C# Solver.Branches方法代码示例

  /**
   *
   * Solve the Least diff problem
   * For more info, see http://www.hakank.org/google_or_tools/least_diff.py
   *
   */
  private static void Solve()
  {
    Solver solver = new Solver("LeastDiff");

    //
    // Decision variables
    //
    IntVar A = solver.MakeIntVar(0, 9, "A");
    IntVar B = solver.MakeIntVar(0, 9, "B");
    IntVar C = solver.MakeIntVar(0, 9, "C");
    IntVar D = solver.MakeIntVar(0, 9, "D");
    IntVar E = solver.MakeIntVar(0, 9, "E");
    IntVar F = solver.MakeIntVar(0, 9, "F");
    IntVar G = solver.MakeIntVar(0, 9, "G");
    IntVar H = solver.MakeIntVar(0, 9, "H");
    IntVar I = solver.MakeIntVar(0, 9, "I");
    IntVar J = solver.MakeIntVar(0, 9, "J");

    IntVar[] all = new IntVar[] {A,B,C,D,E,F,G,H,I,J};
    int[] coeffs = {10000,1000,100,10,1};
    IntVar x = new IntVar[]{A,B,C,D,E}.ScalProd(coeffs).Var();
    IntVar y = new IntVar[]{F,G,H,I,J}.ScalProd(coeffs).Var();
    IntVar diff = (x - y).VarWithName("diff");


    //
    // Constraints
    //
    solver.Add(all.AllDifferent());
    solver.Add(A > 0);
    solver.Add(F > 0);
    solver.Add(diff > 0);


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

    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(all,
                                          Solver.CHOOSE_PATH,
                                          Solver.ASSIGN_MIN_VALUE);

    solver.NewSearch(db, obj);
    while (solver.NextSolution()) {
      Console.WriteLine("{0} - {1} = {2}  ({3}",x.Value(), y.Value(), diff.Value(), diff.ToString());
    }

    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();

  }

  /**
   *
   * Implements the all interval problem.
   * See http://www.hakank.org/google_or_tools/all_interval.py
   *
   */
  private static void Solve(int n=12)
  {
    Solver solver = new Solver("AllInterval");


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

    //
    // Constraints
    //
    solver.Add(x.AllDifferent());
    solver.Add(diffs.AllDifferent());

    for(int k = 0; k < n - 1; k++) {
      // solver.Add(diffs[k] == (x[k + 1] - x[k]).Abs());
      solver.Add(diffs[k] == (x[k + 1] - x[k].Abs()));
    }


    // symmetry breaking
    solver.Add(x[0] < x[n - 1]);
    solver.Add(diffs[0] < diffs[1]);


    //
    // 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("{0} ", x[i].Value());
      }
      Console.Write("  diffs: ");
      for(int i = 0; i < n-1; i++) {
          Console.Write("{0} ", diffs[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();

  }

    private static long Solve(long num_buses_check = 0)
    {
        SolverParameters sPrm = new SolverParameters();
        sPrm.compress_trail = 0;
        sPrm.trace_level = 0;
        sPrm.profile_level = 0;
        Solver solver = new Solver("OrTools",sPrm);

        //this works
        // IntVar[,] x = solver.MakeIntVarMatrix(2,2, new int[] {-2,0,1,2}, "x");

        //this doesn't work
        IntVar[,] x = solver.MakeIntVarMatrix(2, 2, new int[] { 0, 1, 2 }, "x");

        for (int w = 0; w < 2; w++)
        {
          IntVar[] b = new IntVar[2];
          for (int i = 0; i < 2; i++)
          {
        b[i] = solver.MakeIsEqualCstVar(x[w, i], 0);
          }
          solver.Add(solver.MakeSumGreaterOrEqual(b, 2));
        }

        IntVar[] x_flat = x.Flatten();
        DecisionBuilder db = solver.MakePhase(x_flat,
                                          Solver.CHOOSE_FIRST_UNBOUND,
                                          Solver.ASSIGN_MIN_VALUE);
        solver.NewSearch(db);
        while (solver.NextSolution())
        {
          Console.WriteLine("x: ");
          for (int j = 0; j < 2; j++)
          {
        Console.Write("worker" + (j + 1).ToString() + ":");
        for (int i = 0; i < 2; i++)
        {
          Console.Write(" {0,2} ", x[j, i].Value());
        }
        Console.Write("\n");
          }
          Console.WriteLine("End   at---->" + DateTime.Now);
        }

