cp_is_fun_sat.py

#!/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.

# [START program]
"""Cryptarithmetic puzzle.

First attempt to solve equation CP + IS + FUN = TRUE
where each letter represents a unique digit.

This problem has 72 different solutions in base 10.
"""
# [START import]
from ortools.sat.python import cp_model
# [END import]


# [START solution_printer]
class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):
    """Print intermediate solutions."""

    def __init__(self, variables: list[cp_model.IntVar]):
        cp_model.CpSolverSolutionCallback.__init__(self)
        self.__variables = variables
        self.__solution_count = 0

    def on_solution_callback(self) -> None:
        self.__solution_count += 1
        for v in self.__variables:
            print(f"{v}={self.value(v)}", end=" ")
        print()

    @property
    def solution_count(self) -> int:
        return self.__solution_count
        # [END solution_printer]


def main() -> None:
    """solve the CP+IS+FUN==TRUE cryptarithm."""
    # Constraint programming engine
    # [START model]
    model = cp_model.CpModel()
    # [END model]

    # [START variables]
    base = 10

    c = model.new_int_var(1, base - 1, "C")
    p = model.new_int_var(0, base - 1, "P")
    i = model.new_int_var(1, base - 1, "I")
    s = model.new_int_var(0, base - 1, "S")
    f = model.new_int_var(1, base - 1, "F")
    u = model.new_int_var(0, base - 1, "U")
    n = model.new_int_var(0, base - 1, "N")
    t = model.new_int_var(1, base - 1, "T")
    r = model.new_int_var(0, base - 1, "R")
    e = model.new_int_var(0, base - 1, "E")

    # We need to group variables in a list to use the constraint AllDifferent.
    letters = [c, p, i, s, f, u, n, t, r, e]

    # Verify that we have enough digits.
    assert base >= len(letters)
    # [END variables]

    # Define constraints.
    # [START constraints]
    model.add_all_different(letters)

    # CP + IS + FUN = TRUE
    model.add(
        c * base + p + i * base + s + f * base * base + u * base + n
        == t * base * base * base + r * base * base + u * base + e
    )
    # [END constraints]

    # Creates a solver and solves the model.
    # [START solve]
    solver = cp_model.CpSolver()
    solution_printer = VarArraySolutionPrinter(letters)
    # Enumerate all solutions.
    solver.parameters.enumerate_all_solutions = True
    # Solve.
    status = solver.solve(model, solution_printer)
    # [END solve]

    # Statistics.
    # [START statistics]
    print("\nStatistics")
    print(f"  status   : {solver.status_name(status)}")
    print(f"  conflicts: {solver.num_conflicts}")
    print(f"  branches : {solver.num_branches}")
    print(f"  wall time: {solver.wall_time} s")
    print(f"  sol found: {solution_printer.solution_count}")
    # [END statistics]


if __name__ == "__main__":
    main()
# [END program]