slidingpuzzle 0.0.6

Sliding Puzzle solver and utilities

Sliding Puzzle

• Sliding Puzzle
  • Installation
  • Documentation
  • Examples
  • Algorithms
  • Heuristics
    • Neural Nets
  • Custom Models
  • Creating a Pull Request

A package for solving and working with sliding tile puzzles.

Installation

pip install slidingpuzzle

Documentation

https://slidingtilepuzzle.readthedocs.io/en/latest/slidingpuzzle.html

Examples

>>> from slidingpuzzle import *
>>> b = new_board(3, 3)
>>> print_board(b)
1 2 3
4 5 6
7 8
>>> shuffle_board(b)
([1, 6, 7], [4, 0, 8], [5, 3, 2])
>>> print_board(b)
1 6 7
4   8
5 3 2

The boards are just a tuple of list[int]. The number 0 is reserved for the blank. You can easily build your own board:

>>> b = ([4, 5, 6], [7, 8, 0], [1, 2, 3])
>>> print_board(b)
4 5 6
7 8
1 2 3
>>> manhattan_distance(b)
11
>>> is_solvable(b)
False

Not all board configurations are solvable. The search() routine will validate the board before beginning, and may throw a ValueError if the board is illegal.

>>> search(b, "bfs")
solution=[3, 2, 8, 3, 6, 7, 3, 6, 7, 1, 4, 7, 2, 5, 7, 4, 1, 2, 5, 8]
solution_len=20, generated=165616, expanded=120653, unvisited=44964, visited=62277
>>> search(b, "greedy")
solution=[8, 2, 3, 8, 2, 7, 6, 2, 7, 3, 8, 5, 4, 7, 5, 4, 7, 5, 3, 6, 2, 3, 4, 8, 6, 2, 3, 1, 5, 4, 2, 6, 8, 7, 4, 5, 1, 2, 5, 4, 7, 8]
solution_len=42, generated=711, expanded=490, unvisited=222, visited=258

As expected, greedy search finds a solution must faster than BFS, but the solution is of lower quality.

We can get a rough comparison of two heuristics like this:

>>> compare_heuristics(3, 3, manhattan_distance, euclidean_distance)
(1594.8666666666666, 3377.5)

This tells us the average number of states expanded over multiple runs for each heuristic. In this case, manhattan_distance was superior.

The default search is A* with manhattan_distance as the heuristic:

>>> search(b)
solution=[3, 2, 8, 3, 6, 7, 3, 6, 7, 1, 4, 7, 2, 5, 7, 4, 1, 2, 5, 8]
solution_len=20, generated=829, expanded=518, unvisited=312, visited=313

In this case, it finds the optimal solution almost as quickly as greedy search.

The solutions are actually stored as a list of (y, x)-coords of moves, indicating which tile is to be moved next:

>>> result = search(b)
>>> result.solution
[(2, 1), (2, 2), (1, 2), (1, 1), (0, 1), (0, 2), (1, 2), (1, 1), (0, 1), (0, 0), (1, 0), (1, 1), (2, 1), (2, 0), (1, 0), (0, 0), (0, 1), (1, 1), (2, 1), (2, 2)]

If you are working with a physical puzzle and actual tile numbers would be easier to read, you can obtain them the same way str(SearchResult) does internally:

>>> solution_as_tiles(result.board, result.solution)
[8, 2, 3, 8, 2, 7, 6, 2, 7, 3, 8, 5, 4, 7, 5, 4, 7, 5, 3, 6, 2, 3, 4, 8, 6, 2, 3, 1, 5, 4, 2, 6, 8, 7, 4, 5, 1, 2, 5, 4, 7, 8]

Algorithms

>>> print(ALGORITHMS)
('a*', 'beam', 'bfs', 'dfs', 'greedy', 'ida*', 'iddfs')

The available algorithms for search() are:

• "a*" - A* search
• "beam" - Beam search
• "bfs" (default) - Breadth-first search
• "dfs" - Depth-first search
• "greedy" - Greedy best-first search
• "ida*" - Iterative deepening A*
• "iddfs" - Iterative deepening depth-first search

Some algorithms support additional customization via kwargs. These are:

a*: {
    "bound": default is float("inf"),
        restricts search to f-values < bound
    "weight": default is 1
}
beam: {
    "bound": default is float("inf"),
        restricts search to f-values < bound
    "width", default is 3
}
bfs: {
    "bound": default is float("inf"),
        restricts search to depth < bound
}
dfs: {
    "bound": default is float("inf"),
        restricts search to depth < bound
}
ida*: {
    "bound", default is manhattan_distance(board),
        restricts search to f-values < bound
    "weight": default is 1
}
iddfs: {
    "bound", default is manhattan_distance(board),
        restricts search to depth < bound
}

