Q: How do we use constraint propagation to solve the naked twins problem?
A: The naked twins are represented in the game of Sudoku by two boxes (i.e. twins) with two potentially correct and identical values in a given unit. For instance, given a unit in the region of 'DEF' (i.e. rows) and '123' (i.e. columns), if we are presented with the boxes D2 and E2 with possibilities {2,3} - as a result of our box by box assesment in the board - we deduce that D2 must hold either 2 or 3 as value. The same logic applies to E2. Therefore, at this stage we do not know with certainty where to apply the values. The next step is to eliminate the values {2,3} from other boxes in the same unit.
The ultimate goal of constraint propagation is to apply a constraint as much as possible until a solution is found or until the constraint ceases to produce any effect.
Therefore, the function naked_twins() is implemented to identify the boxes with two elements - let's call them, 'twins candidates'. Then, we identify those which hold the same values - the twins. Finally, we remove the identical values from the other boxes in the same unit - peers.
As a result, the implementations of the functions eliminate(), only_choice() and naked_twins() combined together under reduce_puzzle() eventually succeed in applying constraint propagation in order to find a suitable solution for the Sudoku puzzle.
Q: How do we use constraint propagation to solve the diagonal sudoku problem?
A: In order to solve this problem we have to insert a further unit (i.e. diagonal_units) in the list of units available (i.e. row_units, column_units, square_units) so that the diagonal constraint acts as a further filter and it will not accept any solution that does not satisfy the correspondance between the diagonal entries and its related peers.
This project requires Python 3.
We recommend students install Anaconda, a pre-packaged Python distribution that contains all of the necessary libraries and software for this project. Please try using the environment we provided in the Anaconda lesson of the Nanodegree.
Optionally, you can also install pygame if you want to see your visualization. If you've followed our instructions for setting up our conda environment, you should be all set.
If not, please see how to download pygame here.
solution.py- You'll fill this in as part of your solution.utils.py- File that contains variables and helper functions forsolution.pysolution_test.py- Do not modify this. You can test your solution by runningpython solution_test.py.PySudoku.py- Do not modify this. This is code for visualizing your solution.visualize.py- Do not modify this. This is code for visualizing your solution.
To visualize your solution, please only assign values to the values_dict using the assign_values function provided in solution.py
Before submitting your solution to a reviewer, you are required to submit your project to Udacity's Project Assistant, which will provide some initial feedback.
The setup is simple. If you have not installed the client tool already, then you may do so with the command pip install udacity-pa.
To submit your code to the project assistant, run udacity submit from within the top-level directory of this project. You will be prompted for a username and password. If you login using google or facebook, visit [this link](https://project-assistant.udacity.com/auth_tokens/jwt_login for alternate login instructions.
This process will create a zipfile in your top-level directory named sudoku-.zip. This is the file that you should submit to the Udacity reviews system.