110 lines
3.3 KiB
Python
110 lines
3.3 KiB
Python
#!/usr/bin/env python3
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# Copyright 2010-2025 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# [START program]
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"""OR-Tools solution to the N-queens problem."""
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# [START import]
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import sys
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import time
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from ortools.sat.python import cp_model
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# [END import]
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# [START solution_printer]
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class NQueenSolutionPrinter(cp_model.CpSolverSolutionCallback):
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"""Print intermediate solutions."""
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def __init__(self, queens: list[cp_model.IntVar]):
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cp_model.CpSolverSolutionCallback.__init__(self)
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self.__queens = queens
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self.__solution_count = 0
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self.__start_time = time.time()
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@property
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def solution_count(self) -> int:
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return self.__solution_count
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def on_solution_callback(self):
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current_time = time.time()
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print(
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f"Solution {self.__solution_count}, "
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f"time = {current_time - self.__start_time} s"
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)
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self.__solution_count += 1
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all_queens = range(len(self.__queens))
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for i in all_queens:
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for j in all_queens:
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if self.value(self.__queens[j]) == i:
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# There is a queen in column j, row i.
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print("Q", end=" ")
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else:
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print("_", end=" ")
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print()
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print()
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# [END solution_printer]
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def main(board_size: int) -> None:
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# Creates the solver.
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# [START model]
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model = cp_model.CpModel()
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# [END model]
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# Creates the variables.
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# [START variables]
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# There are `board_size` number of variables, one for a queen in each column
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# of the board. The value of each variable is the row that the queen is in.
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queens = [model.new_int_var(0, board_size - 1, f"x_{i}") for i in range(board_size)]
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# [END variables]
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# Creates the constraints.
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# [START constraints]
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# All rows must be different.
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model.add_all_different(queens)
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# No two queens can be on the same diagonal.
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model.add_all_different(queens[i] + i for i in range(board_size))
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model.add_all_different(queens[i] - i for i in range(board_size))
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# [END constraints]
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# Solve the model.
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# [START solve]
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solver = cp_model.CpSolver()
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solution_printer = NQueenSolutionPrinter(queens)
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solver.parameters.enumerate_all_solutions = True
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solver.solve(model, solution_printer)
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# [END solve]
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# Statistics.
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# [START statistics]
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print("\nStatistics")
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print(f" conflicts : {solver.num_conflicts}")
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print(f" branches : {solver.num_branches}")
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print(f" wall time : {solver.wall_time} s")
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print(f" solutions found: {solution_printer.solution_count}")
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# [END statistics]
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if __name__ == "__main__":
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# By default, solve the 8x8 problem.
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size = 8
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if len(sys.argv) > 1:
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size = int(sys.argv[1])
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main(size)
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# [END program]
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