Example:

>>> for weight in range(1, 16):
...     r = search(b, weight=weight)
...     print(f"weight: {weight}, solution_len: {len(r.solution)}, expanded: {r.expanded}")
...
weight: 1, solution_len: 27, expanded: 1086
weight: 2, solution_len: 35, expanded: 1026
weight: 3, solution_len: 35, expanded: 814
weight: 4, solution_len: 43, expanded: 640
weight: 5, solution_len: 45, expanded: 531
weight: 6, solution_len: 45, expanded: 563
weight: 7, solution_len: 43, expanded: 407
weight: 8, solution_len: 43, expanded: 578
weight: 9, solution_len: 43, expanded: 648
weight: 10, solution_len: 43, expanded: 689
weight: 11, solution_len: 43, expanded: 764
weight: 12, solution_len: 43, expanded: 601
weight: 13, solution_len: 43, expanded: 786
weight: 14, solution_len: 43, expanded: 733
weight: 15, solution_len: 43, expanded: 782

With the default parameters, we see that A* finds the optimal solution after expanding 1086 states. If we are willing to sacrifice optimality of the solution, we can try different weights to tradeoff solution quality for search time. Note that for a given problem and quality criteria, there will be an optimal weight. Beyond a certain point, the weight will have no positive effect. In the example above, using weights beyond ~38 produces further change in neither solution quality nor nodes expanded.

Of the provided algorithms, only beam search is incomplete. This means it may miss the goal, even thought the board is solvable.

Heuristics

Heuristics are most relevant for "greedy", "a*", and "ida*" as they are used to sort all known moves before selecting the next action.

For other algorithms, the heuristic is only used to sort the local nodes. For example, when the 2 <= N <= 4 nearby available moves are generated they will be immediately sorted using the heuristic.

The available heuristics are:

• euclidean_distance - The straight line distance in Euclidean space between two tiles. This is essentially the hypotenuse of a right triangle. (The square root is not used as it does not affect the sorting order.)
• hamming_distance - Count of how many tiles are in the correct position
• manhattan_distance - Count of how many moves it would take each tile to arrive in the correct position, if other tiles could be ignored
• random_distance - This is a random number (but a consistent random number for a given board state). It is useful as a baseline.
• Any heuristic you want! Just pass any function that accepts a board and returns a number. The lower the number, the closer the board is to the goal (lower = better).

Neural Nets

Well-trained neural networks are generally superior to the other heuristics. Pre-trained nets will be available for download soon. For now, you can follow the steps below to train and use your own net from scratch using the models defined in slidingpuzzle/nn/models.py.

pip install -r requirements-nn.txt

You can then train a new network easily:

>>> import slidingpuzzle.nn as nn
>>> model = nn.Model_v1(3, 3)
>>> nn.train(model)

After training, your model will automatically be available for the board size as heuristic:

• nn.v1_distance

For example:

>>> board = shuffle_board(new_board(3, 3))
>>> search(board)
[solution=[8, 7, 3, 8, 7, 6, 5, 3, 8, 7, 6, 5, 3, 2, 1, 4, 7, 8, 5, 6]
solution_len=20, generated=1350, expanded=864, unvisited=487, visited=503]
>>> search(board, heuristic=nn.v1_distance)
[solution=[8, 6, 5, 7, 3, 8, 6, 3, 7, 5, 3, 6, 8, 7, 5, 2, 1, 4, 7, 8]
solution_len=20, generated=662, expanded=406, unvisited=257, visited=247]

Custom Models

First define your model somewhere. Your model class must:

• Have a unique self.version string
• Have self.h and self.w for the board size it expects
• Accept the board as an input tensor created by:
  • torch.tensor(board, dtype=torch.float32)

Then train your model as above. You can then define your heuristic like this:

def my_model_distance(board: tuple[list[int], ...]) -> float:
    h, w = len(board), len(board[0])
    heuristic = nn.get_heuristic(h, w, "my_model_version")
    return heuristic(board)

And use it as normal:

>>> search(board, "a*", heuristic=my_model_distance)

Creating a Pull Request

First of all, thanks for contributing! Setup your dev environment:

pip install -r requirements-dev.txt

First and most importantly verify you haven't broken anything by running pytest:

pytest

Don't forget to add new tests for anything you've added.

You can also run mypy and look for any new violations:

mypy src

Finally, check that the docs look correct:

cd docs
./make html

Black and flake8 are used for formatting and linting, but they are automatically run by the pre-commit hooks installed in the Git repo.

If you made changes in the nn submodule, you also need to install requirements-nn.txt and run pytest tests/test_nn.py to validate.