Sudoku.

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Presentation transcript:

Sudoku

What is Sudoku? A number based combinatorial puzzle The objective is to fill a 9x9 grid The allowed values are [1,9] Different digits in each column Different digits in each row Every 3x3 subgrid contains all of the digits A few cells are filled to start https://en.wikipedia.org/wiki/Sudoku

Minimal Sudoku No starting value can be removed without violating the unambiguousness. Around 3.1 × 10 37 minimal table exist. 2.55× 10 25 are different. Lots of minimal table collected at http://staffhome.ecm.uwa.edu.au/~00013890/sudokumin.php

Solving strategies Backtracking: This is implemented in the example code. Find an empty cell. Find a value which is allowed in the cell. Try to solve the new table. If the new table cannot be solved then back track to a previous state.

Solving strategies Stochastic search Random based search Fill the table randomly Search for violations in the filled table Permute the violating numbers If the number of violations is zero then we found a real solution Simulated annealing, genetic algorithms, etc.

Solving strategies Other strategies Constraint based algorithms Humanistic strategy Combination of simpler methods

Assignment Implement an efficient Sudoku solver! Minimum: able to solve a 9x9 table stop if the given table cannot be solved if multiple solutions are available gather all of them Be able to solve larger tables! Be able to generate valid sudokus!