Stride tricks for Sudoku

The ndarray class has a strides field, which is a tuple indicating the number of bytes to step in each dimension when going through an array. Let's apply some stride tricks to the problem of splitting a Sudoku puzzle to the 3 by 3 squares of which it is composed.

Note

Explaining the Sudoku rules is outside the scope of this book. For more information see http://en.wikipedia.org/wiki/Sudoku.

How to do it...

  1. Define the Sudoku puzzle array

    Let's define the Sudoku puzzle array. This one is filled with the contents of an actual, solved Sudoku puzzle:

    sudoku = numpy.array([
    [2, 8, 7, 1, 6, 5, 9, 4, 3],
    [9, 5, 4, 7, 3, 2, 1, 6, 8],
    [6, 1, 3, 8, 4, 9, 7, 5, 2],
    [8, 7, 9, 6, 5, 1, 2, 3, 4],
    [4, 2, 1, 3, 9, 8, 6, 7, 5],
    [3, 6, 5, 4, 2, 7, 8, 9, 1],
    [1, 9, 8, 5, 7, 3, 4, 2, 6],
    [5, 4, 2, 9, 1, 6, 3, 8, 7],
    [7, 3, 6, 2, 8, 4, 5, 1, 9]
    ])
  2. Calculate the strides. The itemsize field of ndarray gives us the number of bytes in an array. Using the itemsize, calculate the strides:
    strides = sudoku.itemsize * numpy.array([27, 3, 9, 1])
  3. Split into squares.

    Now we can split the puzzle into squares with the as_strided function of the numpy.lib.stride_tricks module:

    squares = numpy.lib.stride_tricks.as_strided(sudoku, shape=shape, strides=strides)
print(squares)

    This prints separate Sudoku squares:

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

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

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


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

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

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


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

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

The following is the complete source code for this recipe:

import numpy

sudoku = numpy.array([
    [2, 8, 7, 1, 6, 5, 9, 4, 3],
    [9, 5, 4, 7, 3, 2, 1, 6, 8],
    [6, 1, 3, 8, 4, 9, 7, 5, 2],
    [8, 7, 9, 6, 5, 1, 2, 3, 4],
    [4, 2, 1, 3, 9, 8, 6, 7, 5],
    [3, 6, 5, 4, 2, 7, 8, 9, 1],
    [1, 9, 8, 5, 7, 3, 4, 2, 6],
    [5, 4, 2, 9, 1, 6, 3, 8, 7],
    [7, 3, 6, 2, 8, 4, 5, 1, 9]
    ])

shape = (3, 3, 3, 3)

strides = sudoku.itemsize * numpy.array([27, 3, 9, 1])

squares = numpy.lib.stride_tricks.as_strided(sudoku, shape=shape, strides=strides)
print(squares)

How it works...

We applied stride tricks to decompose a Sudoku puzzle in its constituent 3 by 3 squares. The strides tell us how many bytes we need to skip at each step when going through the Sudoku array.

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset