--- /dev/null
+#!/usr/bin/env python
+
+import numpy
+
+
+class Sudoku (object):
+ r"""
+ >>> puzzle = '\n'.join([
+ ... '5 3 - - 7 - - - -',
+ ... '6 - - 1 9 5 - - -',
+ ... '- 9 8 - - - - 6 -',
+ ... '',
+ ... '8 - - - 6 - - - 3',
+ ... '4 - - 8 - 3 - - 1',
+ ... '7 - - - 2 - - - 6',
+ ... '',
+ ... '- 6 - - - - 2 8 -',
+ ... '- - - 4 1 9 - - 5',
+ ... '- - - - 8 - - 7 9',
+ ... ])
+ >>> s = Sudoku()
+ >>> s.load(puzzle)
+ >>> s._num_solved()
+ 30
+ >>> s.solve()
+ >>> print s.status
+ solved in 408 steps
+ >>> print s.dump()
+ 5 3 4 6 7 8 9 1 2
+ 6 7 2 1 9 5 3 4 8
+ 1 9 8 3 4 2 5 6 7
+ <BLANKLINE>
+ 8 5 9 7 6 1 4 2 3
+ 4 2 6 8 5 3 7 9 1
+ 7 1 3 9 2 4 8 5 6
+ <BLANKLINE>
+ 9 6 1 5 3 7 2 8 4
+ 2 8 7 4 1 9 6 3 5
+ 3 4 5 2 8 6 1 7 9
+ >>> s._num_solved()
+ 81
+
+ >>> s._row(0)
+ array([5, 3, 4, 6, 7, 8, 9, 1, 2])
+ >>> s._col(0)
+ array([5, 6, 1, 8, 4, 7, 9, 2, 3])
+ >>> s._cell(0,0)
+ array([[5, 3, 4],
+ [6, 7, 2],
+ [1, 9, 8]])
+ """
+ def __init__(self):
+ self._puzzle = numpy.zeros((9,9), dtype=numpy.int)
+ self._empty = 0
+ self._external_empty = '-'
+ self.status = None
+
+ def load(self, text):
+ row = 0
+ for line in text.splitlines():
+ if len(line) == 0 or line.startswith('#'):
+ continue
+ assert row < 9, row
+ for col,value in enumerate(line.split()):
+ assert col < 9, col
+ self._puzzle[row,col] = self._convert_to_internal_value(value)
+ row += 1
+ self.status = 'loaded puzzle'
+
+ def _convert_to_internal_value(self, value):
+ """
+ >>> s = Sudoku()
+ >>> s._convert_to_internal_value(s._external_empty)
+ 0
+ >>> s._convert_to_internal_value('0')
+ Traceback (most recent call last):
+ ...
+ AssertionError: 0
+ >>> s._convert_to_internal_value('1')
+ 1
+ >>> s._convert_to_internal_value('9')
+ 9
+ >>> s._convert_to_internal_value('10')
+ Traceback (most recent call last):
+ ...
+ AssertionError: 10
+ """
+ if value == self._external_empty:
+ value = self._empty
+ else:
+ value = int(value)
+ assert value >= 1 and value <= 9, value
+ return value
+
+ def dump(self):
+ lines = []
+ for row in range(9):
+ if row in [3, 6]:
+ lines.append('') # blank rows between cells
+ line = []
+ for col in range(9):
+ if col in [3, 6]:
+ line.append(' ') # blank columns between cells
+ line.append(self._convert_to_external_value(
+ self._puzzle[row,col]))
+ lines.append(' '.join(line))
+ return '\n'.join(lines)
+
+ def _convert_to_external_value(self, value):
+ """
+ >>> s = Sudoku()
+ >>> s._convert_to_external_value(s._empty)
+ '-'
+ >>> s._convert_to_external_value(1)
+ '1'
+ >>> s._convert_to_external_value(9)
+ '9'
+ """
+ if value == self._empty:
+ value = self._external_empty
+ else:
+ assert value >= 1 and value <= 9, value
+ value = str(value)
+ return value
+
+ def _row(self, row):
+ return self._puzzle[row,:]
+
+ def _col(self, col):
+ return self._puzzle[:,col]
+
+ def _cell(self, cell_row, cell_col):
+ ri = cell_row * 3
+ rf = ri + 3
+ ci = cell_col * 3
+ cf = ci + 3
+ return self._puzzle[ri:rf,ci:cf]
+
+ def _nonempty(self, values):
+ return [x for x in values if x != self._empty]
+
+ def _is_valid(self):
+ r"""
+ >>> puzzle = '\n'.join([
+ ... '5 3 - - 7 - - - -',
+ ... '6 - - 1 9 5 - - -',
+ ... '- 9 8 - - - - 6 -',
+ ... '',
+ ... '8 - - - 6 - - - 3',
+ ... '4 - - 8 - 3 - - 1',
+ ... '7 - - - 2 - - - 6',
+ ... '',
+ ... '- 6 - - - - 2 8 -',
+ ... '- - - 4 1 9 - - 5',
+ ... '- - - - 8 - - 7 9',
+ ... ])
+ >>> s = Sudoku()
+ >>> s.load(puzzle)
+ >>> s._is_valid()
+ True
+
+ Test an invalid row.
