Eryn Wells
6cc3fed4b3
- Remove __setitem__; it was getting in the way... - deepcopy the board for each trial in search()
239 lines
10 KiB
Python
239 lines
10 KiB
Python
#!/usr/bin/env python3
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# Eryn Wells <eryn@erynwells.me>
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'''
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A Sudoku solver.
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'''
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import copy
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import logging
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import math
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LOG = logging.getLogger(__name__)
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class Board(dict):
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def __init__(self, size=9, **kwargs):
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self.size = size
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# Verify size is a perfect square. The sqrt(size) is also the dimension of each box on the
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# Sudoku grid.
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self.box_size = int(math.sqrt(size))
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assert self.box_size == int(self.box_size), 'Invalid size; value must be a perfect square'
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# The range of possible values for a square.
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self.possible_values = range(1, self.size + 1)
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# Make the grid.
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super(Board, self).__init__([(Board.xy_key(x, y), list(self.possible_values))
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for x in range(self.size)
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for y in range(self.size)])
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for square in self:
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initial_value = kwargs.get(Board.xy_kwargs_key(*square))
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if initial_value is None:
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continue
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if initial_value not in self.possible_values:
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raise ValueError('Invalid initial value for square ({}, {}): {}'.format(x, y, initial_value))
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LOG.debug('Setting initial value of {} to {}'.format(square, initial_value))
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self.assign(square, [initial_value])
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@classmethod
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def xy_key(self, x, y):
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'''Given {x} and {y}, generate a key to refer to the square at coordinate (x, y) in the grid.'''
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return (int(x), int(y))
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@classmethod
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def xy_kwargs_key(self, x, y):
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'''
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Given {x} and {y}, generate a key to refer to the square in the __init__ kwargs at coordinate (x, y) in the
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grid.
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'''
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return 'x{}y{}'.format(x, y)
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@property
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def solved(self):
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'''
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Determines if the board has been solved. First, determine if all squares have no more than one value (i.e. they
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have had values assigned to them). If not, return False. If so, check each unit (rows, columns, and boxes) to
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make sure that each has one and only one of each value in the range of possible values for a unit. If not,
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return False; otherwise, return True.
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'''
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if not all(len(s) == 1 for s in self.values()):
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return False
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def validate_unit(unit):
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'''
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Validate {unit} by ensuring it has exactly 1 of each value in the range of possible values.
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'''
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necessary_values = list(self.possible_values)
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for square, values in unit.items():
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v = values[0]
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if v in necessary_values:
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necessary_values.remove(v)
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else:
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return False
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if len(necessary_values) != 0:
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return False
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return True
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return ( all(validate_unit(self.row(r)) for r in range(self.size))
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and all(validate_unit(self.col(c)) for c in range(self.size))
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and all(validate_unit(self.box(x, y))
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for x in range(0, self.size, self.box_size)
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for y in range(0, self.size, self.box_size)))
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def row(self, idx):
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'''
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Return a dict of all squares in the {idx}'th row.
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'''
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assert idx >= 0 and idx < self.size, 'Invalid row index; value must be >= 0 and < {}'.format(self.size)
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# key[1] is Y coordinate in the grid.
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return {k: v for k, v in self.items() if k[1] == idx}
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def col(self, idx):
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'''
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Return a dict of all squares in the {idx}'th column.
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'''
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assert idx >= 0 and idx < self.size, 'Invalid column index; value must be >= 0 and < {}'.format(self.size)
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# key[0] is X coordinate in the grid.
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return {k: v for k, v in self.items() if k[0] == idx}
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def box(self, x, y):
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'''
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Given a square at coordinates ({x}, {y}), return a dictionary containing the squares that make up the box that
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contains the point.
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'''
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bx = int(x / self.box_size) * self.box_size
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by = int(y / self.box_size) * self.box_size
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bx_range = range(bx, bx + self.box_size)
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by_range = range(by, by + self.box_size)
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return {k: v for k, v in self.items() if k[0] in bx_range and k[1] in by_range}
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def peers(self, x, y):
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'''
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Generate and return a list of peers for the square at coordinates ({x}, {y}). Peers are defined as all the
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squares in the same row, column, and box as the given square.
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'''
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# Generate a dictionary of all the squares in the row, column, and box containing the given square.
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peers = dict(list(self.row(y).items()) + list(self.col(x).items()) + list(self.box(x, y).items()))
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# Remove the given square.
