send_most_money.cs

//
// Copyright 2012 Hakan Kjellerstrand
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

using System;
using Google.OrTools.ConstraintSolver;

public class SendMostMoney
{
  /**
   *
   * Solve the SEND+MOST=MONEY problem
   * where the object is to maximize MONEY
   * See http://www.hakank.org/google_or_tools/send_most_money.py
   *
   */
  private static long Solve(long MONEY)
  {

    Solver solver = new Solver("SendMostMoney");

    //
    // Decision variables
    //
    IntVar S = solver.MakeIntVar(0, 9, "S");
    IntVar E = solver.MakeIntVar(0, 9, "E");
    IntVar N = solver.MakeIntVar(0, 9, "N");
    IntVar D = solver.MakeIntVar(0, 9, "D");
    IntVar M = solver.MakeIntVar(0, 9, "M");
    IntVar O = solver.MakeIntVar(0, 9, "O");
    IntVar T = solver.MakeIntVar(0, 9, "T");
    IntVar Y = solver.MakeIntVar(0, 9, "Y");

    // for AllDifferent()
    IntVar[] x = new IntVar[] {S,E,N,D,M,O,T,Y};

    IntVar[] eq = {S,E,N,D,  M,O,S,T, M,O,N,E,Y};
    int[] coeffs = {  1000, 100, 10, 1,        //    S E N D +
                      1000, 100, 10, 1,        //    M O S T
                    -10000,-1000, -100,-10,-1  // == M O N E Y
                    };
    solver.Add(eq.ScalProd(coeffs) == 0);

    // IntVar money = solver.MakeScalProd(new IntVar[] {M, O, N, E, Y},
    //                                    new int[] {10000, 1000, 100, 10, 1}).Var();
    IntVar money = (new IntVar[] {M, O, N, E, Y}).
                          ScalProd(new int[] {10000, 1000, 100, 10, 1}).Var();

    //
    // Constraints
    //
    solver.Add(x.AllDifferent());
    solver.Add(S > 0);
    solver.Add(M > 0);

    if (MONEY > 0) {
      solver.Add(money == MONEY);
    }

    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x,
                                          Solver.CHOOSE_FIRST_UNBOUND,
                                          Solver.ASSIGN_MIN_VALUE);

    if (MONEY == 0) {
      OptimizeVar obj = money.Maximize(1);
      solver.NewSearch(db, obj);
    } else {
      solver.NewSearch(db);
    }

    long money_ret = 0;
    while (solver.NextSolution()) {
      money_ret = money.Value();
      Console.WriteLine("money: {0}", money.Value() );
      for(int i = 0; i < x.Length; i++) {
        Console.Write(x[i].Value() + " ");
      }
      Console.WriteLine();
    }

    Console.WriteLine("\nSolutions: {0}", solver.Solutions());
    Console.WriteLine("WallTime: {0}ms", solver.WallTime());
    Console.WriteLine("Failures: {0}", solver.Failures());
    Console.WriteLine("Branches: {0} ", solver.Branches());

    solver.EndSearch();

    return money_ret;

  }

  public static void Main(String[] args)
  {
    Console.WriteLine("First get the max value of money:");
    long this_money = Solve(0);
    Console.WriteLine("\nThen we find all solutions for MONEY = {0}:", this_money);
    long tmp = Solve(this_money);
  }
}