şifreleme bulmacası, bazı sayıların rakamlarının harfler (veya semboller) ile temsil edildiği matematiksel bir alıştırmadır. Her harf benzersiz bir basamağı temsil eder. Amaç, sayıları bulmak ve böylece belirli bir matematiksel denklemin doğrulanabilmesi için rakamları bulmaktır:
CP + IS + FUN -------- = TRUE
Harfler ve rakamlar arasında bir atama aşağıdaki denklemi sağlar:
23 + 74 + 968 -------- = 1065
Bu sorunun başka yanıtları da vardır. Tüm çözümleri nasıl bulabileceğinizi göstereceğiz.
Problemin modellemesi
Tüm optimizasyon problemlerinde olduğu gibi, değişkenleri ve kısıtlamaları belirleyerek başlıyoruz. Değişkenler, herhangi bir tek basamaklı değeri alabilen harflerdir.
CP + IS + FUN = TRUE için kısıtlamalar aşağıdaki gibidir:
- Denklem:
CP + IS + FUN = TRUE
. - On harfin her biri farklı bir rakam olmalıdır.
C
,I
,F
veT
sıfır olamaz (sayıların başındaki sıfırları yazmadığımız için).
Kriparitmetik problemleri, daha verimli olan yeni CP-SAT çözücüyü veya orijinal CP çözücüyü kullanarak çözebilirsiniz. CP-SAT ile başlayarak her iki çözücünün de kullanıldığı örnekler göstereceğiz.
CP-SAT Çözümü
Değişkenleri, kısıtlamaları, çözücü çağrısını ve son olarak da tüm programları göstereceğiz.
Kitaplıkları içe aktarın
Aşağıdaki kod gerekli kitaplığı içe aktarır.
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;
Modeli bildirin
Aşağıdaki kod, sorunun modelini tanımlar.
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()}"); } }
Değişkenleri tanımlama
CP-SAT çözücüyü kullanırken, tanımlanmasının yararlı olduğu bazı yardımcı yöntemler vardır.
Tamsayımızı belirtmek için bunlardan birini (NewIntVar
) kullanırız.
Potansiyel olarak sıfır olabilecek harfler (C
, I
, F
ve T
) arasında ayrım yaparız.
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 };
Kısıtlamaları tanımlama
Sırada kısıtlamalar var. Öncelikle, AddAllDifferent
yardımcı yöntemini kullanarak tüm harflerin farklı değerlere sahip olduğundan emin oluruz. Ardından CP + IS + FUN = TRUE
eşitliğini zorunlu kılan kısıtlamalar oluşturmak için AddEquality
yardımcı yöntemini kullanırız.
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);
Çözüm yazıcısı
Çözücü tarafından bulunan her bir çözümü gösteren çözüm yazıcısının kodu aşağıda gösterilmiştir.
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_; }
Çözücüyü çağırma
Son olarak da sorunu çözer ve çözümü gösteririz. İşin sırrı operations_research::sat::SolveCpModel()
yönteminde saklı.
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);
Programı çalıştırdığınızda, her satırın çözüm olduğu aşağıdaki çıkışı gösterir:
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
Programları tamamlayın
Programların tamamını burada bulabilirsiniz.
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()}"); } }
Orijinal CP Çözümü
Bu örnekte, daha yüksek tabanlar için denklemi çözebilmeniz için tabanı değişken olarak ele alacağız. (On harfin tümü farklı olduğundan CP + IS + FUN = TRUE
için alt temel çözüm olamaz.)
Kitaplıkları içe aktarın
Aşağıdaki kod gerekli kitaplığı içe aktarır.
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;
Çözme aracı oluşturma
İlk adım, Solver
oluşturmaktır.
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!");
Değişkenleri tanımlama
İlk adım, her harf için bir IntVar
oluşturmaktır. Potansiyel olarak sıfır olabilecek harfler (C
, I
, F
ve T
) arasında ayrım yaparız.
Daha sonra, her harf için yeni bir IntVar
içeren bir dizi oluştururuz. Bu sadece kısıtlamalarımızı tanımlarken AllDifferent
kullanacağımızdan her öğenin farklı olması gereken bir diziye ihtiyacımız olduğu için bunu yapabilirsiniz.
Son olarak, tabanımızın en az harf sayısı kadar büyük olduğunu doğrularız. Aksi takdirde, herhangi bir çözüm yoktur.
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"); }
Kısıtlamaları tanımlama
Değişkenlerimizi tanımladığımıza göre, sonraki adım kısıtlamaları tanımlamaktır.
Öncelikle, AllDifferent
kısıtlamasını ekleyerek her harfi farklı bir basamağa sahip olmaya zorlarız.
Sonra, CP + IS + FUN = TRUE
kısıtlamasını ekleriz. Örnek programlar bunu
farklı şekillerde yapar.
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);
Çözücüyü çağırma
Artık değişkenlerimizi ve kısıtlamalarımızı öğrendiğimize göre, çözmeye hazırız.
Çözücü tarafından bulunan her bir çözümü gösteren çözüm yazıcısının kodu aşağıda gösterilmiştir.
Problemimiz için birden fazla çözüm olduğundan çözümleri while solver.NextSolution()
döngüsüyle yineliyoruz. Tek bir çözüm bulmaya çalışıyor olsaydık şu deyimi kullanırdık:\
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}");
Programları tamamlayın
Programların tamamını burada bulabilirsiniz.
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}"); } }