Artificial Intelligence Nanodegree
Introductory Project: Diagonal Sudoku Solver
Question 1 (Naked Twins)
Q: How do we use constraint propagation to solve the naked twins problem?
A: Sudoku has 29 units in total, which are 9 row units, 9 column units, 9 square units and 2 diagonal units. So the constraints will be propagated into every 29 units using a loop. And keep in mind that every unit has 9 boxes (or numbers). First, in every loop for 29 units, we don't care the numbers with a length of 1 in a box. We're just going to take the box of 1-length values as solved boxes. Because we don't need to unnecessary computation for the solved ones in 9 boxes.
Next, we should investigate which one has the naked twins in 9 boxes. In every unit, all the values whose length is 2 could be considered as a candidate for the naked twins. But to be the naked twins between the boxes with two-length values, their values must be duplicated in boxes.
To find out which boxes are duplicated, we're going to introduce a dictionary, its keys is going to be each number in a box and its values is going to be a list with the name of boxes (ex. D4, E6) that has every duplicated number.
If the length of the list is greater than 1, it means there are duplicated boxes at where that value is located. Therefore, we can take all the boxes which are greater than 1 in a list into the naked twins.
So far, we could find out what the unsolved boxes and the naked twin boxes are. Now, we investigate 9 boxes in a unit again with these boxes. We're going to choose only the unsolved boxes from 9 boxes, and also exclude the naked twin boxes itself from 9 boxes. Then, replace the value of the unsolved box with the value of the naked twin box.
Question 2 (Diagonal Sudoku)
Q: How do we use constraint propagation on to solve the diagonal sudoku problem?
A: Diagonal Sudoku is just like regular sudoku but with two extra grid. So the constraints is the two diagonal grid must put the digits from 1 to 9 in each unit.
We can get each grid of the two diagonal units with the following code:
diagonal_unit_1 = [rows[x] + cols[x] for x in range(len(rows))]
diagonal_unit_2 = [rows[::-1][x] + cols[x] for x in range(len(rows))]
Then, the only way to propagate the constraint is just to make regular sudoku have the above additional grid. We don't need to have a further modification to the constraints propagation code. Because the constraint propagation can be applied to two extra unit just like regular units without worrying about where each unit is located.
Install
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.
Optional: Pygame
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.
Code
solution.py- You'll fill this in as part of your solution.solution_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.
Visualizing
To visualize your solution, please only assign values to the values_dict using the assign_values function provided in solution.py
Submission
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.