85 lines
2.6 KiB
Python
Executable File
85 lines
2.6 KiB
Python
Executable File
#!/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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from ortools.constraint_solver import pywrapcp
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# [END import]
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def main(board_size):
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# Creates the solver.
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# [START solver]
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solver = pywrapcp.Solver("n-queens")
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# [END solver]
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# Creates the variables.
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# [START variables]
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# The array index is the column, and the value is the row.
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queens = [solver.IntVar(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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solver.Add(solver.AllDifferent(queens))
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# No two queens can be on the same diagonal.
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solver.Add(solver.AllDifferent([queens[i] + i for i in range(board_size)]))
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solver.Add(solver.AllDifferent([queens[i] - i for i in range(board_size)]))
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# [END constraints]
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# [START db]
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db = solver.Phase(queens, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)
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# [END db]
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# [START solve]
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# Iterates through the solutions, displaying each.
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num_solutions = 0
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solver.NewSearch(db)
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while solver.NextSolution():
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# Displays the solution just computed.
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for i in range(board_size):
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for j in range(board_size):
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if queens[j].Value() == 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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num_solutions += 1
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solver.EndSearch()
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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" failures: {solver.Failures()}")
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print(f" branches: {solver.Branches()}")
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print(f" wall time: {solver.WallTime()} ms")
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print(f" Solutions found: {num_solutions}")
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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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