Assignment 1: Solvability of the NxN sliding tile puzzle

The sliding tile puzzle is a game that requires you to move tiles on a board. The board is NxN, and there are N-1 tiles numbered from 1..N-1 that occupy the board. There is hence 1 location on the board that is empty (referred to as a blank).

There is some (arbitrary) start configuration of the numbered tiles on the board. Starting with this configuration, the aim is to move tiles until some chosen goal configuration is reached, and to do this in the least possible number of moves. You may only move a tile into the blank if the tile neighbours the blank. Moves can be only be in the horizontal and vertical directions (not diagonal).

The sliding-tile puzzle also has other names, such as the 8 Puzzle (for the special case of a 3x3 board) or 15 Puzzle (a 4x4 board) and so on. Sometimes the name N Puzzle is used (indicating an NxN board).

You can play the game online at:

In this assignment you are asked to write a C program that determines whether a given puzzle is solvable. (Note that you do not have to actually solve the puzzle.)

There are some conditions that you should strictly adhere to:

  1. the program reads from stdin text in a prescribed format, described below (we will be auto-testing your program with our input so you must conform to this format)

  2. your program should be able to handle any sized board, starting with 2x2

    • note that the size of the board is determined by the number of tiles on the input
  3. if the input is correct:

    • and the end configuration is reachable from the start configuration, your program should generate the output text solvable (to stdout)

    • and the end configuration is not reachable from the start configuration, your program should generate the output text unsolvable (to stdout)

  4. if the input is not correct, your program should generate an error message (to stdout)

  5. if a system call fails in your program, the program should generate an error message (to stderr)

  6. design and programming restrictions:
    • you are not allowed to use any arrays
    • you are not allowed to use linked lists/trees/graphs
    • you should use an ADT to represent the board and provide the required functionality (such as input checking, creating a board and determining solvability)

Input format

Two lines of text on stdin specifies the start and end configurations, read from left to right, top to bottom. Each line consists of a sequence of integers, separated by any number (>0) of blanks and/or tabs, that represent the tile numbers, and a single letter b to represent the blank space on the board. These integers should of course be in the range 1..N-1 where the board is of size NxN. The first line specifies the start board, the second line the goal board. For example: 

1 2 3 4 b 5 7 8 6
1 2 3 4 5 6 7 8 b

represents a sliding-tile puzzle on a 4x4 board with start and goal configurations: 

start:  1 2 3           goal:  1 2 3
        4   5                  4 5 6
        7 8 6                  7 8

Bad input

Checking the correctness of each configuration is vital. For example, an input line may not represent an NxN board, or the blank may be missing, or one or more of the tile numbers 1..N may be missing, or the 2 boards may not be the same size or the input contains something other than a number or b. There may be more possibilities.

If the configuration is erroneous, your program must generate an appropriate error message (to stdout). Note that it is possible to have more than one error, and in that case you only need to generate a single error message. For example, consider the configuration 1 2 b 1. It does not matter which error is reported by your program in this case: either board is missing tile 3 or board has duplicate tile 1 is okay. The point is that your program should exit gracefully (with status EXIT_FAILURE) and inform the user of at least one problem. The text you use in error messages is not important, but it should be informative.

Good input

If the input is correct, the program should write the following 3 lines to stdout:

Two sample outputs are for example: 

start: b 12 9 13 15 11 10 14 7 8 5 6 4 3 2 1
goal: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 b
solvable

and 

start: 2 1 3 b
goal: 1 2 3 b
unsolvable

If the input is correct the program should exit with EXIT_SUCCESS.

Design

You should make an ADT to implement the puzzle. The client, which is the main program, calls functions in the ADT to read the input, check for correctness and determine solvability. The interface between the client and the ADT is a header file.

Marking

Marks will be deducted if you fail any of our tests for incorrect input, or incorrectly determine the solvability of the puzzle. Marks will also be deducted for poor design (e.g. not using an ADT), poor programming practice or violating any of the rules above.

The assignment is worth 10 marks.

Submission

You should submit exactly 4 files:

  1. a Makefile that generates the executable puzzle (use the dcc compiler)

  2. the C source code of the ADT (call it boardADT.c)

  3. the header file of the ADT (boardADT.h)

  4. the main program (puzzle.c)

To submit the assignment, use the command: 

     ~cs9024/bin/classrun -give assign1  Makefile boardADT.c  boardADT.h  puzzle.c