def queens_problem(n):
board = make_board(n)
return conjoin(
flatten(exactly_one(row) for row in board),
flatten(at_most_one(col) for col in transpose(board)),
flatten(at_most_one(diag) for diag in rising_diagonals(board)),
flatten(at_most_one(diag) for diag in falling_diagonals(board)))
def queens_problem(n):
board = make_board(n)
return conjoin(
flatten(exactly_one(row) for row in board),
flatten(at_most_one(col) for col in transpose(board)),
flatten(at_most_one(diag) for diag in rising_diagonals(board)),
flatten(at_most_one(diag) for diag in falling_diagonals(board)))
def make_sudoku_grid(n):
problem = []
def add_permutation(slots):
for variables in transpose(slots):
problem.extend(at_most_one(variables))
make_variable = count(1).next
def make_slot():
slot = [make_variable() for i in range(n*n)]
problem.extend(exactly_one(slot))
return slot
def make_block():
block = [[make_slot() for c in range(n)] for r in range(n)]
add_permutation(flatten(block))
return block
superblock = [[make_block() for c in range(n)] for r in range(n)]
rows = flatten([map(flatten, transpose(row)) for row in superblock])
for row in rows:
add_permutation(row)
for column in transpose(rows):
add_permutation(column)
return rows, problem
def make_sudoku_grid(n):
problem = []
def add_permutation(slots):
for variables in transpose(slots):
problem.extend(at_most_one(variables))
make_variable = count(1).next
def make_slot():
slot = [make_variable() for i in range(n * n)]
problem.extend(exactly_one(slot))
return slot
def make_block():
block = [[make_slot() for c in range(n)] for r in range(n)]
add_permutation(flatten(block))
return block
superblock = [[make_block() for c in range(n)] for r in range(n)]
rows = flatten([map(flatten, transpose(row)) for row in superblock])
for row in rows:
add_permutation(row)
for column in transpose(rows):
add_permutation(column)
return rows, problem
def make_block():
block = [[make_slot() for c in range(n)] for r in range(n)]
add_permutation(flatten(block))
return block
def make_block():
block = [[make_slot() for c in range(n)] for r in range(n)]
add_permutation(flatten(block))
return block
