diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..d646835 --- /dev/null +++ b/.gitignore @@ -0,0 +1,2 @@ +*.pyc +__pycache__/ diff --git a/puzzles.py b/puzzles.py new file mode 100644 index 0000000..62f5199 --- /dev/null +++ b/puzzles.py @@ -0,0 +1,58 @@ +#!/usr/bin/env python3 +# Eryn Wells + +''' +Parser for puzzles in the ./puzzles directory. +''' + +import sudoku + + +euler = [] +norvig = [] + + +def parse_euler(filename='./puzzles/euler.txt'): + with open(filename, 'r') as f: + puzzle_lines = f.readlines() + + for puzzle in puzzle_lines: + # Chop the newline + if puzzle[-1] == '\n': + puzzle = puzzle[:-1] + print('Parsing puzzle: {}'.format(puzzle)) + if len(puzzle) != 81: + continue + kwargs = {} + for idx in range(len(puzzle)): + sq = puzzle[idx] + if sq not in '1234567890.': + continue + sq_int = 0 if sq == '.' else int(sq) + x, y = int(idx % 9), int(idx / 9) + if sq_int != 0: + kwargs[sudoku.Board.xy_kwargs_key(x, y)] = sq_int + euler.append(sudoku.Board(**kwargs)) + + +def parse_norvig(filename='./puzzles/norvig.txt'): + with open(filename, 'r') as f: + puzzle_lines = f.readlines() + + for puzzle in puzzle_lines: + # Chop the newline + if puzzle[-1] == '\n': + puzzle = puzzle[:-1] + print('Parsing puzzle: {}'.format(puzzle)) + if len(puzzle) != 81: + continue + kwargs = {} + for idx in range(len(puzzle)): + sq = puzzle[idx] + if sq not in '1234567890.': + continue + sq_int = 0 if sq == '.' else int(sq) + x, y = int(idx % 9), int(idx / 9) + if sq_int != 0: + kwargs[sudoku.Board.xy_kwargs_key(x, y)] = sq_int + norvig.append(sudoku.Board(**kwargs)) diff --git a/puzzles/euler.txt b/puzzles/euler.txt new file mode 100644 index 0000000..b0bb576 --- /dev/null +++ b/puzzles/euler.txt @@ -0,0 +1,50 @@ +003020600900305001001806400008102900700000008006708200002609500800203009005010300 +200080300060070084030500209000105408000000000402706000301007040720040060004010003 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+....75....1..2.....4...3...5.....3.2...8...1.......6.....1..48.2........7........ +6.....7.3.4.8.................5.4.8.7..2.....1.3.......2.....5.....7.9......1.... +....6...4..6.3....1..4..5.77.....8.5...8.....6.8....9...2.9....4....32....97..1.. +.32.....58..3.....9.428...1...4...39...6...5.....1.....2...67.8.....4....95....6. +...5.3.......6.7..5.8....1636..2.......4.1.......3...567....2.8..4.7.......2..5.. +.5.3.7.4.1.........3.......5.8.3.61....8..5.9.6..1........4...6...6927....2...9.. +..5..8..18......9.......78....4.....64....9......53..2.6.........138..5....9.714. +..........72.6.1....51...82.8...13..4.........37.9..1.....238..5.4..9.........79. +...658.....4......12............96.7...3..5....2.8...3..19..8..3.6.....4....473.. +.2.3.......6..8.9.83.5........2...8.7.9..5........6..4.......1...1...4.22..7..8.9 +.5..9....1.....6.....3.8.....8.4...9514.......3....2..........4.8...6..77..15..6. +.....2.......7...17..3...9.8..7......2.89.6...13..6....9..5.824.....891.......... +3...8.......7....51..............36...2..4....7...........6.13..452...........8.. + \ No newline at end of file diff --git a/sudoku.py b/sudoku.py new file mode 100644 index 0000000..964e6be --- /dev/null +++ b/sudoku.py @@ -0,0 +1,237 @@ +#!/usr/bin/env python3 +# Eryn Wells + +''' +A Sudoku solver. +''' + +import copy +import logging +import math + +LOG = logging.getLogger(__name__) + + +class Board(dict): + def __init__(self, size=9, **kwargs): + self.size = size + + # Verify size is a perfect square. The sqrt(size) is also the dimension of each box on the + # Sudoku grid. + self.box_size = int(math.sqrt(size)) + assert self.box_size == int(self.box_size), 'Invalid size; value must be a perfect square' + + # The range of possible values for a square. + self.possible_values = range(1, self.size + 1) + + # Make the grid. + super(Board, self).__init__([(Board.xy_key(x, y), list(self.possible_values)) + for x in range(self.size) + for y in range(self.size)]) + for square in self: + initial_value = kwargs.get(Board.xy_kwargs_key(*square)) + if initial_value is None: + continue + if initial_value not in self.possible_values: + raise ValueError('Invalid initial value for square ({}, {}): {}'.format(x, y, initial_value)) + LOG.debug('Setting initial value of {} to {}'.format(square, initial_value)) + self.assign(square, [initial_value]) + + @classmethod + def xy_key(self, x, y): + '''Given {x} and {y}, generate a key to refer to the square at coordinate (x, y) in the grid.''' + return (int(x), int(y)) + + @classmethod + def xy_kwargs_key(self, x, y): + ''' + Given {x} and {y}, generate a key to refer to the square in the __init__ kwargs at coordinate (x, y) in the + grid. + ''' + return 'x{}y{}'.format(x, y) + + @property + def solved(self): + ''' + Determines if the board has been solved. First, determine if all squares have no more than one value (i.e. they + have had values assigned to them). If not, return False. If so, check each unit (rows, columns, and boxes) to + make sure that each has one and only one of each value in the range of possible values for a unit. If not, + return False; otherwise, return True. + ''' + if not all(len(s) == 1 for s in self.values()): + return False + + def validate_unit(unit): + ''' + Validate {unit} by ensuring it has exactly 1 of each value in the range of possible values. + ''' + necessary_values = list(self.possible_values) + for square, values in unit.items(): + v = values[0] + if v in necessary_values: + necessary_values.remove(v) + else: + return False + if len(necessary_values) != 0: + return False + return True + + return ( all(validate_unit(self.row(r)) for r in range(self.size)) + and all(validate_unit(self.col(c)) for c in range(self.size)) + and all(validate_unit(self.box(x, y)) + for x in range(0, self.size, self.box_size) + for y in range(0, self.size, self.box_size))) + + def row(self, idx): + ''' + Return a dict of all squares in the {idx}'th row. + ''' + assert idx >= 0 and idx < self.size, 'Invalid row index; value must be >= 0 and < {}'.format(self.size) + # key[1] is Y coordinate in the grid. + return {k: v for k, v in self.items() if k[1] == idx} + + def col(self, idx): + ''' + Return a dict of all squares in the {idx}'th column. + ''' + assert idx >= 0 and idx < self.size, 'Invalid column index; value must be >= 0 and < {}'.format(self.size) + # key[0] is X coordinate in the grid. + return {k: v for k, v in self.items() if k[0] == idx} + + def box(self, x, y): + ''' + Given a square at coordinates ({x}, {y}), return a dictionary containing the squares that make up the box that + contains the point. + ''' + bx = int(x / self.box_size) * self.box_size + by = int(y / self.box_size) * self.box_size + bx_range = range(bx, bx + self.box_size) + by_range = range(by, by + self.box_size) + return {k: v for k, v in self.items() if k[0] in bx_range and k[1] in by_range} + + def peers(self, x, y): + ''' + Generate and return a list of peers for the square at coordinates ({x}, {y}). Peers are defined as all the + squares in the same row, column, and box as the given square. + ''' + # Generate a dictionary of all the squares in the row, column, and box containing the given square. + peers = dict(list(self.row(y).items()) + list(self.col(x).items()) + list(self.box(x, y).items())) + # Remove the given square. + del peers[Board.xy_key(x, y)] + return peers + + def clear(self, squares=None): + ''' + Clear the board. Resets each square's possible value list to the full range of possible values for this board. + ''' + for square in (self if squares is None else squares): + self.assign(square, list(self.possible_values)) + + def solve(self): + return self.search() + + def search(self): + ''' + Search for a solution, depth-first. Return the solved Board as a new instance of this class. + ''' + if self.solved: + return self + + # Chose the square with the fewest possible values. + _, smallest = min((len(self[sq]), sq) for sq in self if len(self[sq]) > 1) + # Deepcopy the board. + trials = [] + for v in self[smallest]: + trial_board = copy.deepcopy(self) + if trial_board.assign(smallest, [v]): + trials.append(trial_board) + trial_board.search() + else: + trials.append(None) + for t in trials: + if t is not None: + return t + return False + + + def assign(self, square, value): + ''' + Assign {value} to {square}. {value} is expected to be an iterable (a list). {key} should be a valid (x, y) + coordinate pair for referencing a square on the board. + ''' + LOG.debug('Assigning values {} to square {}.'.format(value, square)) + removed_values = set(self[square]) - set(value) + for v in removed_values: + if not self.eliminate(square, v): + return False + return True + + def eliminate(self, square, value): + ''' + Eliminate {value} from {square}, propagating changes to the squares peers as necessary. This process involves + two logical rules of Sudoku. First, if a square is reduced to a single possible value, assign that value to the + square and remove the value from the possible value lists of its peers. Second, if a unit has only one square + that can hold a value, put the value in that square and propagate that change to its peers. + ''' + if value not in self[square]: + LOG.debug('Value {} not in square {}; skipping'.format(value, square)) + return True + + # Update peer value list. + super(Board, self).