Cryptarithmetic পাজল

ক্রিপ্টারিদমেটিক ধাঁধা হল একটি গাণিতিক অনুশীলন যেখানে কিছু সংখ্যার সংখ্যা অক্ষর (বা প্রতীক) দ্বারা উপস্থাপন করা হয়। প্রতিটি অক্ষর একটি অনন্য অঙ্ক প্রতিনিধিত্ব করে। লক্ষ্য হল অঙ্কগুলি খুঁজে বের করা যাতে একটি প্রদত্ত গাণিতিক সমীকরণ যাচাই করা হয়:

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

অঙ্কগুলিতে অক্ষরের একটি বরাদ্দ নিম্নলিখিত সমীকরণটি দেয়:

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

এই সমস্যার অন্যান্য উত্তর আছে। আমরা দেখাব কিভাবে সব সমাধান খুঁজে বের করতে হয়।

সমস্যা মডেলিং

যেকোনো অপ্টিমাইজেশান সমস্যার মতো, আমরা ভেরিয়েবল এবং সীমাবদ্ধতা সনাক্ত করে শুরু করব। ভেরিয়েবল হল অক্ষর, যা যেকোনো একক অঙ্কের মান নিতে পারে।

CP + IS + FUN = TRUE এর জন্য, সীমাবদ্ধতাগুলি নিম্নরূপ:

• সমীকরণ: CP + IS + FUN = TRUE ।
• দশটি অক্ষরের প্রতিটি একটি আলাদা অঙ্ক হতে হবে।
• C , I , F , এবং T শূন্য হতে পারে না (যেহেতু আমরা সংখ্যায় অগ্রণী শূন্য লিখি না)।

আপনি হয় নতুন CP-SAT সমাধানকারীর সাথে ক্রিপ্টারিদমেটিক সমস্যাগুলি সমাধান করতে পারেন, যা আরও দক্ষ, অথবা আসল CP সমাধানকারী৷ আমরা আপনাকে CP-SAT দিয়ে শুরু করে উভয় সমাধানকারী ব্যবহার করে উদাহরণ দেখাব।

CP-SAT সমাধান

আমরা ভেরিয়েবল, সীমাবদ্ধতা, সমাধানকারী আমন্ত্রণ এবং অবশেষে সম্পূর্ণ প্রোগ্রামগুলি দেখাব।

লাইব্রেরি আমদানি করুন

নিম্নলিখিত কোড প্রয়োজনীয় লাইব্রেরি আমদানি করে।

পাইথন

from ortools.sat.python import cp_model

সি++

#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"

জাভা

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;

সি#

using System;
using Google.OrTools.Sat;

মডেল ঘোষণা করুন

নিম্নলিখিত কোডটি সমস্যার জন্য মডেল ঘোষণা করে।

পাইথন

model = cp_model.CpModel()

সি++

CpModelBuilder cp_model;

জাভা

CpModel model = new CpModel();

সি#

        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()}");
    }
}

ভেরিয়েবল সংজ্ঞায়িত করা

CP-SAT সমাধানকারী ব্যবহার করার সময়, কিছু সহায়ক পদ্ধতি রয়েছে যা সংজ্ঞায়িত করা কার্যকর। আমরা তাদের মধ্যে একটি ব্যবহার করব, NewIntVar , আমাদের (পূর্ণসংখ্যা) সংখ্যা ঘোষণা করতে। আমরা সম্ভাব্যভাবে শূন্য হতে পারে এমন অক্ষর এবং যেগুলি করতে পারে না ( C , I , F , এবং T ) এর মধ্যে পার্থক্য করি।

পাইথন

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)

সি++

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");

জাভা

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};

সি#

        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 };

সীমাবদ্ধতা সংজ্ঞায়িত করা

পরবর্তী, সীমাবদ্ধতা. প্রথমে, আমরা নিশ্চিত করি যে সমস্ত অক্ষরের আলাদা মান আছে, AddAllDifferent সহায়ক পদ্ধতি ব্যবহার করে। তারপরে আমরা সীমাবদ্ধতা তৈরি করতে AddEquality সহায়ক পদ্ধতি ব্যবহার করি যা CP + IS + FUN = TRUE সমতা প্রয়োগ করে।

পাইথন

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
)

সি++

// 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);

জাভা

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);

সি#

// 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);

সমাধান প্রিন্টার

সমাধান প্রিন্টারের কোড, যা প্রতিটি সমাধানকে সমাধানকারী এটি খুঁজে পাওয়ার সাথে সাথে প্রদর্শন করে, নীচে দেখানো হয়েছে।

পাইথন

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 

সি++

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++;
}));

জাভা

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;
}

সি#

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_;
}

সমাধানকারীকে আহ্বান করা হচ্ছে

অবশেষে আমরা সমস্যার সমাধান করি এবং সমাধান প্রদর্শন করি। সমস্ত জাদু আছে operations_research::sat::SolveCpModel() পদ্ধতিতে।

পাইথন

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

সি++

// 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;

জাভা

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);

সি#

// 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);

আপনি যখন প্রোগ্রামটি চালান, এটি নিম্নলিখিত আউটপুটটি প্রদর্শন করে, যেখানে প্রতিটি সারি একটি সমাধান:

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

সম্পূর্ণ প্রোগ্রাম

এখানে সম্পূর্ণ প্রোগ্রাম আছে.

