JaimieVos / Elysium-Puzzle-Engine

🧩 | Simulation of Strategies for Variations of the 15-Puzzle Problem in C++

About

This engine is being created with the purpose of simulating combinatorical strategies for variations of the 15-Puzzle problem in C++.

List of Features

Name	Description	Version	Tests	Status
User Interface Design	A loop prompting user input.
Puzzle Console Output	Multiple valid puzzle configurations can be formatted and streamed to the console.
Random Configuration Generation	Up to 20,000 valid puzzle configurations can be generated.
Writing Configurations To Files	Possible to write configurations created directly into a file.
Reading Configurations From Files	Possible to read configuration files in order to process configurations further.
Writing Solution Data To Files	Possible to write correctly formatted solution files.
Read/Write NxN Configurations	Writing and Reading files containing arbitrarily sized puzzles is now possible.
Solution File for Arbitrary Sized Partials	It is possible to create a solution file that contains any of the (N^2-1) partials.
Puzzle Analysis for Continous Rows/Columns	It is possible to analyse a puzzle configuration for the total number of continuous rows / columns + reverse.
Puzzle Analysis for Partial Continous Rows/Columns	It is possible to analyse a puzzle configuration for the total number of partial continuous rows / columns + reverse, for any partial N, s.t. N <= M (M = puzzle size).

The current implementation of this system is not optimized, the following is a list of tasks which I plan to complete in the future.

List of Tasks:

• Implement Threading to speed up puzzle processing.
• Implement machine code augmentation for exploration purposes.
• Optimize loop processing, currently there is quite abit of wasteful looping and conditioning within the logic of this project.
• Replace the BigInteger parameter passing and return values from pass-by-value, to pass-by-references or pointers.

References

Puzzle Research

• Research Papers
  • Ya. Perelman 1988 - Fun with Maths and Physics
  • Aaron F. Archer - A Modern Treatment of the 15 Puzzle
  • Ratner & Warmuth - Finding a Shortest Solution for the NxN Extension of the 15-Puzzle
  • Ratner & Warmuth - The (n^2 -1)-Puzzle and Related Relocation Problems
• Blogs
  • Kevin Gong
  • Neos
  • Math-Stackexchange - What is the parity of a permutation in the 15 puzzle
  • UBC Math
  • Wolfram-Math-World
• Wikipedia
  • The 15 Puzzle
  • Parity of a Permutation
  • Mathematical Invariance
• Finite Set Theory
  • Finite Sets
  • Alternating Groups
  • Even Permutations (Parity)
  • Cardinality of a Set

Optimization Research

• Bit twiddling hacks
• Aggregate magic algorithms
• Real-Time-Mantra
• Agner
• Optimizing Software in C++

C++

• C++ Reference
• Stackoverflow
• Cplusplus
• Isocpp
• C++ Patterns

Build Configuration

Premake is the build system tools used for this repository, I prefer it to CMake as I have experience with Lua, and have used this framework previously.

Testing Framework

GoogleTest is the Testing framework used for this repository. The main advantages of using this framework is that it is portable, reusable and based on the xUnit architecture.

• Primer