149 lines
4.4 KiB
Python
149 lines
4.4 KiB
Python
#!env python3
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# Eryn Wells <eryn@erynwells.me>
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'''
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A Sudoku puzzle solver.
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'''
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import itertools
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import math
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class Sudoku:
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def __init__(self, size=3, board=None):
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self._size = size
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sz4 = size ** 4
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if board:
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self._board = bytes(board)[:sz4]
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else:
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self._board = bytes(sz4)
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@property
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def size(self):
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'''
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The size of the board. This dictates the length of one side of the boxes that the board is subdivided into.
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'''
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return self._size
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@property
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def row_size(self):
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'''
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The length of a row or column, or the area of a box in the grid.
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'''
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return self.size ** 2
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@property
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def grid_size(self):
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'''
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The total number of squares in the grid.
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'''
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return self.size ** 4
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@property
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def all_boxes(self):
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'''
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Iterator of xy-coordinates for every box in the grid.
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'''
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return itertools.product(range(self.size), repeat=2)
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@property
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def possible_values(self):
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'''
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The set of valid values for any grid square. This method does not account for values made invalid by already
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being present in a peer of a given square.
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'''
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return set(range(1, self.row_size + 1))
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@property
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def rows(self):
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return self._apply_index_ranges(self.index_rows)
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@property
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def columns(self):
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return self._apply_index_ranges(self.index_columns)
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@property
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def boxes(self):
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return self._apply_index_ranges(self.index_boxes)
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def peers(self, x, y):
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'''
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Return a set of values of the peers for a given square.
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'''
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return {self._board[i] for i in self.index_peers(x, y) if self._board[i] != 0}
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@property
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def index_rows(self):
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'''
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Return an iterable of ranges of indexes into the board, each defining a row.
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'''
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return (self._row(i) for i in range(self.row_size))
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@property
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def index_columns(self):
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'''
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Return an iterable of ranges of indexes into the board, each defining a column.
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'''
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return (self._column(i) for i in range(self.row_size))
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@property
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def index_boxes(self):
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'''
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Return an iterable of ranges of indexes into the board, each defining a box.
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'''
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return (self._box(x, y) for (x,y) in self.all_boxes)
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def index_peers(self, x, y):
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'''
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Return a set of the peers, indexes into the board, for a given square.
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'''
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box = int(x / sz), int(y / sz)
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return set(self._row(y)) | set(self._column(x)) | set(self._box(*box))
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def _row(self, r):
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row_size = self.row_size
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return range(r * row_size, r * row_size + row_size)
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def _column(self, c):
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return range(c, self.grid_size, self.row_size)
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def _box(self, x, y):
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size = self.size
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row_size = self.row_size
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offx, offy = (x * size, y * size * row_size)
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def _range(i):
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start = (offy + i * row_size) + offx
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return range(start, start + size)
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ranges = itertools.chain(*[_range(i) for i in range(size)])
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return ranges
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@property
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def solved(self):
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expected = self.possible_values
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all_groups = itertools.chain(self.rows, self.columns, self.boxes)
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return all(expected == set(g) for g in all_groups)
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def _apply_index_ranges(self, ranges):
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return ((self._board[i] for i in r) for r in ranges)
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def __str__(self):
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field_width = len(str(max(self.possible_values)))
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sz = self.size
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lines = []
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spacer = '{0}{1}{0}'.format('+', '+'.join(['-' * (field_width * sz) for _ in range(sz)]))
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for line in range(self.size):
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chunks = []
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for i in range(sz):
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fields = []
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for j in range(sz):
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idx = line * self.size + i * sz + j
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fields.append('{{board[{i}]:^{width}}}'.format(i=idx, width=field_width))
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chunks.append(''.join(fields))
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if (line % sz) == 0:
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lines.append(spacer)
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lines.append('{0}{1}{0}'.format('|', '|'.join(chunks)))
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lines.append(spacer)
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fmt = '\n'.join(lines)
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str_board = [str(n) if n != 0 else ' ' for n in self._board]
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out = fmt.format(board=str_board)
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return out
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