stable_marriage.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.IO;
using System.Text.RegularExpressions;
using Google.OrTools.ConstraintSolver;

public class StableMarriage
{

  /**
   *
   * Solves some stable marriage problems.
   * See http://www.hakank.org/or-tools/stable_marriage.py
   *
   */
  private static void Solve(int[][][] ranks, String problem_name)
  {

    Solver solver = new Solver("StableMarriage");

    //
    // data
    //
    int n = ranks[0].Length;

    Console.WriteLine("\n#####################");
    Console.WriteLine("Problem: " + problem_name);

    int[][] rankWomen = ranks[0];
    int[][] rankMen   = ranks[1];

    //
    // Decision variables
    //
    IntVar[] wife = solver.MakeIntVarArray(n, 0, n - 1, "wife");
    IntVar[] husband = solver.MakeIntVarArray(n, 0, n - 1, "husband");

    //
    // Constraints
    //
    // (The comments below are the Comet code)

    //
    //   forall(m in Men)
    //      cp.post(husband[wife[m]] == m);
    for(int m = 0; m < n; m++) {
      solver.Add(husband.Element(wife[m]) == m);
    }

    //   forall(w in Women)
    //     cp.post(wife[husband[w]] == w);
    for(int w = 0; w < n; w++) {
      solver.Add(wife.Element(husband[w]) == w);
    }


    //   forall(m in Men, o in Women)
    //       cp.post(rankMen[m,o] < rankMen[m, wife[m]] =>
    //               rankWomen[o,husband[o]] < rankWomen[o,m]);
    for(int m = 0; m < n; m++) {
      for(int o = 0; o < n; o++) {
        IntVar b1 = rankMen[m].Element(wife[m]) > rankMen[m][o];
        IntVar b2 = rankWomen[o].Element(husband[o]) < rankWomen[o][m];
        solver.Add(b1 <= b2);
      }

    }

    //   forall(w in Women, o in Men)
    //      cp.post(rankWomen[w,o] < rankWomen[w,husband[w]] =>
    //              rankMen[o,wife[o]] < rankMen[o,w]);
    for(int w = 0; w < n; w++) {
      for(int o = 0; o < n; o++) {
        IntVar b1 = rankWomen[w].Element(husband[w]) > rankWomen[w][o];
        IntVar b2 = rankMen[o].Element(wife[o]) < rankMen[o][w];
        solver.Add(b1 <= b2);
        }
      }

    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(wife,
                                          Solver.INT_VAR_DEFAULT,
                                          Solver.INT_VALUE_DEFAULT);

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      Console.Write("wife   : ");
      for(int i = 0; i < n; i++) {
        Console.Write(wife[i].Value() + " ");
      }
      Console.Write("\nhusband: ");
      for(int i = 0; i < n; i++) {
        Console.Write(husband[i].Value() + " ");
      }
      Console.WriteLine("\n");
    }

    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)
  {
    //
    // From Pascal Van Hentenryck's OPL book
    //
    int[][][] van_hentenryck = {
      // rankWomen
      new int[][] {
        new int[] {1, 2, 4, 3, 5},
        new int[] {3, 5, 1, 2, 4},
        new int[] {5, 4, 2, 1, 3},
        new int[] {1, 3, 5, 4, 2},
        new int[] {4, 2, 3, 5, 1}},

      // rankMen
      new int[][] {
        new int[] {5, 1, 2, 4, 3},
        new int[] {4, 1, 3, 2, 5},
        new int[] {5, 3, 2, 4, 1},
        new int[] {1, 5, 4, 3, 2},
        new int[] {4, 3, 2, 1, 5}}
    };

    //
    // Data from MathWorld
    // http://mathworld.wolfram.com/StableMarriageProblem.html
    //
    int[][][] mathworld = {
      // rankWomen
      new int[][] {
        new int[] {3, 1, 5, 2, 8, 7, 6, 9, 4},
        new int[] {9, 4, 8, 1, 7, 6, 3, 2, 5},
        new int[] {3, 1, 8, 9, 5, 4, 2, 6, 7},
        new int[] {8, 7, 5, 3, 2, 6, 4, 9, 1},
        new int[] {6, 9, 2, 5, 1, 4, 7, 3, 8},
        new int[] {2, 4, 5, 1, 6, 8, 3, 9, 7},
        new int[] {9, 3, 8, 2, 7, 5, 4, 6, 1},
        new int[] {6, 3, 2, 1, 8, 4, 5, 9, 7},
        new int[] {8, 2, 6, 4, 9, 1, 3, 7, 5}},

      // rankMen
      new int[][] {
        new int[] {7, 3, 8, 9, 6, 4, 2, 1, 5},
        new int[] {5, 4, 8, 3, 1, 2, 6, 7, 9},
        new int[] {4, 8, 3, 9, 7, 5, 6, 1, 2},
        new int[] {9, 7, 4, 2, 5, 8, 3, 1, 6},
        new int[] {2, 6, 4, 9, 8, 7, 5, 1, 3},
        new int[] {2, 7, 8, 6, 5, 3, 4, 1, 9},
        new int[] {1, 6, 2, 3, 8, 5, 4, 9, 7},
        new int[] {5, 6, 9, 1, 2, 8, 4, 3, 7},
        new int[] {6, 1, 4, 7, 5, 8, 3, 9, 2}}
    };

    //
    // Data from
    // http://www.csee.wvu.edu/~ksmani/courses/fa01/random/lecnotes/lecture5.pdf
    //
    int[][][] problem3 = {
      // rankWomen
      new int[][] {
        new int[] {1,2,3,4},
        new int[] {4,3,2,1},
        new int[] {1,2,3,4},
        new int[] {3,4,1,2}},

      // rankMen
      new int[][] {
        new int[] {1,2,3,4},
        new int[] {2,1,3,4},
        new int[] {1,4,3,2},
        new int[] {4,3,1,2}}
    };


    //
    // Data from
    // http://www.comp.rgu.ac.uk/staff/ha/ZCSP/additional_problems/stable_marriage/stable_marriage.pdf
    // page 4
    //
    int[][][] problem4 = {
      // rankWomen
      new int[][] {
        new int[] {1,5,4,6,2,3},
        new int[] {4,1,5,2,6,3},
        new int[] {6,4,2,1,5,3},
        new int[] {1,5,2,4,3,6},
        new int[] {4,2,1,5,6,3},
        new int[] {2,6,3,5,1,4}},

      // rankMen
      new int[][] {
        new int[] {1,4,2,5,6,3},
        new int[] {3,4,6,1,5,2},
        new int[] {1,6,4,2,3,5},
        new int[] {6,5,3,4,2,1},
        new int[] {3,1,2,4,5,6},
        new int[] {2,3,1,6,5,4}}};


    Solve(van_hentenryck, "Van Hentenryck");
    Solve(mathworld, "MathWorld");
    Solve(problem3, "Problem 3");
    Solve(problem4, "Problem 4");

  }
}