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Taquin (8-puzzle)

The famous sliding tiles game implemented in Prolog using A* graph search algorithm for N×M size puzzles.

Usage

The code is implemented for SWI Prolog environment.

Run the following command in your shell (provided you have SWI Prolog installed):

swipl test_3x3.pl

You can also try test_3x4.pl or test_4x4.pl.

Then run in your prolog console the following query

puzzle(Puzzle, Difficulty), testPuzzle(Puzzle, ?Algorithm, ?Heuristic).
  • The Heuristic value can be ommitted, the program would call the most adapted heuristic for the chosen algorithm (recommended).
  • The Algorithm can be ommitted, the default value is astar.

Project Structure

taquin
├── util
│   ├── core.pl....................core predicates
│   ├── hamming.pl.................hamming heuristic definition
│   ├── heuristic.pl...............heuristics wrapper predicates
│   ├── manhattan.pl...............manhattan heuristic definition
│   ├── moves.pl...................states adjacency
│   └── test.pl....................testing tools
├── taquin_astar.pl................A* algorithm
├── taquin_dfs.pl..................DFS-style algorithms
├── taquin.pl......................taquin solver wrapper
├── test_3x3.pl....................3×3 example puzzles
├── test_3x4.pl....................3×4 example puzzles
├── test_4x4.pl....................4×4 example puzzles
└── README.md......................quick usage guide

Search Algorithms

  • Depth-First Search (DFS): a simple implementation of DFS using prolog's search trees, there is no optimality guaranty, probable overflow because of the lack of depth control.
  • Iterative Deepening DFS (ID-DFS): analog to DFS with a given Depth, starts with an underestimate of the optimal depth (an admissible heuristic) and increments the depth successively until a solution is found. Optimality is guarantied, solutions are almost always fast for 3×3 puzzles. Nevertheless, for complex puzzles bigger than 3×3 the ID-DFS is as hopeless as DFS.
  • Greedy Search: a simple greedy algorithms that chooses each step by minimizing a heuristic (admissible or not), there is no optimality guaranty but the algorithm is fast and finds a solution for all 3x3 puzzles with the m3h heuristic, possible overflow for complex puzzles because of th lack of depth control.
  • A* Search: a rigourous A* implementation using a priority queue that is guarantied to find an optimal solution with an admissible heuristic manhattan or hamming. Is relatively slow, but is significantly faster and more performant in the case of complex puzzles.

The code is well-documented and readable, for more details the report is in docs/book.pdf written in French (as the project is part of Masters program at INSA Rouen).

To-Do List

  • Implement IDA*
  • Implement random puzzle generator
  • Implement comparison (time and solution optimality-wise)