences of moves that are sorted from top left to bottom right, and that do not contain duplicate moves. 5.3 (10 points) Come up with a nontrivial admissible heuristic for this puzzle. Describe your heuristic and explain why it is admissible. Heuristic: h(n) = #On/5. This is admissible because you can turn off at most five On cells per action. 5.4 (30 points) Implement three functions to solve the Lights Out puzzle, using each of the following algorithms respectively: Depth-First, Breadth-First, A*. A* should use the heuristic you designed above. Each function should take a puzzle as input and return a list of moves that solves the puzzle. In addition, each function should output the number of steps it took to find the solution, measured by the number of times the search algorithm used perform move() to find the next board state. (You only need to output a single solution (i.e. one list of moves), not all possible solutions.) Hint: Your implementations of Depth-First and Breadth-First search should have worst-case running time of O(2 nm ), where n and m are the numbers of rows and columns respectively. You may want to make use of next cell(). 5

6 5.5 (5 points) Create 100 random puzzles with 4 rows and 4 columns, and run each of the three algorithms on each puzzle. For each algorithm, report (1) the total length of the 100 solutions, (2) the total number of steps taken by the search algorithm to generate all the solutions, and (3) the wallclock time taken by the algorithm. Hint: This should take less than 5 minutes to run. Depth-First search: moves = 597; steps = ; wallclock = 14.03s Breadth-First search: moves = 463; steps = ; wallclock = 22.08s A*: moves = 463; steps = ; wallclock = 11.24s 5.6 (Challenge problem: +10 points extra credit). Come up with your own algorithms for searching for a solution. You may use A* with any heuristic you like, rely on precomputed sub-problems, or use any other algorithm you can think of. Run your algorithm on 100 n n puzzles and report moves, search steps and wallclock time, as above. We will post a leaderboard on the course web page with the top solutions for n = 5 and n = 8, and award extra credit for solutions that perform particularly well on either measure. If you decide to use an algorithm that does not run perform move() directly as part of its search, it may not be obvious how to measure how many steps it takes. If that is the case, use your judgement and measure the number of steps in whatever way is most appropriate. In particular, every step should take O(1) time: the running time of a step should not depend on the number of rows and columns of the puzzle. If you like, you can do any amount of pre-computation, such as storing the results of puzzles with partial solutions. However, your algorithm must do the pre-computation before seeing any of the 100 test puzzles. There will likely be some variation in results due to random chance; however, this will likely be small because of the large number of puzzles. You are allowed to repeat the 100-puzzle process as many times as you like and report the best results. We are counting on everyone to report their results faithfully. This is a friendly competition; please do not cheat and report different numbers than you got. We may verify specific results if we suspect the numbers are 6

7 mis-reported. 6 Feedback (5 points) Give one short piece of feedback about the course so far. What have you found most interesting? Is there a topic that you had trouble understanding? Are there any changes that could improve the value of the course to you? 7 Time (5 points) How many hours did you spend on this assignment? 7

CMPT 310 Assignment 1

CMPT 310 Assignment 1 October 4, 2017 100 points total, worth 10% of the course grade. Turn in on CourSys. Submit a compressed directory (.zip or.tar.gz) with your solutions. Code should be submitted as