subset_sum.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 SubsetSum
{

  public static IntVar[] subset_sum(Solver solver, 
                                    int[] values, 
                                    int total) {
    int n = values.Length;
    IntVar[] x = solver.MakeIntVarArray(n, 0, n, "x");
    solver.Add(x.ScalProd(values) == total);

    return x;
  }


  /**
   *
   * Subset sum problem.
   *
   * From Katta G. Murty: 'Optimization Models for Decision Making', page 340
   * http://ioe.engin.umich.edu/people/fac/books/murty/opti_model/junior-7.pdf
   * """
   * Example 7.8.1
   * 
   * A bank van had several bags of coins, each containing either
   * 16, 17, 23, 24, 39, or 40 coins. While the van was parked on the
   * street, thieves stole some bags. A total of 100 coins were lost.
   * It is required to find how many bags were stolen.
   * """
   *
   * Also see http://www.hakank.org/or-tools/subset_sum.py
   *
   */
  private static void Solve(int[] coins, int total)
  {

    Solver solver = new Solver("SubsetSum");

    int n = coins.Length;
    Console.Write("Coins: ");
    for(int i = 0; i < n; i++) {
      Console.Write(coins[i] + " ");
    }
    Console.WriteLine("\nTotal: {0}", total);

    //
    // Variables
    //
    // number of coins
    IntVar s = solver.MakeIntVar(0, coins.Sum(), "s");


    //
    // Constraints
    // 
    IntVar[] x = subset_sum(solver, coins, total);
    solver.Add(x.Sum() == s);


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

    solver.NewSearch(db);

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

    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)
  {

    int[] coins = {16, 17, 23, 24, 39, 40};
    int total = 100;

    if (args.Length > 0) {
      total = Convert.ToInt32(args[0]);
    }

    Solve(coins, total);
  }
}