Rompecabezas criptaritméticos

rompecabezas criptométicos es un ejercicio matemático en el que los dígitos de algunos números están representados por letras (o símbolos). Cada letra representa un dígito único. El objetivo es encontrar los dígitos de modo que se verifique una ecuación matemática determinada:

      CP
+     IS
+    FUN
--------
=   TRUE

Una asignación de letras a números arroja la siguiente ecuación:

      23
+     74
+    968
--------
=   1065

Hay otras respuestas a este problema. Te mostraremos cómo encontrar todas las soluciones.

Modelado del problema

Al igual que con cualquier problema de optimización, comenzaremos por identificar variables y restricciones. Las variables son las letras, que pueden asumir cualquier valor de dígito.

Para CP + IS + FUN = TRUE, las restricciones son las siguientes:

• La ecuación: CP + IS + FUN = TRUE.
• Cada una de las diez letras debe ser un dígito diferente.
• C, I, F y T no pueden ser cero (ya que no se escriben ceros a la izquierda en los números).

Puedes resolver problemas criptoaritméticos con el nuevo solucionador CP-SAT, que es más eficiente, o con el solucionador de CP original. Te mostraremos ejemplos usando ambos solucionadores, comenzando por CP-SAT.

Solución CP-SAT

Te mostraremos las variables, las restricciones, la invocación del solucionador y, por último, los programas completos.

Importa las bibliotecas

Con el siguiente código, se importa la biblioteca requerida.

Python

from ortools.sat.python import cp_model

C++

#include <stdlib.h>

#include <cstdint>

#include "ortools/base/logging.h"
#include "ortools/sat/cp_model.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/util/sorted_interval_list.h"

Java

import com.google.ortools.Loader;
import com.google.ortools.sat.CpModel;
import com.google.ortools.sat.CpSolver;
import com.google.ortools.sat.CpSolverSolutionCallback;
import com.google.ortools.sat.IntVar;
import com.google.ortools.sat.LinearExpr;

C#

using System;
using Google.OrTools.Sat;

Declara el modelo

El siguiente código declara el modelo para el problema.

Python

model = cp_model.CpModel()

C++

CpModelBuilder cp_model;

Java

CpModel model = new CpModel();

C#

        CpModel model = new CpModel();

        int kBase = 10;

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

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

        // Define constraints.
        model.AddAllDifferent(letters);

        // CP + IS + FUN = TRUE
        model.Add(c * kBase + p + i * kBase + s + f * kBase * kBase + u * kBase + n ==
                  t * kBase * kBase * kBase + r * kBase * kBase + u * kBase + e);

        // Creates a solver and solves the model.
        CpSolver solver = new CpSolver();
        VarArraySolutionPrinter cb = new VarArraySolutionPrinter(letters);
        // Search for all solutions.
        solver.StringParameters = "enumerate_all_solutions:true";
        // And solve.
        solver.Solve(model, cb);

        Console.WriteLine("Statistics");
        Console.WriteLine($"  conflicts : {solver.NumConflicts()}");
        Console.WriteLine($"  branches  : {solver.NumBranches()}");
        Console.WriteLine($"  wall time : {solver.WallTime()} s");
        Console.WriteLine($"  number of solutions found: {cb.SolutionCount()}");
    }
}

Define las variables

Cuando se usa el solucionador de CP-SAT, existen ciertos métodos de ayuda que es útil definir. Usaremos uno de ellos, NewIntVar, para declarar nuestros dígitos (número entero). Distinguimos entre las letras que pueden ser cero y las que no (C, I, F y T).

Python

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)

C++

const int64_t kBase = 10;

// Define decision variables.
Domain digit(0, kBase - 1);
Domain non_zero_digit(1, kBase - 1);

IntVar c = cp_model.NewIntVar(non_zero_digit).WithName("C");
IntVar p = cp_model.NewIntVar(digit).WithName("P");
IntVar i = cp_model.NewIntVar(non_zero_digit).WithName("I");
IntVar s = cp_model.NewIntVar(digit).WithName("S");
IntVar f = cp_model.NewIntVar(non_zero_digit).WithName("F");
IntVar u = cp_model.NewIntVar(digit).WithName("U");
IntVar n = cp_model.NewIntVar(digit).WithName("N");
IntVar t = cp_model.NewIntVar(non_zero_digit).WithName("T");
IntVar r = cp_model.NewIntVar(digit).WithName("R");
IntVar e = cp_model.NewIntVar(digit).WithName("E");

Java

int base = 10;
IntVar c = model.newIntVar(1, base - 1, "C");
IntVar p = model.newIntVar(0, base - 1, "P");
IntVar i = model.newIntVar(1, base - 1, "I");
IntVar s = model.newIntVar(0, base - 1, "S");
IntVar f = model.newIntVar(1, base - 1, "F");
IntVar u = model.newIntVar(0, base - 1, "U");
IntVar n = model.newIntVar(0, base - 1, "N");
IntVar t = model.newIntVar(1, base - 1, "T");
IntVar r = model.newIntVar(0, base - 1, "R");
IntVar e = model.newIntVar(0, base - 1, "E");

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

C#

        int kBase = 10;

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

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

Define las restricciones

Luego, restricciones. Primero, nos aseguramos de que todas las letras tengan valores diferentes mediante el método de ayuda AddAllDifferent. Luego, usaremos el método auxiliar AddEquality para crear restricciones que apliquen la igualdad CP + IS + FUN = TRUE.

Python

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
)

C++

// Define constraints.
cp_model.AddAllDifferent({c, p, i, s, f, u, n, t, r, e});

// CP + IS + FUN = TRUE
cp_model.AddEquality(
    c * kBase + p + i * kBase + s + f * kBase * kBase + u * kBase + n,
    kBase * kBase * kBase * t + kBase * kBase * r + kBase * u + e);

Java

model.addAllDifferent(letters);

// CP + IS + FUN = TRUE
model.addEquality(LinearExpr.weightedSum(new IntVar[] {c, p, i, s, f, u, n, t, r, u, e},
                      new long[] {base, 1, base, 1, base * base, base, 1, -base * base * base,
                          -base * base, -base, -1}),
    0);

C#

// Define constraints.
model.AddAllDifferent(letters);

// CP + IS + FUN = TRUE
model.Add(c * kBase + p + i * kBase + s + f * kBase * kBase + u * kBase + n ==
          t * kBase * kBase * kBase + r * kBase * kBase + u * kBase + e);

Impresora de solución

A continuación, se muestra el código para la impresora de la solución, que muestra cada solución a medida que la encuentra el solucionador.

