Write a solver for sudoku puzzles using a constraint satisfaction approach based on constraint propagation and backtracking, and one based on Relaxation Labeling. compare the approaches, their strengths and weaknesses.
A sudoku puzzle is composed of a square 9x9 board divided into 3 rows and 3 columns of smaller 3x3 boxes. The goal is to fill the board with digits from 1 to 9 such that
each number appears only once for each row column and 3x3 box; each row, column, and 3x3 box should containg all 9 digits. The solver should take as input a matrix withwhere empty squares are represented by a standars symbol (e.g., ".", "_", or "0"), while known square should be represented by the corresponding digit (1,...,9). For example: 37. 5.. ..6 ... 36. .12 ... .91 75. ... 154 .7. ..3 .7. 6.. .5. 638 ... .64 98. ... 59. .26 ... 2.. ..5 .64
Hints for Constraint Propagation and Backtracking:
- Each cell should be a variable that can take values in the domain (1, … ,9).
- The two types of constraints in the definition form as many types of constraints:
- Direct constraints impose that no two equal digits appear for each row, column, and box.
- Indirect constrains impose that each digit must appear in each row, column, and box.
- You can think of other types of (pairwise) constraints to further improve the constraint propagation phase.
- Note: most puzzles found in the magazines can be solved with only the constraint propagation step.
Hints for Relaxation Labeling:
- Each cell should be an object, the values between 1 and 9 labels.
- The compatibility 𝑟𝑖𝑗(𝜆, 𝜇) should be 1 if the assignments satisfy direct constraints, 0 otherwise.
In order to run this project, Python 3 and a basic C++ compiler are required, along with the numpy module for Python:
pip3 install numpyIn order to run the Constraint Propagation based solver:
g++ main.cpp -o out
./outFor the Relaxation labeling based solver:
python main.pygit clone https://github.com/jgurakuqi/search-based-sudoku-solverMIT License
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