+from weakref import proxy
+
+symbols = [str(x + 1) for x in range(9)] + [chr(x + 97) for x in xrange(26)]
+
+
+class CellGroup(object):
+ """Represents any group of cells in a grid."""
+
+ ### Accessors
+
+ cells = []
+
+ ### Methods
+ # XXX inherited __init__
+
+ def find_value(self, value):
+ """Returns the cells that can be a specific value."""
+ possible_cells = []
+ for cell in self.cells:
+ if value in cell._values:
+ possible_cells.append(cell)
+
+ if len(possible_cells) == 0:
+ raise Exception # XXX
+
+ return possible_cells
+
+ def resolve_uniques(self):
+ for value in xrange(self._grid._size):
+ # XXX cache values that are taken care of
+ possible_cells = self.find_value(value)
+
+ if len(possible_cells) > 1:
+ # Not unique
+ continue
+
+ target_cell = possible_cells[0]
+ if target_cell.solved:
+ # Already seen this
+ # XXX this is what cache is for
+ continue
+
+ # Only cell in the group that can be value
+ target_cell.set(value)
+
+
+class Box(CellGroup):
+ def _get_box_row(self):
+ return self._pos // self._grid._box_width
+ box_row = property(_get_box_row)
+
+ def _get_box_column(self):
+ return self._pos % self._grid._box_height
+ box_column = property(_get_box_column)
+
+ def _get_cells(self):
+ # XXX generator + docstring
+ cells = []
+ for row in xrange(self._grid._box_height):
+ for col in xrange(self._grid._box_width):
+ cell_row = row + self.box_row * self._grid._box_height
+ cell_col = col + self.box_column * self._grid._box_width
+ cells.append(self._grid.cell(cell_row, cell_col))
+ return cells
+ cells = property(_get_cells)
+
+ def __init__(self, grid, position):
+ self._grid = proxy(grid)
+ self._pos = position
+
+
+class Row(CellGroup):
+ def _get_cells(self):
+ # XXX generator + docstring
+ cells = []
+ for col in xrange(self._grid._size):
+ cells.append(self._grid.cell(self._pos, col))
+ return cells
+ cells = property(_get_cells)
+
+ def __init__(self, grid, position):
+ self._grid = proxy(grid)
+ self._pos = position
+
+
+class Column(CellGroup):
+ def _get_cells(self):
+ # XXX generator + docstring
+ cells = []
+ for row in xrange(self._grid._size):
+ cells.append(self._grid.cell(row, self._pos))
+ return cells
+ cells = property(_get_cells)
+
+ def __init__(self, grid, position):
+ self._grid = proxy(grid)
+ self._pos = position
+
+
+class Cell(object):
+ """Represents a single cell/value within a sudoku grid."""
+
+ ### Accessors
+
+ def _get_solved(self):
+ """True iff this cell has been solved."""
+ return len(self._values) == 1
+ solved = property(_get_solved)
+
+ def _get_value(self):
+ """Returns this cell's value, if it has one known."""
+ if self.solved:
+ return self._values[0]
+ return None
+ value = property(_get_value)
+
+ def _get_row(self):
+ """Returns the Row object associated with this cell."""
+ return self._grid._rows[self._row]
+ row = property(_get_row)
+
+ def _get_column(self):
+ """Returns the Column object associated with this cell."""
+ return self._grid._columns[self._col]
+ column = property(_get_column)
+
+ def _get_box(self):
+ """Returns the Box object associated with this cell."""
+ # Some actual math required here!
+ # Row 0..2 -> box 0..2
+ # Col 0..2 -> box 0, 3, 6 (box col 0)
+ box_row = self._row // self._grid._box_height
+ box_col = self._col // self._grid._box_width
+ box_idx = box_row * self._grid._box_height + box_col
+ return self._grid._boxes[box_idx]
+ box = property(_get_box)
+
+ def __init__(self, grid, row, column):
+ self._grid = proxy(grid)
+ self._row = row
+ self._col = column
+ self._values = range(self._grid.size)
+ self._normalized = False
+
+ def set_naively(self, value):
+ """Sets the value of this cell, WITHOUT eliminating the value from
+ every other cell in its row/column/box.
+ """
+
+ self._values = [value]
+
+ def set(self, value):
+ """Sets the value of this cell and adjusts the grid accordingly."""
+ self.set_naively(value)
+ self._normalized = False
+ self.normalize()
+
+
+
+ def normalize(self):
+ """Checks to see if this cell has only one possible value left. If
+ so, sets that as its value and eliminates it from every related cell.
+ This method is exhaustive; that repeated calls should have no effect.