পাইথন

"""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()

সি++

// 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;
}

জাভা

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() {}
}

সি#

// 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()}");
    }
}

অরিজিনাল সিপি সলিউশন

এই ক্ষেত্রে আমরা ভিত্তিটিকে একটি পরিবর্তনশীল হিসাবে বিবেচনা করব, যাতে আপনি উচ্চতর বেসের জন্য সমীকরণটি সমাধান করতে পারেন। ( CP + IS + FUN = TRUE এর জন্য কোন নিম্ন ভিত্তি সমাধান হতে পারে না যেহেতু দশটি অক্ষর অবশ্যই আলাদা হতে হবে।)

লাইব্রেরি আমদানি করুন

নিম্নলিখিত কোড প্রয়োজনীয় লাইব্রেরি আমদানি করে।

পাইথন

from ortools.constraint_solver import pywrapcp

সি++

#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"

জাভা

সি#

using System;
using Google.OrTools.ConstraintSolver;

সমাধানকারী তৈরি করা হচ্ছে

প্রথম ধাপ হল Solver তৈরি করা।

পাইথন

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

সি++

Solver solver("CP is fun!");

জাভা

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

সি#

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

ভেরিয়েবল সংজ্ঞায়িত করা

প্রথম ধাপ হল প্রতিটি অক্ষরের জন্য একটি IntVar তৈরি করা। আমরা সম্ভাব্যভাবে শূন্য হতে পারে এমন অক্ষর এবং যেগুলি করতে পারে না ( C , I , F , এবং T ) এর মধ্যে পার্থক্য করি।

এর পরে, আমরা প্রতিটি অক্ষরের জন্য একটি নতুন IntVar ধারণকারী একটি অ্যারে তৈরি করি। এটি শুধুমাত্র প্রয়োজনীয় কারণ আমরা যখন আমাদের সীমাবদ্ধতাগুলি সংজ্ঞায়িত করি, তখন আমরা AllDifferent ব্যবহার করতে যাচ্ছি, তাই আমাদের এমন কিছু অ্যারে দরকার যার জন্য প্রতিটি উপাদানের পার্থক্য প্রয়োজন।

অবশেষে, আমরা যাচাই করি যে আমাদের ভিত্তি অন্তত অক্ষরের সংখ্যার মতো বড়; অন্যথায়, কোন সমাধান নেই।

পাইথন

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)

সি++

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());

জাভা

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");
}

সি#

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");
}

সীমাবদ্ধতা সংজ্ঞায়িত করা

এখন যেহেতু আমরা আমাদের ভেরিয়েবলগুলিকে সংজ্ঞায়িত করেছি, পরবর্তী ধাপ হল সীমাবদ্ধতাগুলিকে সংজ্ঞায়িত করা। প্রথমত, আমরা AllDifferent সীমাবদ্ধতা যোগ করি, প্রতিটি অক্ষরের একটি ভিন্ন সংখ্যা থাকতে বাধ্য করে।

এরপরে, আমরা CP + IS + FUN = TRUE সীমাবদ্ধতা যোগ করি। নমুনা প্রোগ্রামগুলি বিভিন্ন উপায়ে এটি করে।

পাইথন

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
)

সি++

// 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));

জাভা

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));

সি#

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);

সমাধানকারীকে আহ্বান করা হচ্ছে

এখন যেহেতু আমাদের ভেরিয়েবল এবং সীমাবদ্ধতা রয়েছে, আমরা সমাধান করতে প্রস্তুত।

সমাধান প্রিন্টারের কোড, যা প্রতিটি সমাধানকে সমাধানকারী এটি খুঁজে পাওয়ার সাথে সাথে প্রদর্শন করে, নীচে দেখানো হয়েছে।

কারণ আমাদের সমস্যার একাধিক সমাধান রয়েছে, আমরা while solver.NextSolution() লুপ। যদি আমরা শুধুমাত্র একটি একক সমাধান খুঁজে বের করার চেষ্টা করছি, আমরা এই বাগধারাটি ব্যবহার করব:\

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

পাইথন

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}")

সি++

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;

জাভা

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);

সি#

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}");

সম্পূর্ণ প্রোগ্রাম

এখানে সম্পূর্ণ প্রোগ্রাম আছে.

পাইথন

"""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()

সি++

// 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;
}

জাভা

// 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() {}
}

সি#

// 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}");
    }
}