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del peers[Board.xy_key(x, y)]
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return peers
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def clear(self, squares=None):
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'''
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Clear the board. Resets each square's possible value list to the full range of possible values for this board.
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'''
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for square in (self if squares is None else squares):
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self.assign(square, list(self.possible_values))
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def solve(self):
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return self.search()
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def search(self):
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'''
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Search for a solution, depth-first. Return the solved Board as a new instance of this class.
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'''
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if self.solved:
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return self
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# Chose the square with the fewest possible values.
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_, smallest = min((len(self[sq]), sq) for sq in self if len(self[sq]) > 1)
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# Deepcopy the board.
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for v in self[smallest]:
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trial_board = copy.deepcopy(self)
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try:
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trial_board.assign(smallest, [v])
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if trial_board.search():
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return trial_board
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except ValueError:
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continue
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raise ValueError('No possible solution found.')
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def assign(self, square, value):
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'''
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Assign {value} to {square}. {value} is expected to be an iterable (a list). {key} should be a valid (x, y)
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coordinate pair for referencing a square on the board.
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'''
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LOG.debug('Assigning values {} to square {}.'.format(value, square))
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removed_values = set(self[square]) - set(value)
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for v in removed_values:
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try:
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self.eliminate(square, v)
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except ValueError:
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raise
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# TODO: To make this work right, I should probably also do the same as above for the values added *back* into
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# the values for {square}.
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return True
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def eliminate(self, square, value):
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'''
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Eliminate {value} from {square}, propagating changes to the squares peers as necessary. This process involves
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two logical rules of Sudoku. First, if a square is reduced to a single possible value, assign that value to the
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square and remove the value from the possible value lists of its peers. Second, if a unit has only one square
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that can hold a value, put the value in that square and propagate that change to its peers.
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'''
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if value not in self[square]:
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LOG.debug('Value {} not in square {}; skipping'.format(value, square))
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return True
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# Update peer value list.
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super(Board, self).__setitem__(square, [v for v in self[square] if v != value])
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LOG.debug('Eliminating {} from square {}'.format(value, square))
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# (1) If a square is reduced to one value, eliminate that value from its peers.
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if len(self[square]) == 0:
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# Whoops. Removed the last value... We have a contradiction now.
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LOG.error('Removed last value from square {}'.format(square))
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raise ValueError('Removed last value from square {}; board is now invalid'.format(square))
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elif len(self[square]) == 1:
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# One value left in this square. Propagate changes to its peers.
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LOG.debug('One value left in square {}; eliminating {} from its peers'.format(square, self[square][0]))
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try:
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for peer in self.peers(*square):
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self.eliminate(peer, self[square][0])
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except ValueError:
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raise
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# (2) If a unit has only one square for a value, put it there.
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for unit in (self.row(square[1]), self.col(square[0]), self.box(*square)):
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places = [sq for sq in unit if value in unit[sq]]
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if len(places) == 0:
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LOG.error('No place for value {} to go in unit {}'.format(value, unit))
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raise ValueError('No place for value {} to go in unit {}; board is now invalid'.format(value, unit))
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elif len(places) == 1:
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LOG.debug('One place for value {} to be in unit {}; setting'.format(value, unit))
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self.assign(places[0], [value])
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return True
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def __delitem__(self, key):
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# Don't allow deleting keys from self.
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pass
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def __str__(self):
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lines = []
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box_lines = []
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square_size = len(str(self.size))
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for y in range(self.size):
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row_squares = []
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box_squares = []
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for x in range(self.size):
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square = self.get(Board.xy_key(x, y))
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if len(square) == 1:
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box_squares.append(str(square[0]).center(square_size))
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else:
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box_squares.append('.'.center(square_size))
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if len(box_squares) == self.box_size:
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row_squares.append(' '.join(box_squares))
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box_squares = []
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# Print a divider between boxes.
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box_lines.append(' | '.join(row_squares))
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if len(box_lines) == self.box_size:
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lines.append('\n'.join(box_lines))
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box_lines = []
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if y < self.size - 1:
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# Don't print a divider on the last line.
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box_dividers = ['-' * ((square_size + 1) * self.box_size - 1) for box in range(self.box_size)]
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lines.append('\n{}\n'.format('-+-'.join(box_dividers)))
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return ''.join(lines)
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