+ """
+
+ if self._normalized:
+ # Already done
+ return
+
+ # Set this now just in case of infinite looping
+ self._normalized = True
+
+ if not self.solved:
+ # Don't know the value yet
+ return
+
+ # Elimination time
+ for group_type in 'row', 'column', 'box':
+ group = getattr(self, group_type)
+ for cell in group.cells:
+ if cell == self:
+ continue
+ cell.eliminate(self.value)
+
+
+ def eliminate(self, value):
+ """Eliminates the given value as a possibility for this cell."""
+ if value in self._values:
+ self._values.remove(value)
+
+ if len(self._values) == 0:
+ # XXX give me a real exception here
+ raise Exception
+
+ self._normalized = False
+ self.normalize()
+
+
+ def __str__(self):
+ """Stringification for pretty-printing."""
+ if self.value != None:
+ return symbols[self.value]
+
+ return '.'
+
+
+
+
+class Grid(object):
+ """Represents a Sudoku grid."""
+
+ ### Utilities
+
+ def _cellidx(self, row, col):
+ """Hashes a row and column into a flat array index."""
+ return row * self._size + col
+
+ ### Accessors
+
+ def _get_box_height(self):
+ return self._box_height
+ box_height = property(_get_box_height)
+
+ def _get_box_width(self):
+ return self._box_width
+ box_width = property(_get_box_width)
+
+ def _get_size(self):
+ return self._size
+ size = property(_get_size)
+
+ def _get_cell_groups(self):
+ return self._rows + self._columns + self._boxes
+ cell_groups = property(_get_cell_groups)
+
+ ### Methods
+
+ def __init__(self, box_height=3, box_width=None):
+ if not box_width:
+ box_width = box_height
+
+ self._box_height = box_height
+ self._box_width = box_width
+ self._size = box_height * box_width
+
+ self._rows = [Row(self, i) for i in xrange(self._size)]
+ self._columns = [Column(self, i) for i in xrange(self._size)]
+ self._boxes = [Box(self, i) for i in xrange(self._size)]
+
+ self._cells = range(self._size ** 2)
+ for row in xrange(self._size):
+ for col in xrange(self._size):
+ self._cells[self._cellidx(row, col)] \
+ = Cell(self, row, col)
+
+ def from_lists(self, *rows):
+ for row in xrange(self._size):
+ for col in xrange(self._size):
+ value = rows[row][col]
+ if not value:
+ continue
+ self.cell(row, col).set_naively(value - 1)
+
+
+ def cell(self, row, column):
+ return self._cells[self._cellidx(row, column)]
+
+
+ ### Solving
+
+ def check(self):
+ """Returns True iff the grid is solved. Raises an exception if an
+ integrity problem is found, such as a value appearing twice in a row.
+ """
+ # TODO
+ return None
+
+ def solve(self):
+ """Attempts to solve the grid."""
+ # XXX track how many cells are changed and repeat as appropriate
+
+ # Step 0: Normalize cells, i.e. find any that can only be one value
+ self.normalize_cells()
+
+ # Step 1: Find values that can only go in one cell in a group
+ for group in self.cell_groups:
+ group.resolve_uniques()
+
+
+ def normalize_cells(self):
+ """Normalizes every cell in the grid."""
+ for cell in self._cells:
+ cell.normalize()
+
+
+ def __str__(self):
+ """Pretty-printing."""
+ divider = '+'
+ for box in xrange(self._box_height):
+ for col in xrange(self._box_width):
+ divider += '-'
+ divider += '+'
+
+ res = ''
+ for row in xrange(self._size):
+ if row % self._box_height == 0:
+ res += divider
+ res += "\n"
+
+ for col in xrange(self._size):
+ if col % self._box_width == 0:
+ res += '|'
+ res += str(self.cell(row, col))
+
+ res += '|'
+ res += "\n"
+
+ res += divider
+ res += "\n"
+
+ return res
+
+
+
+grid = Grid(3, 3)
+grid.from_lists(
+ [ 0, 0, 0, 6, 9, 0, 0, 0, 0 ],
+ [ 9, 0, 5, 0, 0, 8, 7, 6, 0 ],
+ [ 0, 0, 4, 0, 0, 1, 0, 2, 0 ],
+ [ 6, 0, 0, 0, 5, 0, 0, 0, 3 ],
+ [ 3, 8, 0, 0, 0, 0, 0, 4, 9 ],
+ [ 7, 0, 0, 0, 3, 0, 0, 0, 2 ],
+ [ 0, 7, 0, 9, 0, 0, 3, 0, 0 ],
+ [ 0, 2, 3, 1, 0, 0, 4, 0, 8 ],
+ [ 0, 0, 0, 0, 8, 3, 0, 0, 0 ],
+)
+
+print grid
+
+grid.solve()
+
+print grid
projects / pseudoku.git / commitdiff
