Documentation

A Sudoku puzzle looks like this:

\[ \begin{array}{|ccc|ccc|ccc|} \hline . & . & 4 & 8 & . & . & . & 1 & 7 \\ 6 & 7 & . & 9 & . & . & . & . & . \\ 5 & . & 8 & . & 3 & . & . & 2 & 4 \\ \hline 3 & . & . & 7 & 4 & . & 1 & . & . \\ . & 6 & 9 & . & . & . & 7 & 8 & . \\ . & . & 1 & . & 6 & 9 & . & . & 5 \\ \hline 1 & . & . & . & 8 & . & 3 & . & . \\ . & . & . & . & . & 6 & . & 9 & 1 \\ 2 & 4 & . & . & . & 1 & 5 & . & . \\ \hline \end{array} \]

The solution for the above is:

\[ \begin{array}{|ccc|ccc|ccc|} \hline 9 & 3 & 4 & 8 & 2 & 5 & 6 & 1 & 7 \\ 6 & 7 & 2 & 9 & 1 & 4 & 8 & 5 & 3 \\ 5 & 1 & 8 & 6 & 3 & 7 & 9 & 2 & 4 \\ \hline 3 & 2 & 5 & 7 & 4 & 8 & 1 & 6 & 9 \\ 4 & 6 & 9 & 1 & 5 & 3 & 7 & 8 & 2 \\ 7 & 8 & 1 & 2 & 6 & 9 & 4 & 3 & 5 \\ \hline 1 & 9 & 7 & 5 & 8 & 2 & 3 & 4 & 6 \\ 8 & 5 & 3 & 4 & 7 & 6 & 2 & 9 & 1 \\ 2 & 4 & 6 & 3 & 9 & 1 & 5 & 7 & 8 \\ \hline \end{array} \]

Every spot in the puzzle on a \(9 \times 9\) board belongs to a row and a column, as well as to one single \(3 \times 3\) square, which we will simply call "square" for short. At the beginning, some of the spots carry a single-digit number from 1 to 9. The problem is to fill the missing spots with digits in such a way that every number between 1 and 9 appears exactly once in each row, in each column, and in each square.

Write a function which returns a solution given a Sudoku puzzle. Both will be expressed as a list of 9 rows. Each row will be a list of 9 numbers from 0 to 9, where 0 signifies a blank spot.

Examples

>>> printSudoku $ sudoku sudokuPuzzle
9 3 4 8 2 5 6 1 7
6 7 2 9 1 4 8 5 3
5 1 8 6 3 7 9 2 4
3 2 5 7 4 8 1 6 9
4 6 9 1 5 3 7 8 2
7 8 1 2 6 9 4 3 5
1 9 7 5 8 2 3 4 6
8 5 3 4 7 6 2 9 1
2 4 6 3 9 1 5 7 8

An example Sudoku puzzle which can be fed into sudoku.

Prints a puzzle or solution for sudoku in tabular form.