Python

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 

C++

Model model;
int num_solutions = 0;
model.Add(NewFeasibleSolutionObserver([&](const CpSolverResponse& response) {
  LOG(INFO) << "Solution " << num_solutions;
  LOG(INFO) << "C=" << SolutionIntegerValue(response, c) << " "
            << "P=" << SolutionIntegerValue(response, p) << " "
            << "I=" << SolutionIntegerValue(response, i) << " "
            << "S=" << SolutionIntegerValue(response, s) << " "
            << "F=" << SolutionIntegerValue(response, f) << " "
            << "U=" << SolutionIntegerValue(response, u) << " "
            << "N=" << SolutionIntegerValue(response, n) << " "
            << "T=" << SolutionIntegerValue(response, t) << " "
            << "R=" << SolutionIntegerValue(response, r) << " "
            << "E=" << SolutionIntegerValue(response, e);
  num_solutions++;
}));

Java

static class VarArraySolutionPrinter extends CpSolverSolutionCallback {
  public VarArraySolutionPrinter(IntVar[] variables) {
    variableArray = variables;
  }

  @Override
  public void onSolutionCallback() {
    for (IntVar v : variableArray) {
      System.out.printf("  %s = %d", v.getName(), value(v));
    }
    System.out.println();
    solutionCount++;
  }

  public int getSolutionCount() {
    return solutionCount;
  }

  private int solutionCount;
  private final IntVar[] variableArray;
}

C#

public class VarArraySolutionPrinter : CpSolverSolutionCallback
{
    public VarArraySolutionPrinter(IntVar[] variables)
    {
        variables_ = variables;
    }

    public override void OnSolutionCallback()
    {
        {
            foreach (IntVar v in variables_)
            {
                Console.Write(String.Format("  {0}={1}", v.ToString(), Value(v)));
            }
            Console.WriteLine();
            solution_count_++;
        }
    }

    public int SolutionCount()
    {
        return solution_count_;
    }

    private int solution_count_;
    private IntVar[] variables_;
}

Cómo invocar el solucionador

Por último, resolvemos el problema y mostramos la solución. Toda la magia está en el método operations_research::sat::SolveCpModel().

Python

solver = cp_model.CpSolver()
solution_printer = VarArraySolutionPrinter(letters)
# Enumerate all solutions.
solver.parameters.enumerate_all_solutions = True
# Solve.
status = solver.solve(model, solution_printer)

C++

// Tell the solver to enumerate all solutions.
SatParameters parameters;
parameters.set_enumerate_all_solutions(true);
model.Add(NewSatParameters(parameters));

const CpSolverResponse response = SolveCpModel(cp_model.Build(), &model);
LOG(INFO) << "Number of solutions found: " << num_solutions;

Java

CpSolver solver = new CpSolver();
VarArraySolutionPrinter cb = new VarArraySolutionPrinter(letters);
// Tell the solver to enumerate all solutions.
solver.getParameters().setEnumerateAllSolutions(true);
// And solve.
solver.solve(model, cb);

C#

// Creates a solver and solves the model.
CpSolver solver = new CpSolver();
VarArraySolutionPrinter cb = new VarArraySolutionPrinter(letters);
// Search for all solutions.
solver.StringParameters = "enumerate_all_solutions:true";
// And solve.
solver.Solve(model, cb);

Cuando ejecutas el programa, se muestra el siguiente resultado, en el que cada fila es una solución:

C=2 P=3 I=7 S=4 F=9 U=6 N=8 T=1 R=0 E=5
C=2 P=4 I=7 S=3 F=9 U=6 N=8 T=1 R=0 E=5
C=2 P=5 I=7 S=3 F=9 U=4 N=8 T=1 R=0 E=6
C=2 P=8 I=7 S=3 F=9 U=4 N=5 T=1 R=0 E=6
C=2 P=8 I=7 S=3 F=9 U=6 N=4 T=1 R=0 E=5
C=3 P=7 I=6 S=2 F=9 U=8 N=5 T=1 R=0 E=4
C=6 P=7 I=3 S=2 F=9 U=8 N=5 T=1 R=0 E=4
C=6 P=5 I=3 S=2 F=9 U=8 N=7 T=1 R=0 E=4
C=3 P=5 I=6 S=2 F=9 U=8 N=7 T=1 R=0 E=4
C=3 P=8 I=6 S=4 F=9 U=2 N=5 T=1 R=0 E=7
C=3 P=7 I=6 S=5 F=9 U=8 N=2 T=1 R=0 E=4
C=3 P=8 I=6 S=5 F=9 U=2 N=4 T=1 R=0 E=7
C=3 P=5 I=6 S=4 F=9 U=2 N=8 T=1 R=0 E=7
C=3 P=4 I=6 S=5 F=9 U=2 N=8 T=1 R=0 E=7
C=3 P=2 I=6 S=5 F=9 U=8 N=7 T=1 R=0 E=4
C=3 P=4 I=6 S=8 F=9 U=2 N=5 T=1 R=0 E=7
C=3 P=2 I=6 S=7 F=9 U=8 N=5 T=1 R=0 E=4
C=3 P=5 I=6 S=8 F=9 U=2 N=4 T=1 R=0 E=7
C=3 P=5 I=6 S=7 F=9 U=8 N=2 T=1 R=0 E=4
C=2 P=5 I=7 S=6 F=9 U=8 N=3 T=1 R=0 E=4
C=2 P=5 I=7 S=8 F=9 U=4 N=3 T=1 R=0 E=6
C=2 P=6 I=7 S=5 F=9 U=8 N=3 T=1 R=0 E=4
C=2 P=4 I=7 S=8 F=9 U=6 N=3 T=1 R=0 E=5
C=2 P=3 I=7 S=8 F=9 U=6 N=4 T=1 R=0 E=5
C=2 P=8 I=7 S=5 F=9 U=4 N=3 T=1 R=0 E=6
C=2 P=8 I=7 S=4 F=9 U=6 N=3 T=1 R=0 E=5
C=2 P=6 I=7 S=3 F=9 U=8 N=5 T=1 R=0 E=4
C=2 P=5 I=7 S=3 F=9 U=8 N=6 T=1 R=0 E=4
C=2 P=3 I=7 S=5 F=9 U=4 N=8 T=1 R=0 E=6
C=2 P=3 I=7 S=5 F=9 U=8 N=6 T=1 R=0 E=4
C=2 P=3 I=7 S=6 F=9 U=8 N=5 T=1 R=0 E=4
C=2 P=3 I=7 S=8 F=9 U=4 N=5 T=1 R=0 E=6
C=4 P=3 I=5 S=8 F=9 U=2 N=6 T=1 R=0 E=7
C=5 P=3 I=4 S=8 F=9 U=2 N=6 T=1 R=0 E=7
C=6 P=2 I=3 S=7 F=9 U=8 N=5 T=1 R=0 E=4
C=7 P=3 I=2 S=6 F=9 U=8 N=5 T=1 R=0 E=4
C=7 P=3 I=2 S=8 F=9 U=4 N=5 T=1 R=0 E=6
C=6 P=4 I=3 S=8 F=9 U=2 N=5 T=1 R=0 E=7
C=5 P=3 I=4 S=6 F=9 U=2 N=8 T=1 R=0 E=7
C=4 P=3 I=5 S=6 F=9 U=2 N=8 T=1 R=0 E=7
C=5 P=6 I=4 S=3 F=9 U=2 N=8 T=1 R=0 E=7
C=7 P=4 I=2 S=3 F=9 U=6 N=8 T=1 R=0 E=5
C=7 P=3 I=2 S=4 F=9 U=6 N=8 T=1 R=0 E=5
C=6 P=2 I=3 S=5 F=9 U=8 N=7 T=1 R=0 E=4
C=7 P=3 I=2 S=5 F=9 U=4 N=8 T=1 R=0 E=6
C=6 P=4 I=3 S=5 F=9 U=2 N=8 T=1 R=0 E=7
C=6 P=5 I=3 S=4 F=9 U=2 N=8 T=1 R=0 E=7
C=7 P=5 I=2 S=3 F=9 U=4 N=8 T=1 R=0 E=6
C=4 P=6 I=5 S=3 F=9 U=2 N=8 T=1 R=0 E=7
C=6 P=5 I=3 S=8 F=9 U=2 N=4 T=1 R=0 E=7
C=6 P=5 I=3 S=7 F=9 U=8 N=2 T=1 R=0 E=4
C=7 P=5 I=2 S=8 F=9 U=4 N=3 T=1 R=0 E=6
C=7 P=5 I=2 S=6 F=9 U=8 N=3 T=1 R=0 E=4
C=5 P=8 I=4 S=6 F=9 U=2 N=3 T=1 R=0 E=7
C=4 P=8 I=5 S=6 F=9 U=2 N=3 T=1 R=0 E=7
C=4 P=8 I=5 S=3 F=9 U=2 N=6 T=1 R=0 E=7
C=5 P=8 I=4 S=3 F=9 U=2 N=6 T=1 R=0 E=7
C=7 P=8 I=2 S=3 F=9 U=4 N=5 T=1 R=0 E=6
C=7 P=8 I=2 S=3 F=9 U=6 N=4 T=1 R=0 E=5
C=7 P=8 I=2 S=4 F=9 U=6 N=3 T=1 R=0 E=5
C=7 P=8 I=2 S=5 F=9 U=4 N=3 T=1 R=0 E=6
C=6 P=8 I=3 S=5 F=9 U=2 N=4 T=1 R=0 E=7
C=6 P=8 I=3 S=4 F=9 U=2 N=5 T=1 R=0 E=7
C=6 P=7 I=3 S=5 F=9 U=8 N=2 T=1 R=0 E=4
C=7 P=6 I=2 S=5 F=9 U=8 N=3 T=1 R=0 E=4
C=7 P=3 I=2 S=5 F=9 U=8 N=6 T=1 R=0 E=4
C=7 P=4 I=2 S=8 F=9 U=6 N=3 T=1 R=0 E=5
C=7 P=3 I=2 S=8 F=9 U=6 N=4 T=1 R=0 E=5
C=5 P=6 I=4 S=8 F=9 U=2 N=3 T=1 R=0 E=7
C=4 P=6 I=5 S=8 F=9 U=2 N=3 T=1 R=0 E=7
C=7 P=6 I=2 S=3 F=9 U=8 N=5 T=1 R=0 E=4
C=7 P=5 I=2 S=3 F=9 U=8 N=6 T=1 R=0 E=4

Statistics
  - status          : OPTIMAL
  - conflicts       : 110
  - branches        : 435
  - wall time       : 0.014934 ms
  - solutions found : 72

Programas completos

Estos son los programas completos.

Python

"""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.
"""
from ortools.sat.python import cp_model


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


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

    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)

    # Define 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
    )

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

    # 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}")


if __name__ == "__main__":
    main()

C++

// 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.
#include <stdlib.h>

#include <cstdint>

#include "ortools/base/logging.h"
#include "ortools/sat/cp_model.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/util/sorted_interval_list.h"

namespace operations_research {
namespace sat {

void CPIsFunSat() {
  // Instantiate the solver.
  CpModelBuilder cp_model;

  const int64_t kBase = 10;

  // Define decision variables.
  Domain digit(0, kBase - 1);
  Domain non_zero_digit(1, kBase - 1);

  IntVar c = cp_model.NewIntVar(non_zero_digit).WithName("C");
  IntVar p = cp_model.NewIntVar(digit).WithName("P");
  IntVar i = cp_model.NewIntVar(non_zero_digit).WithName("I");
  IntVar s = cp_model.NewIntVar(digit).WithName("S");
  IntVar f = cp_model.NewIntVar(non_zero_digit).WithName("F");
  IntVar u = cp_model.NewIntVar(digit).WithName("U");
  IntVar n = cp_model.NewIntVar(digit).WithName("N");
  IntVar t = cp_model.NewIntVar(non_zero_digit).WithName("T");
  IntVar r = cp_model.NewIntVar(digit).WithName("R");
  IntVar e = cp_model.NewIntVar(digit).WithName("E");

