Assignment 1: Search Methods

1. The 3-digit puzzle

In this assignment, you will implement a number of search algorithms to solve the 3-digit puzzle.

Given are two 3-digit numbers called (start) and (goal) and also a set of 3-digit numbers called . To solve the puzzle, we want to get from to in the smallest number of moves. A move is a transformation of one number into another number by adding or subtracting 1 to one of its digits. For example, a move can take you from 123 to 124 by adding 1 to the last digit or from 953 to 853 by subtracting 1 from the first digit. Moves must satisfy the following constraints:

    1. You cannot add to the digit 9 or subtract from the digit 0;

    2. You cannot make a move that transforms the current number into one of the forbidden numbers;

    3. You cannot change the same digit twice in two successive moves.

Note that since the numbers have 3 digits, at the beginning there are at most 6 possible moves from . After the first move, the branching factor is at most 4, due to the constraints on the moves and especially due to constraint 3.


 For the purpose of this assignment numbers starting with 0, e.g. 018, are considered 3-digit numbers.

    2. Tasks

        1. Write a program to find a solution of the puzzle using the following 6 search strategies: BFS, DFS, IDS, Greedy, A* and Hill-climbing. Use the Manhattan heuristic as a heuristic for A* and Greedy and also as the evaluation function in Hill-climbing.

The Manhattan heuristic for a move between two numbers A and B is the sum of the absolute differences of the corresponding digits of these numbers, e.g. ℎ(123, 492) = |1 − 4| + |2 − 9| + |3−2|=11.

        2. Avoid cycles. When selecting a node from the fringe for expansion, if it hasn’t been expanded yet, expand it, otherwise discard it. Hint: It is not just the three digits that you need to consider when determining if you have expanded a node before. Two nodes are the same if a) they have the same 3 digits; and b) they have the same ‘child’ nodes.

        3. Generate the children in the following order:

            a. 1 is subtracted from the first digit

            b. 1 is added to the first digit

            c. 1 is subtracted from the second digit

            d. 1 is added to the second digit

            e. 1 is subtracted from the third digit

            f. 1 is added to the third digit

Example: the order of the children of node 678 coming from parent 668 is 578, 778, 677, 679. Note that there are no children for the second digit as it already has been changed in the previous move (constraint 3).

        4. For the heuristic search strategies: if there are nodes with the same priority for expansion, expand the last added node.

        5. Set a limit of 1000 expanded nodes maximum, and when it is reached, stop the search and print a message that the limit has been reached (see section “Input and Output” for the exact message required).

    3. Input and Output

As your program will be automatically tested, it is important that you adhere to these strict rules for program input and output.

Input

Your program should be called ThreeDigits, and will be run from the command line with the following arguments:

    1. A single letter representing the algorithm to search with, out of B for BFS, D for DFS, I for IDS, G for Greedy, A for A*, H for Hill-climbing.

    2. A filename of a file to open for the search details. This file will contain the following:


start-state

goal-state


forbidden1,forbidden2,forbidden3,…,forbiddenN (optional)



Page 2 of 4 For example, the file puzzle.txt might contain the following:


345

555


355,445,554


This file means that the search algorithm will start at state 345, and the goal is state 555. The search may not pass through any of 355, 445 or 554. Remember that the last line may not be present; i.e. there are no forbidden values.

The following examples show how the program would be run for each of the submission languages, assuming we want to run the A* search algorithm, and the input is in a file called sample.txt.


Python (version 3.7.0):


python ThreeDigits.py A sample.txt

Java (version 8):


javac ThreeDigits.java

java ThreeDigits A sample.txt


C (gcc version 6.3.0):


gcc –lm -w -std=c99 –o ThreeDigits ThreeDigits.c *.c ./ThreeDigits A sample.txt


C++ (gcc version 6.3.0):


g++ –o ThreeDigits ThreeDigits.cpp

./ThreeDigits A sample.txt


MATLAB (version R2018a):


mcc -m -o ThreeDigits -R -nodisplay -R -nojvm ThreeDigits ./run_ThreeDigits.sh <MATLAB_install_directory> A sample.txt


Note: MATLAB must be run this way (compiled first) to speed up MATLAB running submissions. The arguments are passed to your ThreeDigits function as strings. For example, the example above will be executed as a function call like this:


ThreeDigits('A', 'sample.txt')


Output

You program will output two lines only. The first line will contain the solution path found from the start node to the goal node (inclusive), in the form of states separated by commas. If no path can be found with the given parameters, then the first line should be “No solution found.”.

The second line should be the order of nodes expanded during the search process, in the form of states separated by commas. If no path was found, this should still print the list of expanded nodes. Remember that this list should never exceed 1000 states (point 5 in the Tasks section).

 Examples


sample.txt:


320

110


Note that the outputs of BFS and IDS here are quite long, and so the second line has wrapped. These outputs are still only two lines.


Search Method    Output



320,220,210,110
BFS    320,220,420,310,330,321,210,230,221,410,430,421,210,410,

311,230,430,331,221,421,311,331,110
DFS    320,220,210,110


320,220,210,110



320,220,210,110

IDS    320,320,220,420,310,330,321,320,220,210,230,221,420,410, 430,421,310,210,410,311,330,230,430,331,321,221,421,311, 331,320,220,210,110

Greedy    320,310,210,211,111,110


320,310,210,211,111,110



Hill-Climbing
No solution
found.

320,310,210

A*    320,220,210,110


320,310,210,220,210,110


4.  Submission Details

This assignment is to be submitted electronically via the PASTA submission system.

Your submission files should be zipped together in a single .zip file and include a main program called ThreeDigits. Valid extensions are .java, .py, .c, .cpp, .cc, and .m. Zip only the submission files, not the folder – when your zip file is unzipped there should be only submission files, not a folder with submission files. Only
.zip format is accepted; do not use any other format, e.g. .rar or .7z. If your program contains only a single file, then you can just submit the file without zipping it.

Upload your submission on PASTA under Assignment 1.




Page 4 of 4