        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 1;
    }

  /**
   *
   * Solve the SEND+MORE=MONEY problem
   *
   */
  private static void Solve()
  {
    Solver solver = new Solver("SendMoreMoney");

    //
    // 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 R = solver.MakeIntVar(0, 9, "R");
    IntVar Y = solver.MakeIntVar(0, 9, "Y");

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

    //
    // Constraints
    //
    solver.Add(x.AllDifferent());
    solver.Add(S*1000 + E*100 + N*10 + D + M*1000 + O*100 + R*10 + E ==
               M*10000 + O*1000 + N*100 + E*10 + Y);

    solver.Add(S > 0);
    solver.Add(M > 0);

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

    solver.NewSearch(db);
    while (solver.NextSolution()) {
      for(int i = 0; i < 8; i++) {
        Console.Write(x[i].ToString() + " ");
      }
      Console.WriteLine();
    }

    Console.WriteLine("\nWallTime: " + solver.WallTime() + "ms ");
    Console.WriteLine("Failures: " + solver.Failures());
    Console.WriteLine("Branches: " + solver.Branches());

    solver.EndSearch();

  }

  /**
   *
   * Magic sequence problem.
   *
   * This is a port of the Python model
   * https://code.google.com/p/or-tools/source/browse/trunk/python/magic_sequence_distribute.py
   * """
   * This models aims at building a sequence of numbers such that the number of
   * occurrences of i in this sequence is equal to the value of the ith number.
   * It uses an aggregated formulation of the count expression called
   * distribute().
   * """
   *
   */
  private static void Solve(int size)
  {

    Solver solver = new Solver("MagicSequence");

    Console.WriteLine("\nSize: {0}", size);

    //
    // data
    //
    int[] all_values = new int[size];
    for (int i = 0; i < size; i++) {
      all_values[i] = i;
    }

    //
    // Decision variables
    //
    IntVar[] all_vars  = solver.MakeIntVarArray(size, 0, size - 1, "vars");

    //
    // Constraints
    //
    solver.Add(all_vars.Distribute(all_values, all_vars));
    solver.Add(all_vars.Sum() == size);


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

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      for(int i = 0; i < size; i++) {
        Console.Write(all_vars[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();

  }

  /**
   *
   * Solve the xkcd problem
   * See http://www.hakank.org/google_or_tools/xkcd.py
   *
   */
  private static void Solve()
  {
    Solver solver = new Solver("Xkcd");

    //
    // Constants, inits
    //
    int n = 6;
    // for price and total: multiplied by 100 to be able to use integers
    int[] price = {215, 275, 335, 355, 420, 580};
    int total = 1505;

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(n, 0, 10, "x");

    //
    // Constraints
    //
    solver.Add(x.ScalProd(price) == total);

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

    solver.NewSearch(db);
    while (solver.NextSolution()) {
      for(int i = 0; i < n; 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();

  }

 /**
  * Solves the rabbits + pheasants problem.  We are seing 20 heads
  * and 56 legs. How many rabbits and how many pheasants are we thus
  * seeing?
  */
 private static void Solve()
 {
   Solver solver = new Solver("RabbitsPheasants");
   IntVar rabbits = solver.MakeIntVar(0, 100, "rabbits");
   IntVar pheasants = solver.MakeIntVar(0, 100, "pheasants");
   solver.Add(rabbits + pheasants == 20);
   solver.Add(rabbits * 4 + pheasants * 2 == 56);
   DecisionBuilder db =
       new AssignFirstUnboundToMin(new IntVar[] {rabbits, pheasants});
   solver.NewSearch(db);
   solver.NextSolution();
   Console.WriteLine(
       "Solved Rabbits + Pheasants in {0} ms, and {1} search tree branches.",
       solver.WallTime(),  solver.Branches());
   Console.WriteLine(rabbits.ToString());
   Console.WriteLine(pheasants.ToString());
   solver.EndSearch();
 }

//.........这里部分代码省略.........
    int P = 15;
    int Q = 16;
    int R = 17;
    int S = 18;
    int T = 19;
    int U = 20;
    int V = 21;
    int W = 22;
    int Y = 23;


    String[] letters_str = {"A","B","C","D","E","F","G","H","I","J","K","L","M",
                            "N","O","P","Q","R","S","T","U","V","W","Y"};

    int num_words = 13;
    int[,] words =
      {
        {B,U,O,Y},
        {C,A,V,E},
        {C,E,L,T},
        {F,L,U,B},
        {F,O,R,K},
        {H,E,M,P},
        {J,U,D,Y},
        {J,U,N,K},
        {L,I,M,N},
        {Q,U,I,P},
        {S,W,A,G},
        {V,I,S,A},
        {W,I,S,H}
        };


