"""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):
        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_printer]


def main():
    """Solve the CP+IS+FUN==TRUE cryptarithm."""
    # Constraint programming engine
    # [START model]
    model = cp_model.CpModel()
    # [END model]

    # [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]

    # Define constraints.
    # [START 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]

    # 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.StatusName(status)}')
    print(f'  conflicts: {solver.NumConflicts()}')
    print(f'  branches : {solver.NumBranches()}')
    print(f'  wall time: {solver.WallTime()} s')
    print(f'  sol found: {solution_printer.solution_count()}')
    # [END statistics]


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