coins3.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 System.Collections;
using System.Collections.Generic;
using System.Linq;
using Google.OrTools.ConstraintSolver;


public class Coins3
{

  /**
   *
   * Coin application.
   *
   * From "Constraint Logic Programming using ECLiPSe"
   *  pages 99f and 234 ff.
   * The solution in ECLiPSe is at page 236.
   *
   * """
   * What is the minimum number of coins that allows one to pay _exactly_
   * any amount smaller than one Euro? Recall that there are six different
   * euro cents, of denomination 1, 2, 5, 10, 20, 50
   * """

   * Also see http://www.hakank.org/or-tools/coins3.py 
   *
   */
  private static void Solve()
  {

    Solver solver = new Solver("Coins3");

    //
    // Data
    //
    int n = 6; // number of different coins
    int[] variables = {1, 2, 5, 10, 25, 50};

    IEnumerable<int> RANGE = Enumerable.Range(0, n);

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(n, 0, 99, "x");
    IntVar num_coins = x.Sum().VarWithName("num_coins");


    //
    // Constraints
    //

    // Check that all changes from 1 to 99 can be made.
    for(int j = 1; j < 100; j++) {
      IntVar[] tmp = solver.MakeIntVarArray(n, 0, 99, "tmp");
      solver.Add(tmp.ScalProd(variables) == j);

      foreach(int i in RANGE) {
        solver.Add(tmp[i] <= x[i]);
      }

    }

    //
    // Objective
    //
    OptimizeVar obj = num_coins.Minimize(1);

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

    solver.NewSearch(db, obj);

    while (solver.NextSolution()) {
      Console.WriteLine("num_coins: {0}", num_coins.Value());
      Console.Write("x:  ");
      foreach(int i in RANGE) {
        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();

  }

  public static void Main(String[] args)
  {
    Solve();
  }
}