    //
    // Decision variables
    //
    IntVar[] dice =  solver.MakeIntVarArray(m, 0, n-1, "dice");
    IntVar[] gcc =  solver.MakeIntVarArray(n, 6, 6, "gcc");

    //
    // Constraints
    //


    // the letters in a word must be on a different die
    for(int i = 0; i < num_words; i++) {
      solver.Add( (from j in Enumerable.Range(0, n)
                   select dice[words[i,j]]
                   ).ToArray().AllDifferent());
    }

    // there must be exactly 6 letters of each die
    /*
    for(int i = 0; i < n; i++) {
      solver.Add( ( from j in Enumerable.Range(0, m)
                    select (dice[j] == i)
                   ).ToArray().Sum() == 6 );
    }
    */
    // Use Distribute (Global Cardinality Count) instead.
    solver.Add(dice.Distribute(gcc));

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

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      for(int d = 0; d < n; d++) {
        Console.Write("die {0}: ", d);
        for(int i = 0; i < m; i++) {
          if (dice[i].Value() == d) {
            Console.Write(letters_str[i]);
          }
        }
        Console.WriteLine();
      }

      Console.WriteLine("The words with the cube label:");
      for(int i = 0; i < num_words; i++) {
        for(int j = 0; j < n; j++) {
          Console.Write("{0} ({1})", letters_str[words[i,j]], dice[words[i,j]].Value());
        }
        Console.WriteLine();
      }
      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();

  }

  /**
   *
   * Implements a (decomposition) of the global constraint circuit.
   * See http://www.hakank.org/google_or_tools/circuit.py
   *
   */
  private static void Solve(int n = 5)
  {
    Solver solver = new Solver("Circuit");


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

    //
    // Constraints
    //
    circuit(solver, x);


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


    solver.NewSearch(db);

    while (solver.NextSolution()) {
      for(int i = 0; i < n; i++) {
          Console.Write("{0} ", 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();

  }

  /**
   *
   * Solves a set covering problem.
   * See  See http://www.hakank.org/or-tools/set_covering4.py
   *
   */
  private static void Solve(int set_partition)
  {

    Solver solver = new Solver("SetCovering4");

    //
    // data
    //

    // Set partition and set covering problem from
    // Example from the Swedish book
    // Lundgren, Roennqvist, Vaebrand
    // 'Optimeringslaera' (translation: 'Optimization theory'),
    // page 408.
    int num_alternatives = 10;
    int num_objects = 8;

    // costs for the alternatives
    int[] costs = {19, 16, 18, 13, 15, 19, 15, 17, 16, 15};

    // the alternatives, and their objects
    int[,] a = {
      // 1 2 3 4 5 6 7 8    the objects
        {1,0,0,0,0,1,0,0},  // alternative 1
        {0,1,0,0,0,1,0,1},  // alternative 2
        {1,0,0,1,0,0,1,0},  // alternative 3
        {0,1,1,0,1,0,0,0},  // alternative 4
        {0,1,0,0,1,0,0,0},  // alternative 5
        {0,1,1,0,0,0,0,0},  // alternative 6
        {0,1,1,1,0,0,0,0},  // alternative 7
        {0,0,0,1,1,0,0,1},  // alternative 8
        {0,0,1,0,0,1,0,1},  // alternative 9
        {1,0,0,0,0,1,1,0}}; // alternative 10

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(num_alternatives, 0, 1, "x");
    // number of assigned senators, to be minimized
    IntVar z = x.ScalProd(costs).VarWithName("z");

    //
    // Constraints
    //


    for(int j = 0; j < num_objects; j++) {
      IntVar[] b = new IntVar[num_alternatives];
      for(int i = 0; i < num_alternatives; i++) {
        b[i] = (x[i] * a[i,j]).Var();
      }

      if (set_partition == 1) {
        solver.Add(b.Sum() >= 1);
      } else {
        solver.Add(b.Sum() == 1);
      }
    }


    //
    // objective
    //
    OptimizeVar objective = z.Minimize(1);


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

    solver.NewSearch(db, objective);

    while (solver.NextSolution()) {
      Console.WriteLine("z: " + z.Value());
      Console.Write("Selected alternatives: ");
      for(int i = 0; i < num_alternatives; i++) {
        if (x[i].Value() == 1) {
          Console.Write((i+1) + " ");
        }
      }
      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();

//.........这里部分代码省略.........

