cp_is_fun_sat.py

#!/usr/bin/env python3
# Copyright 2010-2021 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 program]

from ortools.sat.python import cp_model


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

    def __init__(self, variables):
        cp_model.CpSolverSolutionCallback.__init__(self)
        self.__variables = variables
        self.__solution_count = 0

    def on_solution_callback(self):
        self.__solution_count += 1
        for v in self.__variables:
            print('%s=%i' % (v, self.Value(v)), end=' ')
        print()

    def solution_count(self):
        return self.__solution_count
        # [END solution_printing]


def CPIsFunSat():
    """Solve the CP+IS+FUN==TRUE cryptarithm."""
    # Constraint programming engine
    model = cp_model.CpModel()

    # [START variables]
    base = 10

    c = model.NewIntVar(1, base - 1, 'C')
    p = model.NewIntVar(0, base - 1, 'P')
    i = model.NewIntVar(1, base - 1, 'I')
    s = model.NewIntVar(0, base - 1, 'S')
    f = model.NewIntVar(1, base - 1, 'F')
    u = model.NewIntVar(0, base - 1, 'U')
    n = model.NewIntVar(0, base - 1, 'N')
    t = model.NewIntVar(1, base - 1, 'T')
    r = model.NewIntVar(0, base - 1, 'R')
    e = model.NewIntVar(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]

    # [START constraints]
    # Define constraints.
    model.AddAllDifferent(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]

    # [START solve]
    ### Solve model.
    solver = cp_model.CpSolver()
    solution_printer = VarArraySolutionPrinter(letters)
    status = solver.SearchForAllSolutions(model, solution_printer)
    # [END solve]

    print()
    print('Statistics')
    print('  - status          : %s' % solver.StatusName(status))
    print('  - conflicts       : %i' % solver.NumConflicts())
    print('  - branches        : %i' % solver.NumBranches())
    print('  - wall time       : %f s' % solver.WallTime())
    print('  - solutions found : %i' % solution_printer.solution_count())


if __name__ == '__main__':
    CPIsFunSat()
    # [END probram]