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README.md

Sudoku Solver

I had been wondering for a while if I could write a script that would solve sudoku puzzles and I also wanted to learn Python. This is an attempt at both.

So what does it do right now?

Currently this project runs on the command line python3 sudoku.py and it will only solve fairly simple 9x9 Sudoku puzzles.

How does it work?

  • Makes a list of all the cells that are empty
  • Calculates all valid answers for every empty cell
  • Looks for cells that only have one valid answer
  • Looks for answers that only have one valid position within a 3x3 box
  • Looks for answers that only have one valid position in a row or column
  • Inserts the valid answers
  • Loops back through the first five steps until all answers have been found
  • ... or fails if the number of answers left does not decrease after an iteration

How is the puzzle stored?

The puzzle is stored as a list of lists Like this:

[
  [9, 4, 6, 1, 7, 8, 5, 3, 2],
  [7, 3, 2, 5, 4, 9, 1, 8, 6],
  [5, 1, 8, 6, 2, 3, 4, 7, 9],
  [6, 2, 1, 4, 8, 7, 9, 5, 3],
  [4, 5, 7, 3, 9, 1, 2, 6, 8],
  [3, 8, 9, 2, 5, 6, 7, 1, 4],
  [2, 6, 4, 8, 1, 5, 3, 9, 7],
  [1, 9, 3, 7, 6, 4, 8, 2, 5],
  [8, 7, 5, 9, 3, 2, 6, 4, 1]
]

This allows you to retrieve a value by passing in row and column coordinates like puzzle[2][6] which in the example above returns 4.

    0   1   2   3   4   5   6   7   8
0 |0,0|0,1|0,2|0,3|0,4|0,5|0,6|0,7|0,8|
1 |1,0|1,1|1,2|1,3|1,4|1,5|1,6|1,7|1,8|
2 |2,0|2,1|2,2|2,3|2,4|2,5|2,6|2,7|2,8|
3 |3,0|3,1|3,2|3,3|3,4|3,5|3,6|3,7|3,8|
4 |4,0|4,1|4,2|4,3|4,4|4,5|4,6|4,7|4,8|
5 |5,0|5,1|5,2|5,3|5,4|5,5|5,6|5,7|5,8|
6 |6,0|6,1|6,2|6,3|6,4|6,5|6,6|6,7|6,8|
7 |7,0|7,1|7,2|7,3|7,4|7,5|7,6|7,7|7,8|
8 |8,0|8,1|8,2|8,3|8,4|8,5|8,6|8,7|8,8|

Example output

Start

|5|9| |7| |2| |1|6|
|8| | | | | | | |9|
| | | |5|8|9| | | |
| |5| |8| |6| |2| |
| | | | | | | | | |
| |1| |9| |3| |7| |
| | | |6|2|4| | | |
|1| | | | | | | |5|
|4|3| |1| |5| |6|8|

There are 51 answers left to find.


 Iteration 1

|5|9| |7| |2|8|1|6|
|8| | | |6|1| | |9|
| | |1|5|8|9| | |2|
| |5| |8| |6| |2| |
| | | |2| | | |8| |
| |1| |9| |3| |7|4|
| | |5|6|2|4| | | |
|1| | |3| |8| | |5|
|4|3| |1| |5| |6|8|

There are 40 answers left to find.


 Iteration 2

|5|9| |7|3|2|8|1|6|
|8| | |4|6|1| |5|9|
| | |1|5|8|9| | |2|
| |5| |8| |6| |2| |
| | | |2| |7| |8| |
|2|1|8|9|5|3| |7|4|
| |8|5|6|2|4| | |7|
|1| | |3| |8| | |5|
|4|3| |1| |5| |6|8|

There are 31 answers left to find.


 Iteration 3

|5|9|4|7|3|2|8|1|6|
|8| | |4|6|1| |5|9|
| | |1|5|8|9| | |2|
| |5| |8| |6| |2| |
| | | |2| |7|5|8| |
|2|1|8|9|5|3|6|7|4|
|9|8|5|6|2|4|1| |7|
|1| | |3| |8| | |5|
|4|3| |1| |5| |6|8|

There are 26 answers left to find.


 Iteration 4

|5|9|4|7|3|2|8|1|6|
|8| | |4|6|1| |5|9|
| | |1|5|8|9| | |2|
| |5| |8|4|6| |2| |
| |4|9|2| |7|5|8| |
|2|1|8|9|5|3|6|7|4|
|9|8|5|6|2|4|1|3|7|
|1| | |3| |8| |9|5|
|4|3| |1| |5| |6|8|

There are 21 answers left to find.


 Iteration 5

|5|9|4|7|3|2|8|1|6|
|8| | |4|6|1| |5|9|
| | |1|5|8|9| |4|2|
| |5| |8|4|6|9|2|1|
|6|4|9|2|1|7|5|8| |
|2|1|8|9|5|3|6|7|4|
|9|8|5|6|2|4|1|3|7|
|1| |6|3|7|8|4|9|5|
|4|3| |1|9|5|2|6|8|

There are 11 answers left to find.


 Iteration 6

|5|9|4|7|3|2|8|1|6|
|8| |2|4|6|1| |5|9|
| |6|1|5|8|9| |4|2|
| |5| |8|4|6|9|2|1|
|6|4|9|2|1|7|5|8|3|
|2|1|8|9|5|3|6|7|4|
|9|8|5|6|2|4|1|3|7|
|1|2|6|3|7|8|4|9|5|
|4|3|7|1|9|5|2|6|8|

There are 6 answers left to find.


 Iteration 7

|5|9|4|7|3|2|8|1|6|
|8|7|2|4|6|1|3|5|9|
|3|6|1|5|8|9| |4|2|
|7|5|3|8|4|6|9|2|1|
|6|4|9|2|1|7|5|8|3|
|2|1|8|9|5|3|6|7|4|
|9|8|5|6|2|4|1|3|7|
|1|2|6|3|7|8|4|9|5|
|4|3|7|1|9|5|2|6|8|

There are 1 answers left to find.


 Iteration 8

|5|9|4|7|3|2|8|1|6|
|8|7|2|4|6|1|3|5|9|
|3|6|1|5|8|9|7|4|2|
|7|5|3|8|4|6|9|2|1|
|6|4|9|2|1|7|5|8|3|
|2|1|8|9|5|3|6|7|4|
|9|8|5|6|2|4|1|3|7|
|1|2|6|3|7|8|4|9|5|
|4|3|7|1|9|5|2|6|8|

There are 0 answers left to find.

Completed

|5|9|4|7|3|2|8|1|6|
|8|7|2|4|6|1|3|5|9|
|3|6|1|5|8|9|7|4|2|
|7|5|3|8|4|6|9|2|1|
|6|4|9|2|1|7|5|8|3|
|2|1|8|9|5|3|6|7|4|
|9|8|5|6|2|4|1|3|7|
|1|2|6|3|7|8|4|9|5|
|4|3|7|1|9|5|2|6|8|

SOLVED in 9 iterations in 0:00:00.003471

Do you have any plans for the future?

Yes, lots thanks.

I hope to see this project through to completion but it's a hobby so I don't see it happening quickly. The long term aim is to get it to the point where someone can upload a photo of a sudoku puzzle and the app will return the solution. There's a good chance that someone (or many others) has already achieved this but I'm trying to avoid looking into other people's solutions as this is really a learning project for me.

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