  /**
   *
   * 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();

  }

//.........这里部分代码省略.........
   * Problem 26: Shidoku from
   * "Taking Sudoku Seriously", page 61
   *   4 _  _ _
   *   3 1  _ _
   *
   *   _ _  4 1
   *   _ _  _ 2
   *
   */
  private static void Solve()
  {
    Solver solver = new Solver("Sudoku");

    //
    // data
    //
    int block_size = 2;
    IEnumerable<int> BLOCK = Enumerable.Range(0, block_size);
    int n = block_size * block_size;
    IEnumerable<int> RANGE = Enumerable.Range(0, n);

    // 0 marks an unknown value
    int[,] initial_grid = {{4, 0,  0, 0},
                           {3, 1,  0, 0},

                           {0, 0,  4, 1},
                           {0, 0,  0, 2}};
    

    //
    // Decision variables
    //
    IntVar[,] grid =  solver.MakeIntVarMatrix(n, n, 1, n, "grid");
    IntVar[] grid_flat = grid.Flatten();

    //
    // Constraints
    //  

    // init
    foreach(int i in RANGE) {
      foreach(int j in RANGE) {
        if (initial_grid[i,j] > 0) {
          solver.Add(grid[i,j] == initial_grid[i,j]);
        }
      }
    }

    
    foreach(int i in RANGE) {

      // rows
      solver.Add( (from j in RANGE
                   select grid[i,j]).ToArray().AllDifferent());

      // cols
      solver.Add( (from j in RANGE
                   select grid[j,i]).ToArray().AllDifferent());

    }

    // blocks
    foreach(int i in BLOCK) {
      foreach(int j in BLOCK) {
        solver.Add( (from di in BLOCK
                     from dj in BLOCK
                     select grid[i*block_size+di, j*block_size+dj]
                     ).ToArray().AllDifferent());
      }
    }        


    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(grid_flat,
                                          Solver.INT_VAR_SIMPLE,
                                          Solver.INT_VALUE_SIMPLE);

    solver.NewSearch(db);

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

  }

//.........这里部分代码省略.........
   * - v1 and v6
   *
   * How many hours are necessary in order that the lectures can be given
   * without clashes?
   * """
   *
   * Note: This can be seen as a coloring problem.
   *
   * Also see http://www.hakank.org/or-tools/lectures.py
   * 
   */
  private static void Solve()
  {
    Solver solver = new Solver("Lectures");

    //
    // The schedule requirements:
    // lecture a cannot be held at the same time as b
    // Note: 1-based (compensated in the constraints).
    int[,] g = 
      {
        {1, 2},
        {1, 4},
        {3, 5},
        {2, 6},
        {4, 5},
        {5, 6},
        {1, 6}
      };
    
    // number of nodes
    int n = 6;

    // number of edges
    int edges = g.GetLength(0);

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

    // Maximum color (hour) to minimize.
    // Note: since C# is 0-based, the
    // number of colors is max_c+1.
    IntVar max_c = v.Max().VarWithName("max_c");


    //
    // Constraints
    //

    // Ensure that there are no clashes
    // also, adjust to 0-base.
    for(int i = 0; i < edges; i++) {
      solver.Add(v[g[i,0]-1] != v[g[i,1]-1]);
    }

    // Symmetry breaking:
    // - v0 has the color 0,
    // - v1 has either color 0 or 1
    solver.Add(v[0] == 0);
    solver.Add(v[1] <= 1);


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

    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(v,
                                          Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
                                          Solver.ASSIGN_MIN_VALUE);

    solver.NewSearch(db, obj);

    while (solver.NextSolution()) {
      Console.WriteLine("\nmax hours: {0}", max_c.Value()+1);
      Console.WriteLine("v: " +  
                        String.Join(" ", (from i in Enumerable.Range(0, n)
                                          select v[i].Value()).ToArray()));
      for(int i = 0; i < n; i++) {
        Console.WriteLine("Lecture {0} at {1}h", i, v[i].Value());
      }
      Console.WriteLine("\n");
    }

    Console.WriteLine("\nSolutions: " + solver.Solutions());
    Console.WriteLine("WallTime: " + solver.WallTime() + "ms ");
    Console.WriteLine("Failures: " + solver.Failures());
    Console.WriteLine("Branches: " + solver.Branches());

    solver.EndSearch();