__setitem__(square, [v for v in self[square] if v != value]) + LOG.debug('Eliminating {} from square {}'.format(value, square)) + + # (1) If a square is reduced to one value, eliminate that value from its peers. + if len(self[square]) == 0: + # Whoops. Removed the last value... We have a contradiction now. + LOG.error('Removed last value from square {}'.format(square)) + return False + elif len(self[square]) == 1: + # One value left in this square. Propagate changes to its peers. + LOG.debug('One value left in square {}; eliminating {} from its peers'.format(square, self[square][0])) + for peer in self.peers(*square): + if not self.eliminate(peer, self[square][0]): + return False + + # (2) If a unit has only one square for a value, put it there. + for unit in (self.row(square[1]), self.col(square[0]), self.box(*square)): + places = [sq for sq in unit if value in unit[sq]] + if len(places) == 0: + LOG.error('No place for value {} to go in unit {}'.format(value, unit)) + return False + elif len(places) == 1: + LOG.debug('One place for value {} to be in unit {}; setting'.format(value, unit)) + self.assign(places[0], [value]) + + return True + + def __delitem__(self, key): + # Don't allow deleting keys from self. + pass + + def __str__(self): + lines = [] + box_lines = [] + square_size = len(str(self.size)) + for y in range(self.size): + row_squares = [] + box_squares = [] + for x in range(self.size): + square = self.get(Board.xy_key(x, y)) + if len(square) == 1: + box_squares.append(str(square[0]).center(square_size)) + else: + box_squares.append('.'.center(square_size)) + if len(box_squares) == self.box_size: + row_squares.append(' '.join(box_squares)) + box_squares = [] + # Print a divider between boxes. + box_lines.append(' | '.join(row_squares)) + if len(box_lines) == self.box_size: + lines.append('\n'.join(box_lines)) + box_lines = [] + if y < self.size - 1: + # Don't print a divider on the last line. + box_dividers = ['-' * ((square_size + 1) * self.box_size - 1) for box in range(self.box_size)] + lines.append('\n{}\n'.format('-+-'.join(box_dividers))) + return ''.join(lines) diff --git a/tests.py b/tests.py new file mode 100644 index 0000000..32dabd1 --- /dev/null +++ b/tests.py @@ -0,0 +1,128 @@ +#!/usr/bin/env python3 +# Eryn Wells + +''' +Tests for sudoku. +''' + +import nose +import sudoku +import unittest + + +def test_9x9_dimensions(): + ''' + Test dimenions of a 9x9 Sudoku board. + ''' + b = sudoku.Board() + assert len(b.keys()) == 81 + assert b.size == 9 + assert b.box_size == 3 + for square, values in b.items(): + assert len(values) == 9 + + +def test_9x9_units(): + ''' + Test units of a 9x9 Sudoku board. + ''' + b = sudoku.Board() + for r in range(b.size): + row = b.row(r) + assert len(row) == 9 + for sq in row: + assert sq[1] == r + + for c in range(b.size): + col = b.col(c) + assert len(col) == 9 + for sq in col: + assert sq[0] == c + + for x in range(0, b.size, b.box_size): + for y in range(0, b.size, b.box_size): + box = b.box(x, y) + assert len(box) == 9 + # TODO: Finish this test + +def test_9x9_row(): + ''' + A few tests on rows of a 9x9 Sudoku board. + ''' + b = sudoku.Board() + row = b.row(1) + expected_keys = ((x, 1) for x in range(b.size)) + for ekey in expected_keys: + assert ekey in row + # No negative numbers + assert (-1, 1) not in row + # Only squares with the right y-coordinate + assert (0, 0) not in row + # No keys above the size of the board + assert (b.size, 1) not in row + + +def test_9x9_col(): + ''' + A few tests on rows of a 9x9 Sudoku board. + ''' + b = sudoku.Board() + col = b.col(3) + expected_keys = ((3, y) for y in range(b.size)) + for ekey in expected_keys: + assert ekey in col + # No negative numbers + assert (3, -1) not in col + # Only squares with the right x-coordinate + assert (0, 0) not in col + # No keys above the size of the board + assert (3, b.size) not in col + + +def test_9x9_box(): + ''' + A few tests on boxes of a 9x9 Sudoku board. + ''' + b = sudoku.Board() + assert True + + +def test_9x9_peers(): + ''' + Test peers. + ''' + b = sudoku.Board() + peers = b.peers(3, 3) + expected_peers = set( [(x, 3) for x in range(b.size)] + + [(3, y) for y in range(b.size)] + + [(3, 3), (3, 4), (3, 5), (4, 3), (4, 4), (4, 5), (5, 3), (5, 4), (5, 5)]) + expected_peers.remove((3, 3)) + for epeer in expected_peers: + assert epeer in peers, '{} not in peers of (3, 3)'.format(epeer) + + +def test_9x9_str(): + ''' + Test string generation/printing. + ''' + b = sudoku.Board() + expected_str = '\n'.join(['. . . | . . . | . . .', + '. . . | . . . | . . .', + '. . . | . . . | . . .', + '------+-------+------', + '. . . | . . . | . . .', + '. . . | . . . | . . .', + '. . . | . . . | . . .', + '------+-------+------', + '. . . | . . . | . . .', + '. . . | . . . | . . .', + '. . . | . . . | . . .']) + assert str(b) == expected_str + + +def main(): + nose.main() + + +if __name__ == '__main__': + main()