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#!/usr/bin/env python
# A sudoku solver by Peter Norvig
import sys, os, time
def cross(A, B):
return [a+b for a in A for b in B]
digits = '123456789'
rows = 'ABCDEFGHI'
cols = digits
squares = cross(rows, cols)
column_squares = [cross(rows, c) for c in cols]
row_squares = [cross(r, cols) for r in rows]
box_squares = [cross(rs, cs)
for rs in ('ABC','DEF','GHI')
for cs in ('123','456','789')]
unitlist = (column_squares +
row_squares +
units = dict((s, [u for u in unitlist if s in u])
for s in squares)
peers = dict((s, set(s2 for u in units[s] for s2 in u if s2 != s))
for s in squares)
class Puzzle(dict):
"A dict with a counter"
def __init__(self, tuples, count=0):
self.count = count
super(Puzzle, self).__init__(tuples)
def copy(self):
return Puzzle(self.items(), self.count)
def has_failed(puzzle):
return not puzzle
def failed(puzzle):
"Return a failed puzzle"
return Puzzle([], puzzle.count)
def parse_grid(grid):
"""Convert grid to a puzzle of possible values, {square: digits}, or
return a failed puzzle if a contradiction is detected."""
## To start, every square can be any digit; then assign values from the grid.
puzzle = Puzzle((square, digits) for square in squares)
for square, digit in grid_puzzle(grid).items():
if digit in digits and not assign(puzzle, square, digit):
return failed(puzzle) ## (Fail if we can't assign d to square s.)
return puzzle
def grid_puzzle(grid):
"Convert grid into a dict of {square: char} with '0' or '.' for empties."
chars = [c for c in grid if c in digits or c in '0.']
assert len(chars) == 81
return Puzzle(zip(squares, chars))
def assign(puzzle, square, digit):
"""Eliminate all the other values (except digit) from puzzle[square]
and propagate.
Return puzzle, except return failed if a contradiction is detected."""
other_values = puzzle[square].replace(digit, '')
if all(eliminate(puzzle, square, digit2) for digit2 in other_values):
return puzzle
return failed(puzzle)
def eliminate(puzzle, square, digit):
"""Eliminate digit from puzzle[square];
propagate when values or places <= 2.
Return puzzle, except return failed if a contradiction is detected."""
if digit not in puzzle[square]:
return puzzle ## Already eliminated
puzzle[square] = puzzle[square].replace(digit, '')
if len(puzzle[square]) == 0:
return failed(puzzle) ## Contradiction: removed last value
puzzle.count += 1
puzzle = peer_eliminate(puzzle, square)
if has_failed(puzzle):
return failed(puzzle)
puzzle = assign_unique_place(puzzle, square, digit)
if has_failed(puzzle):
return failed(puzzle)
return puzzle
def peer_eliminate(puzzle, square):
## (1) If a square is reduced to one value, then eliminate it from the peers.
if len(puzzle[square]) == 1:
digit = puzzle[square]
if not all(eliminate(puzzle, s2, digit) for s2 in peers[square]):
return failed(puzzle)
return puzzle
def assign_unique_place(puzzle, square, digit):
## (2) If a unit is reduced to only one place for a digit, then put it there
for u in units[square]:
digit_places = [square2 for square2 in u if digit in puzzle[square2]]
if len(digit_places) == 0:
return failed(puzzle) ## Contradiction: no place for this value
elif len(digit_places) == 1:
# digit can only be in one place in unit; assign it there
if not assign(puzzle, digit_places[0], digit):
return failed(puzzle)
return puzzle
def solve(grid):
return search(parse_grid(grid))
def search(puzzle):
"Using depth-first search and propagation, try all possible values."
if has_failed(puzzle):
return failed(puzzle) ## Failed earlier
if is_solved(puzzle):
return puzzle
## Choose the unfilled square s with the fewest possibilities
possibilities, square = min((len(puzzle[s]), s)
for s in squares if len(puzzle[s]) > 1)
return first_valid_result(puzzle, square, puzzle[square])
def first_valid_result(puzzle, square, values):
if len(values) == 0:
return failed(puzzle)
new_puzzle = search(assign(puzzle.copy(), square, values[0]))
if new_puzzle:
return new_puzzle
diff = new_puzzle.count - puzzle.count
puzzle.count += diff
return first_valid_result(puzzle, square, values[1:])
def solve_all(grids, name=''):
"""Attempt to solve a sequence of grids. Report results."""
def time_solve(grid):
start = time.clock()
puzzle = solve(grid)
t = time.clock()-start
return (t, is_solved(puzzle), puzzle)
times, results, puzzles = zip(*[time_solve(grid) for grid in grids])
eliminations = [puzzle.count for puzzle in puzzles]
N = len(grids)
if N >= 1:
hz = N/sum(times)
print "Solved %d of %d puzzles from %s in %.6f secs (%.2f Hz)" % (
sum(results), N, name, sum(times), hz)
[total, avg, median, max_elims, min_elims] = stats(eliminations)
print " (%d total eliminations, avg %.2f, median %d, max %d, min %d)." % (
total, avg, median, max_elims, min_elims)
return puzzles
def stats(lst):
total = sum(lst)
length = len(lst)
avg = total/length
med_index = int(round(length/2))
med = sorted(lst)[med_index]
return [total, avg, med, max(lst), min(lst)]
def is_solved(puzzle):
"A puzzle is solved if each unit is a permutation of the digits 1 to 9."
def unitsolved(unit): return set(puzzle[s] for s in unit) == set(digits)
return (not has_failed(puzzle)) and all(unitsolved(unit) for unit in unitlist)
def to_string(puzzle):
return ''.join([value_or_dot(puzzle[s]) for s in squares])
def value_or_dot(value):
return (value if (len(value) == 1) else '.')
def from_file(filename, sep='\n'):
"Parse a file into a list of strings, separated by sep."
return file(filename).read().strip().split(sep)
def to_file(outfile, solutions):
grids = [to_string(s)+'\n' for s in solutions]
fp = file(outfile, 'w')
def solve_file(filename, sep='\n'):
solutions = solve_all(from_file(filename, sep), filename)
outfile = os.path.splitext(filename)[0] + '.out'
to_file(outfile, solutions)
def solve_files(*filenames):
[solve_file(filename) for filename in filenames]
def test():
"A set of tests that must pass."
assert len(squares) == 81
assert len(unitlist) == 27
assert all(len(units[s]) == 3 for s in squares)
assert all(len(peers[s]) == 20 for s in squares)
assert units['C2'] == [['A2', 'B2', 'C2', 'D2', 'E2', 'F2', 'G2', 'H2', 'I2'],
['C1', 'C2', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C9'],
['A1', 'A2', 'A3', 'B1', 'B2', 'B3', 'C1', 'C2', 'C3']]
assert peers['C2'] == set(['A2', 'B2', 'D2', 'E2', 'F2', 'G2', 'H2', 'I2',
'C1', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C9',
'A1', 'A3', 'B1', 'B3'])
[total, avg, med, max, min] = stats([6, 7, 2])
assert total == 15
assert avg == 5
assert med == 6
assert max == 7
assert min == 2
print 'All tests pass.'
if __name__ == '__main__':
if len(sys.argv) > 1:
solve_files("easy50.txt", "top95.txt", "hardest.txt")
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