  }

    /**
       *
       *
       * Organizing a day.
       *
       * Simple scheduling problem.
       *
       * Problem formulation from ECLiPSe:
       * Slides on (Finite Domain) Constraint Logic Programming, page 38f
       * http://eclipse-clp.org/reports/eclipse.ppt
       *
       *
       * Also see http://www.hakank.org/google_or_tools/organize_day.py
       *
       */
    private static void Solve()
    {
        Solver solver = new Solver("OrganizeDay");

        int n = 4;

        int work = 0;
        int mail = 1;
        int shop = 2;
        int bank = 3;
        int[] tasks = {work, mail, shop, bank};
        int[] durations = {4,1,2,1};

        // task [i,0] must be finished before task [i,1]
        int[,] before_tasks = {
          {bank, shop},
          {mail, work}
        };

        // the valid times of the day
        int begin = 9;
        int end   = 17;

        //
        // Decision variables
        //
        IntVar[] begins = solver.MakeIntVarArray(n, begin, end, "begins");
        IntVar[] ends = solver.MakeIntVarArray(n, begin, end, "ends");

        //
        // Constraints
        //
        foreach(int t in tasks) {
          solver.Add(ends[t] == begins[t] + durations[t]);
        }

        foreach(int i in tasks) {
          foreach(int j in tasks) {
        if (i < j) {
          NoOverlap(solver,
                    begins[i], durations[i],
                    begins[j], durations[j]);
        }
          }
        }

        // specific constraints
        for(int t = 0; t < before_tasks.GetLength(0); t++) {
          solver.Add(ends[before_tasks[t,0]] <= begins[before_tasks[t,1]]);
        }

        solver.Add(begins[work] >= 11);

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

        solver.NewSearch(db);

        while (solver.NextSolution()) {
          foreach(int t in tasks) {
        Console.WriteLine("Task {0}: {1,2} .. ({2}) .. {3,2}",
                          t,
                          begins[t].Value(),
                          durations[t],
                          ends[t].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();
    }

  /**
   *
   * Olympic puzzle.
   * 
   * Benchmark for Prolog (BProlog)
   * """
   * File   : olympic.pl
   * Author : Neng-Fa ZHOU
   * Date   : 1993
   *
   * Purpose: solve a puzzle taken from Olympic Arithmetic Contest
   *
   * Given ten variables with the following configuration:
   *
   *                 X7   X8   X9   X10
   *
   *                    X4   X5   X6
   *
   *                       X2   X3
   *
   *                          X1
   *
   * We already know that X1 is equal to 3 and want to assign each variable
   * with a different integer from {1,2,...,10} such that for any three
   * variables
   *                        Xi   Xj
   *
   *                           Xk
   *
   * the following constraint is satisfied:
   *
   *                      |Xi-Xj| = Xk
   * """
   *
   * Also see http://www.hakank.org/or-tools/olympic.py
   *
   */
  private static void Solve()
  {
    Solver solver = new Solver("Olympic");

    //
    // Data
    //
    int n = 10;

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(n, 1, n, "x");
    IntVar X1  = x[0];
    IntVar X2  = x[1];
    IntVar X3  = x[2];
    IntVar X4  = x[3];
    IntVar X5  = x[4];
    IntVar X6  = x[5];
    IntVar X7  = x[6];
    IntVar X8  = x[7];
    IntVar X9  = x[8];
    IntVar X10 = x[9];


    //
    // Constraints
    //
    solver.Add(x.AllDifferent());

    solver.Add(X1 == 3);
    minus(solver, X2, X3, X1);
    minus(solver, X4, X5, X2);
    minus(solver, X5, X6, X3);
    minus(solver, X7, X8, X4);
    minus(solver, X8, X9, X5);
    minus(solver, X9, X10, X6);


    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x,
                                          Solver.INT_VAR_SIMPLE,
                                          Solver.INT_VALUE_DEFAULT);

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      for(int i = 0; i < n; i++) {
        Console.Write("{0,2} ", x[i].Value());
      }
      Console.WriteLine();
    }

    Console.WriteLine("\nSolutions: " + solver.Solutions());
    Console.WriteLine("WallTime: " + solver.WallTime() + "ms ");
    Console.WriteLine("Failures: " + solver.Failures());
    Console.WriteLine("Branches: " + solver.Branches());

    solver.EndSearch();

  }