  // Define constraints.
  cp_model.AddAllDifferent({c, p, i, s, f, u, n, t, r, e});

  // CP + IS + FUN = TRUE
  cp_model.AddEquality(
      c * kBase + p + i * kBase + s + f * kBase * kBase + u * kBase + n,
      kBase * kBase * kBase * t + kBase * kBase * r + kBase * u + e);

  Model model;
  int num_solutions = 0;
  model.Add(NewFeasibleSolutionObserver([&](const CpSolverResponse& response) {
    LOG(INFO) << "Solution " << num_solutions;
    LOG(INFO) << "C=" << SolutionIntegerValue(response, c) << " "
              << "P=" << SolutionIntegerValue(response, p) << " "
              << "I=" << SolutionIntegerValue(response, i) << " "
              << "S=" << SolutionIntegerValue(response, s) << " "
              << "F=" << SolutionIntegerValue(response, f) << " "
              << "U=" << SolutionIntegerValue(response, u) << " "
              << "N=" << SolutionIntegerValue(response, n) << " "
              << "T=" << SolutionIntegerValue(response, t) << " "
              << "R=" << SolutionIntegerValue(response, r) << " "
              << "E=" << SolutionIntegerValue(response, e);
    num_solutions++;
  }));

  // Tell the solver to enumerate all solutions.
  SatParameters parameters;
  parameters.set_enumerate_all_solutions(true);
  model.Add(NewSatParameters(parameters));

  const CpSolverResponse response = SolveCpModel(cp_model.Build(), &model);
  LOG(INFO) << "Number of solutions found: " << num_solutions;

  // Statistics.
  LOG(INFO) << "Statistics";
  LOG(INFO) << CpSolverResponseStats(response);
}

}  // namespace sat
}  // namespace operations_research

int main(int argc, char** argv) {
  operations_research::sat::CPIsFunSat();
  return EXIT_SUCCESS;
}

Java

package com.google.ortools.sat.samples;
import com.google.ortools.Loader;
import com.google.ortools.sat.CpModel;
import com.google.ortools.sat.CpSolver;
import com.google.ortools.sat.CpSolverSolutionCallback;
import com.google.ortools.sat.IntVar;
import com.google.ortools.sat.LinearExpr;

/** Cryptarithmetic puzzle. */
public final class CpIsFunSat {
  static class VarArraySolutionPrinter extends CpSolverSolutionCallback {
    public VarArraySolutionPrinter(IntVar[] variables) {
      variableArray = variables;
    }

    @Override
    public void onSolutionCallback() {
      for (IntVar v : variableArray) {
        System.out.printf("  %s = %d", v.getName(), value(v));
      }
      System.out.println();
      solutionCount++;
    }

    public int getSolutionCount() {
      return solutionCount;
    }

    private int solutionCount;
    private final IntVar[] variableArray;
  }

  public static void main(String[] args) throws Exception {
    Loader.loadNativeLibraries();
    // Create the model.
    CpModel model = new CpModel();

    int base = 10;
    IntVar c = model.newIntVar(1, base - 1, "C");
    IntVar p = model.newIntVar(0, base - 1, "P");
    IntVar i = model.newIntVar(1, base - 1, "I");
    IntVar s = model.newIntVar(0, base - 1, "S");
    IntVar f = model.newIntVar(1, base - 1, "F");
    IntVar u = model.newIntVar(0, base - 1, "U");
    IntVar n = model.newIntVar(0, base - 1, "N");
    IntVar t = model.newIntVar(1, base - 1, "T");
    IntVar r = model.newIntVar(0, base - 1, "R");
    IntVar e = model.newIntVar(0, base - 1, "E");

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

    // Define constraints.
    model.addAllDifferent(letters);

    // CP + IS + FUN = TRUE
    model.addEquality(LinearExpr.weightedSum(new IntVar[] {c, p, i, s, f, u, n, t, r, u, e},
                          new long[] {base, 1, base, 1, base * base, base, 1, -base * base * base,
                              -base * base, -base, -1}),
        0);

    // Create a solver and solve the model.
    CpSolver solver = new CpSolver();
    VarArraySolutionPrinter cb = new VarArraySolutionPrinter(letters);
    // Tell the solver to enumerate all solutions.
    solver.getParameters().setEnumerateAllSolutions(true);
    // And solve.
    solver.solve(model, cb);

    // Statistics.
    System.out.println("Statistics");
    System.out.println("  - conflicts : " + solver.numConflicts());
    System.out.println("  - branches  : " + solver.numBranches());
    System.out.println("  - wall time : " + solver.wallTime() + " s");
    System.out.println("  - solutions : " + cb.getSolutionCount());
  }

  private CpIsFunSat() {}
}

C#

// 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.
using System;
using Google.OrTools.Sat;

public class CpIsFunSat
{
    public class VarArraySolutionPrinter : CpSolverSolutionCallback
    {
        public VarArraySolutionPrinter(IntVar[] variables)
        {
            variables_ = variables;
        }

        public override void OnSolutionCallback()
        {
            {
                foreach (IntVar v in variables_)
                {
                    Console.Write(String.Format("  {0}={1}", v.ToString(), Value(v)));
                }
                Console.WriteLine();
                solution_count_++;
            }
        }

        public int SolutionCount()
        {
            return solution_count_;
        }

        private int solution_count_;
        private IntVar[] variables_;
    }

    // Solve the CP+IS+FUN==TRUE cryptarithm.
    static void Main()
    {
        // Constraint programming engine
        CpModel model = new CpModel();

        int kBase = 10;

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

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

        // Define constraints.
        model.AddAllDifferent(letters);

        // CP + IS + FUN = TRUE
        model.Add(c * kBase + p + i * kBase + s + f * kBase * kBase + u * kBase + n ==
                  t * kBase * kBase * kBase + r * kBase * kBase + u * kBase + e);

        // Creates a solver and solves the model.
        CpSolver solver = new CpSolver();
        VarArraySolutionPrinter cb = new VarArraySolutionPrinter(letters);
        // Search for all solutions.
        solver.StringParameters = "enumerate_all_solutions:true";
        // And solve.
        solver.Solve(model, cb);

        Console.WriteLine("Statistics");
        Console.WriteLine($"  conflicts : {solver.NumConflicts()}");
        Console.WriteLine($"  branches  : {solver.NumBranches()}");
        Console.WriteLine($"  wall time : {solver.WallTime()} s");
        Console.WriteLine($"  number of solutions found: {cb.SolutionCount()}");
    }
}

Solución de PC original

En este caso, trataremos la base como una variable, por lo que podrás resolver la ecuación de bases más altas. (No puede haber soluciones de base inferiores para CP + IS + FUN = TRUE, ya que las diez letras deben ser todas diferentes).

