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nqueens_sat.py
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nqueens_sat.py
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#!/usr/bin/env python3
# Copyright 2010-2024 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""CP/SAT model for the N-queens problem."""
import time
from absl import app
from absl import flags
from ortools.sat.python import cp_model
_SIZE = flags.DEFINE_integer("size", 8, "Number of queens.")
class NQueenSolutionPrinter(cp_model.CpSolverSolutionCallback):
"""Print intermediate solutions."""
def __init__(self, queens: list[cp_model.IntVar]):
cp_model.CpSolverSolutionCallback.__init__(self)
self._queens = queens
self._solution_count = 0
self._start_time = time.time()
@property
def solution_count(self) -> int:
return self._solution_count
def on_solution_callback(self) -> None:
current_time = time.time()
print(
f"Solution{self._solution_count}, time ="
f" {current_time - self._start_time} s"
)
self._solution_count += 1
all_queens = range(len(self._queens))
for i in all_queens:
for j in all_queens:
if self.value(self._queens[j]) == i:
# There is a queen in column j, row i.
print("Q", end=" ")
else:
print("_", end=" ")
print()
print()
def main(_):
board_size = _SIZE.value
### Creates the solver.
model = cp_model.CpModel()
### Creates the variables.
# The array index is the column, and the value is the row.
queens = [
model.new_int_var(0, board_size - 1, "x%i" % i) for i in range(board_size)
]
### Creates the constraints.
# All columns must be different because the indices of queens are all
# different, so we just add the all different constraint on the rows.
model.add_all_different(queens)
# No two queens can be on the same diagonal.
diag1 = []
diag2 = []
for i in range(board_size):
q1 = model.new_int_var(0, 2 * board_size, "diag1_%i" % i)
q2 = model.new_int_var(-board_size, board_size, "diag2_%i" % i)
diag1.append(q1)
diag2.append(q2)
model.add(q1 == queens[i] + i)
model.add(q2 == queens[i] - i)
model.add_all_different(diag1)
model.add_all_different(diag2)
### Solve model.
solver = cp_model.CpSolver()
solution_printer = NQueenSolutionPrinter(queens)
# Enumerate all solutions.
solver.parameters.enumerate_all_solutions = True
# solve.
solver.solve(model, solution_printer)
print()
print("Statistics")
print(" - conflicts : %i" % solver.num_conflicts)
print(" - branches : %i" % solver.num_branches)
print(" - wall time : %f s" % solver.wall_time)
print(" - solutions found : %i" % solution_printer.solution_count)
if __name__ == "__main__":
app.run(main)