+
+ >>> s._puzzle[0,3] = 5
+ >>> s._is_valid_row(0)
+ False
+ >>> s._is_valid()
+ False
+ >>> s._puzzle[0,3] = s._empty
+
+ Test an invalid column.
+
+ >>> s._puzzle[8,0] = 5
+ >>> s._is_valid_col(0)
+ False
+ >>> s._is_valid()
+ False
+ >>> s._puzzle[8,0] = s._empty
+
+ Test and invalid cell.
+
+ >>> s._puzzle[2,0] = 3
+ >>> s._is_valid_cell(0, 0)
+ False
+ >>> s._is_valid()
+ False
+ >>> s._puzzle[2,0] = s._empty
+ """
+ for row in range(9):
+ if not self._is_valid_row(row):
+ return False
+ for col in range(9):
+ if not self._is_valid_col(col):
+ return False
+ for cell_row in range(3):
+ for cell_col in range(3):
+ if not self._is_valid_cell(cell_row, cell_col):
+ return False
+ return True
+
+ def _is_valid_row(self, row):
+ values = self._nonempty(self._row(row))
+ return len(values) == len(set(values))
+
+ def _is_valid_col(self, col):
+ values = self._nonempty(self._col(col))
+ return len(values) == len(set(values))
+
+ def _is_valid_cell(self, cell_row, cell_col):
+ values = self._nonempty(self._cell(cell_row, cell_col).flatten())
+ return len(values) == len(set(values))
+
+ def _num_solved(self):
+ return len(self._nonempty(self._puzzle.flatten()))
+
+ def solve(self):
+ trials = numpy.zeros((9,9,9), dtype=numpy.int)
+ for row in range(9):
+ for col in range(9):
+ if self._puzzle[row,col] == self._empty:
+ trials[row,col,:] = range(1,10)
+ else:
+ x = self._puzzle[row,col]
+ trials[row,col,x-1] = x
+
+ actions = 0
+ while True:
+ start_actions = 0
+ for row in range(9):
+ for col in range(9):
+ if self._puzzle[row][col] == self._empty:
+ for x in self._nonempty(trials[row,col,:]):
+ self._puzzle[row,col] = x
+ if not self._is_valid():
+ actions += 1
+ trials[row,col,x-1] = self._empty
+ self._puzzle[row,col] = self._empty
+ if len(self._nonempty(trials[row,col,:])) == 1:
+ self._puzzle[row][col] = (
+ self._nonempty(trials[row,col,:])[0])
+ if self._num_solved() == 81:
+ self.status = 'solved in %d steps' % actions
+ return # puzzle solved
+ if actions == start_actions:
+ self.status = 'aborted after %d steps' % actions
+ break # puzzle too hard to solve
+
+def test():
+ import doctest
+ doctest.testmod()
+
+if __name__ == '__main__':
+ import sys
+
+ if len(sys.argv) > 1:
+ assert sys.argv[1] == '--test', sys.argv
+ test()
+ sys.exit(0)
+
+ s = Sudoku()
+ puzzle = sys.stdin.read()
+ s.load(puzzle)
+ s.solve()
+ print >> sys.stderr, s.status
+ print s.dump()
projects / parallel_computing.git / commitdiff