Importa las bibliotecas

Con el siguiente código, se importa la biblioteca requerida.

Python

from ortools.constraint_solver import pywrapcp

C++

#include <cstdint>
#include <vector>

#include "absl/flags/flag.h"
#include "absl/log/flags.h"
#include "ortools/base/init_google.h"
#include "ortools/base/logging.h"
#include "ortools/constraint_solver/constraint_solver.h"

Java

C#

using System;
using Google.OrTools.ConstraintSolver;

Cómo crear el solucionador

El primer paso es crear el Solver.

Python

solver = pywrapcp.Solver("CP is fun!")

C++

Solver solver("CP is fun!");

Java

Solver solver = new Solver("CP is fun!");

C#

Solver solver = new Solver("CP is fun!");

Define las variables

El primer paso es crear un IntVar para cada letra. Distinguimos entre las letras que pueden ser cero y las que no (C, I, F y T).

A continuación, crearemos un array que contenga un IntVar nuevo para cada letra. Esto solo es necesario porque, cuando definamos nuestras restricciones, usaremos AllDifferent. Por lo tanto, necesitamos un array para el que cada elemento deba diferir.

Por último, verificamos que nuestra base sea al menos tan grande como el número de letras. De lo contrario, no hay solución.

Python

base = 10

# Decision variables.
digits = list(range(0, base))
digits_without_zero = list(range(1, base))
c = solver.IntVar(digits_without_zero, "C")
p = solver.IntVar(digits, "P")
i = solver.IntVar(digits_without_zero, "I")
s = solver.IntVar(digits, "S")
f = solver.IntVar(digits_without_zero, "F")
u = solver.IntVar(digits, "U")
n = solver.IntVar(digits, "N")
t = solver.IntVar(digits_without_zero, "T")
r = solver.IntVar(digits, "R")
e = solver.IntVar(digits, "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)

C++

const int64_t kBase = 10;

// Define decision variables.
IntVar* const c = solver.MakeIntVar(1, kBase - 1, "C");
IntVar* const p = solver.MakeIntVar(0, kBase - 1, "P");
IntVar* const i = solver.MakeIntVar(1, kBase - 1, "I");
IntVar* const s = solver.MakeIntVar(0, kBase - 1, "S");
IntVar* const f = solver.MakeIntVar(1, kBase - 1, "F");
IntVar* const u = solver.MakeIntVar(0, kBase - 1, "U");
IntVar* const n = solver.MakeIntVar(0, kBase - 1, "N");
IntVar* const t = solver.MakeIntVar(1, kBase - 1, "T");
IntVar* const r = solver.MakeIntVar(0, kBase - 1, "R");
IntVar* const e = solver.MakeIntVar(0, kBase - 1, "E");

// We need to group variables in a vector to be able to use
// the global constraint AllDifferent
std::vector<IntVar*> letters{c, p, i, s, f, u, n, t, r, e};

// Check if we have enough digits
CHECK_GE(kBase, letters.size());

Java

final int base = 10;

// Decision variables.
final IntVar c = solver.makeIntVar(1, base - 1, "C");
final IntVar p = solver.makeIntVar(0, base - 1, "P");
final IntVar i = solver.makeIntVar(1, base - 1, "I");
final IntVar s = solver.makeIntVar(0, base - 1, "S");
final IntVar f = solver.makeIntVar(1, base - 1, "F");
final IntVar u = solver.makeIntVar(0, base - 1, "U");
final IntVar n = solver.makeIntVar(0, base - 1, "N");
final IntVar t = solver.makeIntVar(1, base - 1, "T");
final IntVar r = solver.makeIntVar(0, base - 1, "R");
final IntVar e = solver.makeIntVar(0, base - 1, "E");

// Group variables in a vector so that we can use AllDifferent.
final IntVar[] letters = new IntVar[] {c, p, i, s, f, u, n, t, r, e};

// Verify that we have enough digits.
if (base < letters.length) {
  throw new Exception("base < letters.Length");
}

C#

const int kBase = 10;

// Decision variables.
IntVar c = solver.MakeIntVar(1, kBase - 1, "C");
IntVar p = solver.MakeIntVar(0, kBase - 1, "P");
IntVar i = solver.MakeIntVar(1, kBase - 1, "I");
IntVar s = solver.MakeIntVar(0, kBase - 1, "S");
IntVar f = solver.MakeIntVar(1, kBase - 1, "F");
IntVar u = solver.MakeIntVar(0, kBase - 1, "U");
IntVar n = solver.MakeIntVar(0, kBase - 1, "N");
IntVar t = solver.MakeIntVar(1, kBase - 1, "T");
IntVar r = solver.MakeIntVar(0, kBase - 1, "R");
IntVar e = solver.MakeIntVar(0, kBase - 1, "E");

// Group variables in a vector so that we can use AllDifferent.
IntVar[] letters = new IntVar[] { c, p, i, s, f, u, n, t, r, e };

// Verify that we have enough digits.
if (kBase < letters.Length)
{
    throw new Exception("kBase < letters.Length");
}

Define las restricciones

Ahora que definimos nuestras variables, el siguiente paso es definir restricciones. Primero, agregamos la restricción AllDifferent, lo que obliga a que cada letra tenga un dígito diferente.

A continuación, agregamos la restricción CP + IS + FUN = TRUE. Los programas de muestra lo hacen de diferentes maneras.

