112 lines
3.3 KiB
Python
112 lines
3.3 KiB
Python
#!/usr/bin/env python3
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# Copyright 2010-2024 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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"""Cryptarithmetic puzzle.
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First attempt to solve equation CP + IS + FUN = TRUE
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where each letter represents a unique digit.
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This problem has 72 different solutions in base 10.
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"""
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# [START import]
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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 VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):
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"""Print intermediate solutions."""
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def __init__(self, variables: list[cp_model.IntVar]):
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cp_model.CpSolverSolutionCallback.__init__(self)
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self.__variables = variables
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self.__solution_count = 0
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def on_solution_callback(self) -> None:
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self.__solution_count += 1
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for v in self.__variables:
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print(f"{v}={self.value(v)}", end=" ")
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print()
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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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# [END solution_printer]
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def main() -> None:
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"""solve the CP+IS+FUN==TRUE cryptarithm."""
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# Constraint programming engine
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# [START model]
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model = cp_model.CpModel()
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# [END model]
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# [START variables]
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base = 10
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c = model.new_int_var(1, base - 1, "C")
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p = model.new_int_var(0, base - 1, "P")
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i = model.new_int_var(1, base - 1, "I")
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s = model.new_int_var(0, base - 1, "S")
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f = model.new_int_var(1, base - 1, "F")
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u = model.new_int_var(0, base - 1, "U")
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n = model.new_int_var(0, base - 1, "N")
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t = model.new_int_var(1, base - 1, "T")
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r = model.new_int_var(0, base - 1, "R")
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e = model.new_int_var(0, base - 1, "E")
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# We need to group variables in a list to use the constraint AllDifferent.
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letters = [c, p, i, s, f, u, n, t, r, e]
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# Verify that we have enough digits.
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assert base >= len(letters)
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# [END variables]
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# Define constraints.
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# [START constraints]
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model.add_all_different(letters)
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# CP + IS + FUN = TRUE
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model.add(
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c * base + p + i * base + s + f * base * base + u * base + n
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== t * base * base * base + r * base * base + u * base + e
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)
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# [END constraints]
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# Creates a solver and solves the model.
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# [START solve]
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solver = cp_model.CpSolver()
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solution_printer = VarArraySolutionPrinter(letters)
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# Enumerate all solutions.
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solver.parameters.enumerate_all_solutions = True
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# Solve.
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status = 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" status : {solver.status_name(status)}")
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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" sol found: {solution_printer.solution_count}")
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# [END statistics]
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if __name__ == "__main__":
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main()
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# [END program]
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