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puzzle15

A Python module that allows to solve the 15-puzzle.

How to Play

The 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. The puzzle also exists in other sizes, particularly the smaller 8-puzzle. The object of the puzzle is to place the tiles in order by making sliding moves that use the empty space.

puzzle15 image

Requirements

In order to play the 15-puzzle you have to download and install Python (2.X version) and the wxPython GUI library.

Launch the game

Once you have correctly installed wxPython you can simply run the script by typing (on Unix-based systems):

./wxPuzzle15.py

You can also play with other types of board by adding the board's size as command argument:

./wxPuzzle15.py 8

puzzle15 image

The only valid configurations are: 15, 8 and 3.

Use the puzzle15 module

If you just want to use the puzzle15 module, that allows you to solve the puzzle, you have to

import puzzle15

and use its functions, for example:

# get a random configuration of a solvable 15-puzzle (a 4x4 grid)
# a valid configuration is a list of integers between 1 and the total
# number of tiles (16 for the 15-puzzle, the "empty cell" is included)
puzzle = puzzle15.spuzzle(size=4)
# find an optimal solution
# that is, the sequence of moves made to solve the puzzle
steps = puzzle15.solve(puzzle)

Other valid configurations are the 8-puzzle (3x3 grid) and the 3-puzzle (2x2 grid). Moreover, you can specify a lower bound which, if reached, stops the search; or you can set a function that will be called every time a new solution is found:

# find the first solution with a number of moves less or equal to the lower bound
steps = puzzle15.solve(puzzle, lowerBound=80)

from __future__ import print_function   # python 2.X
display = lambda s: print(s)
# solve the puzzle and call "display" every time new solution is found
steps = puzzle15.solve(puzzle, solutionFound=display)

If the lower bound specified is equal to -1 the function solve returns the first solution found. Actually the first solution is computed by using heuristic; you can also use these specific functions in order to obtain faster a solution:

# create a solvable 15-puzzle and solve it by using heuristic
puzzle = puzzle15.spuzzle(size=4)
steps = puzzle15.solve15_heuristic(puzzle)

8-puzzle and 3-puzzle versions are available too.

You can solve custom puzzles by checking first if the puzzle is solvable:

# create a custom 8-puzzle
puzzle = [7, 5, 9, 8, 1, 2, 3, 6, 4]
# solve the puzzle only if it is solvable
if puzzle15.is_solvable(puzzle):
  steps = puzzle15.solve(puzzle)

The algorithm used to find an optimal solution is "quite" simple:

  1. Find a first solution using heuristic
  2. Store the best solution every time a new solution is found.
  3. Iterate over all possible configuration stored in a priority queue (sorted by the current configuration "distance" from the solved configuration of the puzzle), by adding new configurations only if it is possible to reach a better solution from these.