Python

solver.Add(solver.AllDifferent(letters))

# CP + IS + FUN = TRUE
solver.Add(
    p + s + n + base * (c + i + u) + base * base * f
    == e + base * u + base * base * r + base * base * base * t
)

C++

// Define constraints.
solver.AddConstraint(solver.MakeAllDifferent(letters));

// CP + IS + FUN = TRUE
IntVar* const term1 = MakeBaseLine2(&solver, c, p, kBase);
IntVar* const term2 = MakeBaseLine2(&solver, i, s, kBase);
IntVar* const term3 = MakeBaseLine3(&solver, f, u, n, kBase);
IntVar* const sum_terms =
    solver.MakeSum(solver.MakeSum(term1, term2), term3)->Var();

IntVar* const sum = MakeBaseLine4(&solver, t, r, u, e, kBase);

solver.AddConstraint(solver.MakeEquality(sum_terms, sum));

Java

solver.addConstraint(solver.makeAllDifferent(letters));

// CP + IS + FUN = TRUE
final IntVar sum1 =
    solver
        .makeSum(new IntVar[] {p, s, n,
            solver.makeProd(solver.makeSum(new IntVar[] {c, i, u}).var(), base).var(),
            solver.makeProd(f, base * base).var()})
        .var();
final IntVar sum2 = solver
                        .makeSum(new IntVar[] {e, solver.makeProd(u, base).var(),
                            solver.makeProd(r, base * base).var(),
                            solver.makeProd(t, base * base * base).var()})
                        .var();
solver.addConstraint(solver.makeEquality(sum1, sum2));

C#

solver.Add(letters.AllDifferent());

// CP + IS + FUN = TRUE
solver.Add(p + s + n + kBase * (c + i + u) + kBase * kBase * f ==
           e + kBase * u + kBase * kBase * r + kBase * kBase * kBase * t);

Cómo invocar el solucionador

Ahora que tenemos nuestras variables y restricciones, estamos listos para resolver.

A continuación, se muestra el código para la impresora de la solución, que muestra cada solución a medida que la encuentra el solucionador.

Debido a que existe más de una solución para nuestro problema, iteramos a través de las soluciones con un bucle while solver.NextSolution(). Si tan solo estuviéramos tratando de encontrar una única solución, utilizaríamos este modismo:

if (solver.NextSolution()) {
    // Print solution.
} else {
    // Print that no solution could be found.
}

Python

solution_count = 0
db = solver.Phase(letters, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)
solver.NewSearch(db)
while solver.NextSolution():
    print(letters)
    # Is CP + IS + FUN = TRUE?
    assert (
        base * c.Value()
        + p.Value()
        + base * i.Value()
        + s.Value()
        + base * base * f.Value()
        + base * u.Value()
        + n.Value()
        == base * base * base * t.Value()
        + base * base * r.Value()
        + base * u.Value()
        + e.Value()
    )
    solution_count += 1
solver.EndSearch()
print(f"Number of solutions found: {solution_count}")

C++

int num_solutions = 0;
// Create decision builder to search for solutions.
DecisionBuilder* const db = solver.MakePhase(
    letters, Solver::CHOOSE_FIRST_UNBOUND, Solver::ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution()) {
  LOG(INFO) << "C=" << c->Value() << " " << "P=" << p->Value() << " "
            << "I=" << i->Value() << " " << "S=" << s->Value() << " "
            << "F=" << f->Value() << " " << "U=" << u->Value() << " "
            << "N=" << n->Value() << " " << "T=" << t->Value() << " "
            << "R=" << r->Value() << " " << "E=" << e->Value();

  // Is CP + IS + FUN = TRUE?
  CHECK_EQ(p->Value() + s->Value() + n->Value() +
               kBase * (c->Value() + i->Value() + u->Value()) +
               kBase * kBase * f->Value(),
           e->Value() + kBase * u->Value() + kBase * kBase * r->Value() +
               kBase * kBase * kBase * t->Value());
  num_solutions++;
}
solver.EndSearch();
LOG(INFO) << "Number of solutions found: " << num_solutions;

Java

int countSolution = 0;
// Create the decision builder to search for solutions.
final DecisionBuilder db =
    solver.makePhase(letters, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);
solver.newSearch(db);
while (solver.nextSolution()) {
  System.out.println("C=" + c.value() + " P=" + p.value());
  System.out.println(" I=" + i.value() + " S=" + s.value());
  System.out.println(" F=" + f.value() + " U=" + u.value());
  System.out.println(" N=" + n.value() + " T=" + t.value());
  System.out.println(" R=" + r.value() + " E=" + e.value());

  // Is CP + IS + FUN = TRUE?
  if (p.value() + s.value() + n.value() + base * (c.value() + i.value() + u.value())
          + base * base * f.value()
      != e.value() + base * u.value() + base * base * r.value()
          + base * base * base * t.value()) {
    throw new Exception("CP + IS + FUN != TRUE");
  }
  countSolution++;
}
solver.endSearch();
System.out.println("Number of solutions found: " + countSolution);

C#

int SolutionCount = 0;
// Create the decision builder to search for solutions.
DecisionBuilder db = solver.MakePhase(letters, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);
solver.NewSearch(db);
while (solver.NextSolution())
{
    Console.Write("C=" + c.Value() + " P=" + p.Value());
    Console.Write(" I=" + i.Value() + " S=" + s.Value());
    Console.Write(" F=" + f.Value() + " U=" + u.Value());
    Console.Write(" N=" + n.Value() + " T=" + t.Value());
    Console.Write(" R=" + r.Value() + " E=" + e.Value());
    Console.WriteLine();

    // Is CP + IS + FUN = TRUE?
    if (p.Value() + s.Value() + n.Value() + kBase * (c.Value() + i.Value() + u.Value()) +
            kBase * kBase * f.Value() !=
        e.Value() + kBase * u.Value() + kBase * kBase * r.Value() + kBase * kBase * kBase * t.Value())
    {
        throw new Exception("CP + IS + FUN != TRUE");
    }
    SolutionCount++;
}
solver.EndSearch();
Console.WriteLine($"Number of solutions found: {SolutionCount}");

Programas completos

Estos son los programas completos.

Python

"""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.
"""
from ortools.constraint_solver import pywrapcp


def main():
    # Constraint programming engine
    solver = pywrapcp.Solver("CP is fun!")

    base = 10

    # Decision variables.
    digits = list(range(0, base))
    digits_without_zero = list(range(1, base))
    c = solver.IntVar(digits_without_zero, "C")
    p = solver.IntVar(digits, "P")
    i = solver.IntVar(digits_without_zero, "I")
    s = solver.IntVar(digits, "S")
    f = solver.IntVar(digits_without_zero, "F")
    u = solver.IntVar(digits, "U")
    n = solver.IntVar(digits, "N")
    t = solver.IntVar(digits_without_zero, "T")
    r = solver.IntVar(digits, "R")
    e = solver.IntVar(digits, "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)

    # Define constraints.
    solver.Add(solver.AllDifferent(letters))

    # CP + IS + FUN = TRUE
    solver.Add(
        p + s + n + base * (c + i + u) + base * base * f
        == e + base * u + base * base * r + base * base * base * t
    )

    solution_count = 0
    db = solver.Phase(letters, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)
    solver.NewSearch(db)
    while solver.NextSolution():
        print(letters)
        # Is CP + IS + FUN = TRUE?
        assert (
            base * c.Value()
            + p.Value()
            + base * i.Value()
            + s.Value()
            + base * base * f.Value()
            + base * u.Value()
            + n.Value()
            == base * base * base * t.Value()
            + base * base * r.Value()
            + base * u.Value()
            + e.Value()
        )
        solution_count += 1
    solver.EndSearch()
    print(f"Number of solutions found: {solution_count}")


if __name__ == "__main__":
    main()

C++

// 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.
#include <cstdint>
#include <vector>

#include "absl/flags/flag.h"
#include "absl/log/flags.h"
#include "ortools/base/init_google.h"
#include "ortools/base/logging.h"
#include "ortools/constraint_solver/constraint_solver.h"

namespace operations_research {

// Helper functions.
IntVar* MakeBaseLine2(Solver* s, IntVar* const v1, IntVar* const v2,
                      const int64_t base) {
  return s->MakeSum(s->MakeProd(v1, base), v2)->Var();
}

IntVar* MakeBaseLine3(Solver* s, IntVar* const v1, IntVar* const v2,
                      IntVar* const v3, const int64_t base) {
  std::vector<IntVar*> tmp_vars;
  std::vector<int64_t> coefficients;
  tmp_vars.push_back(v1);
  coefficients.push_back(base * base);
  tmp_vars.push_back(v2);
  coefficients.push_back(base);
  tmp_vars.push_back(v3);
  coefficients.push_back(1);

  return s->MakeScalProd(tmp_vars, coefficients)->Var();
}

IntVar* MakeBaseLine4(Solver* s, IntVar* const v1, IntVar* const v2,
                      IntVar* const v3, IntVar* const v4, const int64_t base) {
  std::vector<IntVar*> tmp_vars;
  std::vector<int64_t> coefficients;
  tmp_vars.push_back(v1);
  coefficients.push_back(base * base * base);
  tmp_vars.push_back(v2);
  coefficients.push_back(base * base);
  tmp_vars.push_back(v3);
  coefficients.push_back(base);
  tmp_vars.push_back(v4);
  coefficients.push_back(1);

  return s->MakeScalProd(tmp_vars, coefficients)->Var();
}

void CPIsFunCp() {
  // Instantiate the solver.
  Solver solver("CP is fun!");

  const int64_t kBase = 10;

  // Define decision variables.
  IntVar* const c = solver.MakeIntVar(1, kBase - 1, "C");
  IntVar* const p = solver.MakeIntVar(0, kBase - 1, "P");
  IntVar* const i = solver.MakeIntVar(1, kBase - 1, "I");
  IntVar* const s = solver.MakeIntVar(0, kBase - 1, "S");
  IntVar* const f = solver.MakeIntVar(1, kBase - 1, "F");
  IntVar* const u = solver.MakeIntVar(0, kBase - 1, "U");
  IntVar* const n = solver.MakeIntVar(0, kBase - 1, "N");
  IntVar* const t = solver.MakeIntVar(1, kBase - 1, "T");
  IntVar* const r = solver.MakeIntVar(0, kBase - 1, "R");
  IntVar* const e = solver.MakeIntVar(0, kBase - 1, "E");

  // We need to group variables in a vector to be able to use
  // the global constraint AllDifferent
  std::vector<IntVar*> letters{c, p, i, s, f, u, n, t, r, e};

  // Check if we have enough digits
  CHECK_GE(kBase, letters.size());

  // Define constraints.
  solver.AddConstraint(solver.MakeAllDifferent(letters));

  // CP + IS + FUN = TRUE
  IntVar* const term1 = MakeBaseLine2(&solver, c, p, kBase);
  IntVar* const term2 = MakeBaseLine2(&solver, i, s, kBase);
  IntVar* const term3 = MakeBaseLine3(&solver, f, u, n, kBase);
  IntVar* const sum_terms =
      solver.MakeSum(solver.MakeSum(term1, term2), term3)->Var();

  IntVar* const sum = MakeBaseLine4(&solver, t, r, u, e, kBase);

  solver.AddConstraint(solver.MakeEquality(sum_terms, sum));

  int num_solutions = 0;
  // Create decision builder to search for solutions.
  DecisionBuilder* const db = solver.MakePhase(
      letters, Solver::CHOOSE_FIRST_UNBOUND, Solver::ASSIGN_MIN_VALUE);
  solver.NewSearch(db);
  while (solver.NextSolution()) {
    LOG(INFO) << "C=" << c->Value() << " " << "P=" << p->Value() << " "
              << "I=" << i->Value() << " " << "S=" << s->Value() << " "
              << "F=" << f->Value() << " " << "U=" << u->Value() << " "
              << "N=" << n->Value() << " " << "T=" << t->Value() << " "
              << "R=" << r->Value() << " " << "E=" << e->Value();

    // Is CP + IS + FUN = TRUE?
    CHECK_EQ(p->Value() + s->Value() + n->Value() +
                 kBase * (c->Value() + i->Value() + u->Value()) +
                 kBase * kBase * f->Value(),
             e->Value() + kBase * u->Value() + kBase * kBase * r->Value() +
                 kBase * kBase * kBase * t->Value());
    num_solutions++;
  }
  solver.EndSearch();
  LOG(INFO) << "Number of solutions found: " << num_solutions;
}

}  // namespace operations_research

int main(int argc, char** argv) {
  InitGoogle(argv[0], &argc, &argv, true);
  absl::SetFlag(&FLAGS_stderrthreshold, 0);
  operations_research::CPIsFunCp();
  return EXIT_SUCCESS;
}

Java

// 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.
package com.google.ortools.constraintsolver.samples;
import com.google.ortools.Loader;
import com.google.ortools.constraintsolver.DecisionBuilder;
import com.google.ortools.constraintsolver.IntVar;
import com.google.ortools.constraintsolver.Solver;

/** Cryptarithmetic puzzle. */
public final class CpIsFunCp {
  public static void main(String[] args) throws Exception {
    Loader.loadNativeLibraries();
    // Instantiate the solver.
    Solver solver = new Solver("CP is fun!");

    final int base = 10;

    // Decision variables.
    final IntVar c = solver.makeIntVar(1, base - 1, "C");
    final IntVar p = solver.makeIntVar(0, base - 1, "P");
    final IntVar i = solver.makeIntVar(1, base - 1, "I");
    final IntVar s = solver.makeIntVar(0, base - 1, "S");
    final IntVar f = solver.makeIntVar(1, base - 1, "F");
    final IntVar u = solver.makeIntVar(0, base - 1, "U");
    final IntVar n = solver.makeIntVar(0, base - 1, "N");
    final IntVar t = solver.makeIntVar(1, base - 1, "T");
    final IntVar r = solver.makeIntVar(0, base - 1, "R");
    final IntVar e = solver.makeIntVar(0, base - 1, "E");

    // Group variables in a vector so that we can use AllDifferent.
    final IntVar[] letters = new IntVar[] {c, p, i, s, f, u, n, t, r, e};

    // Verify that we have enough digits.
    if (base < letters.length) {
      throw new Exception("base < letters.Length");
    }

    // Define constraints.
    solver.addConstraint(solver.makeAllDifferent(letters));

    // CP + IS + FUN = TRUE
    final IntVar sum1 =
        solver
            .makeSum(new IntVar[] {p, s, n,
                solver.makeProd(solver.makeSum(new IntVar[] {c, i, u}).var(), base).var(),
                solver.makeProd(f, base * base).var()})
            .var();
    final IntVar sum2 = solver
                            .makeSum(new IntVar[] {e, solver.makeProd(u, base).var(),
                                solver.makeProd(r, base * base).var(),
                                solver.makeProd(t, base * base * base).var()})
                            .var();
    solver.addConstraint(solver.makeEquality(sum1, sum2));

    int countSolution = 0;
    // Create the decision builder to search for solutions.
    final DecisionBuilder db =
        solver.makePhase(letters, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);
    solver.newSearch(db);
    while (solver.nextSolution()) {
      System.out.println("C=" + c.value() + " P=" + p.value());
      System.out.println(" I=" + i.value() + " S=" + s.value());
      System.out.println(" F=" + f.value() + " U=" + u.value());
      System.out.println(" N=" + n.value() + " T=" + t.value());
      System.out.println(" R=" + r.value() + " E=" + e.value());

      // Is CP + IS + FUN = TRUE?
      if (p.value() + s.value() + n.value() + base * (c.value() + i.value() + u.value())
              + base * base * f.value()
          != e.value() + base * u.value() + base * base * r.value()
              + base * base * base * t.value()) {
        throw new Exception("CP + IS + FUN != TRUE");
      }
      countSolution++;
    }
    solver.endSearch();
    System.out.println("Number of solutions found: " + countSolution);
  }

  private CpIsFunCp() {}
}

C#

// 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.
using System;
using Google.OrTools.ConstraintSolver;

public class CpIsFunCp
{
    public static void Main(String[] args)
    {
        // Instantiate the solver.
        Solver solver = new Solver("CP is fun!");

        const int kBase = 10;

        // Decision variables.
        IntVar c = solver.MakeIntVar(1, kBase - 1, "C");
        IntVar p = solver.MakeIntVar(0, kBase - 1, "P");
        IntVar i = solver.MakeIntVar(1, kBase - 1, "I");
        IntVar s = solver.MakeIntVar(0, kBase - 1, "S");
        IntVar f = solver.MakeIntVar(1, kBase - 1, "F");
        IntVar u = solver.MakeIntVar(0, kBase - 1, "U");
        IntVar n = solver.MakeIntVar(0, kBase - 1, "N");
        IntVar t = solver.MakeIntVar(1, kBase - 1, "T");
        IntVar r = solver.MakeIntVar(0, kBase - 1, "R");
        IntVar e = solver.MakeIntVar(0, kBase - 1, "E");

        // Group variables in a vector so that we can use AllDifferent.
        IntVar[] letters = new IntVar[] { c, p, i, s, f, u, n, t, r, e };

        // Verify that we have enough digits.
        if (kBase < letters.Length)
        {
            throw new Exception("kBase < letters.Length");
        }

        // Define constraints.
        solver.Add(letters.AllDifferent());

        // CP + IS + FUN = TRUE
        solver.Add(p + s + n + kBase * (c + i + u) + kBase * kBase * f ==
                   e + kBase * u + kBase * kBase * r + kBase * kBase * kBase * t);

        int SolutionCount = 0;
        // Create the decision builder to search for solutions.
        DecisionBuilder db = solver.MakePhase(letters, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);
        solver.NewSearch(db);
        while (solver.NextSolution())
        {
            Console.Write("C=" + c.Value() + " P=" + p.Value());
            Console.Write(" I=" + i.Value() + " S=" + s.Value());
            Console.Write(" F=" + f.Value() + " U=" + u.Value());
            Console.Write(" N=" + n.Value() + " T=" + t.Value());
            Console.Write(" R=" + r.Value() + " E=" + e.Value());
            Console.WriteLine();

            // Is CP + IS + FUN = TRUE?
            if (p.Value() + s.Value() + n.Value() + kBase * (c.Value() + i.Value() + u.Value()) +
                    kBase * kBase * f.Value() !=
                e.Value() + kBase * u.Value() + kBase * kBase * r.Value() + kBase * kBase * kBase * t.Value())
            {
                throw new Exception("CP + IS + FUN != TRUE");
            }
            SolutionCount++;
        }
        solver.EndSearch();
        Console.WriteLine($"Number of solutions found: {SolutionCount}");
    }
}