C# Solver.Solutions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();

  }

  /**
   *
   * Scheduling speakers problem
   *
   *  From Rina Dechter, Constraint Processing, page 72
   *  Scheduling of 6 speakers in 6 slots.
   *
   * See http://www.hakank.org/google_or_tools/scheduling_speakers.py
   *
   */
  private static void Solve()
  {
    Solver solver = new Solver("SchedulingSpeakers");


    // number of speakers
    int n = 6;

    // slots available to speak
    int[][] available = {
                    // Reasoning:
      new int[] {3,4,5,6},    // 2) the only one with 6 after speaker F -> 1
      new int[] {3,4},        // 5) 3 or 4
      new int[] {2,3,4,5},    // 3) only with 5 after F -> 1 and A -> 6
      new int[] {2,3,4},      // 4) only with 2 after C -> 5 and F -> 1
      new int[] {3,4},        // 5) 3 or 4
      new int[] {1,2,3,4,5,6} // 1) the only with 1
    };


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

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

    for(int i = 0; i < n; i++) {
      solver.Add(x[i].Member(available[i]));
    }


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

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      Console.WriteLine(string.Join(",", (from i in x select i.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();

  }

    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;
    }

  /**
   *
   * 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 a set covering problem.
   * See  See http://www.hakank.org/or-tools/set_covering2.py
   *
   */
  private static void Solve()
  {

    Solver solver = new Solver("SetCovering2");

    //
    // data
    //

    // Example 9.1-2 from
    // Taha "Operations Research - An Introduction",
    // page 354ff.
    // Minimize the number of security telephones in street
    // corners on a campus.

    int n = 8;            // maximum number of corners
    int num_streets = 11; // number of connected streets

    // corners of each street
    // Note: 1-based (handled below)
    int[,] corner = {{1,2},
                     {2,3},
                     {4,5},
                     {7,8},
                     {6,7},
                     {2,6},
                     {1,6},
                     {4,7},
                     {2,4},
                     {5,8},
                     {3,5}};

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(n, 0, 1, "x");
    // number of telephones, to be minimized
    IntVar z = x.Sum().Var();

    //
    // Constraints
    //

    // ensure that all streets are covered
    for(int i = 0; i < num_streets; i++) {
      solver.Add(x[corner[i,0] - 1] + x[corner[i,1] - 1]  >= 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: {0}", z.Value());
      Console.Write("x: ");
      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();

  }

  /**
   *
   * 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();

  }

//.........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();

  }

//.........这里部分代码省略.........
    IntVar[] all = new IntVar[2 * n * n]; // for branching
    for(int i = 0; i < n*n; i++) {
      all[i] = hates_flat[i];
      all[(n*n)+i] = richer_flat[i]; 
    }

    //
    // Constraints
    //

    // Agatha, the butler, and Charles live in Dreadsbury Mansion, and
    // are the only ones to live there.

    // A killer always hates, and is no richer than his victim.
    //     hates[the_killer, the_victim] == 1
    //     hates_flat[the_killer * n + the_victim] == 1
    solver.Add(hates_flat.Element(the_killer * n + the_victim) == 1);

    //    richer[the_killer, the_victim] == 0
    solver.Add(richer_flat.Element(the_killer * n + the_victim) == 0);

    // define the concept of richer:
    //     no one is richer than him-/herself...
    for(int i = 0; i < n; i++) {
      solver.Add(richer[i,i] == 0);
    }

    // (contd...) if i is richer than j then j is not richer than i
    //   if (i != j) =>
    //       ((richer[i,j] = 1) <=> (richer[j,i] = 0))
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < n; j++) {
        if (i != j) {
          solver.Add((richer[i, j]==1) - (richer[j, i]==0) == 0);
        }
      }
    }

    // Charles hates no one that Agatha hates.
    //    forall i in 0..2:
    //       (hates[agatha, i] = 1) => (hates[charles, i] = 0)
    for(int i = 0; i < n; i++) {
      solver.Add((hates[agatha,i]==1) - (hates[charles,i]==0) <= 0);

    }

    // Agatha hates everybody except the butler.
    solver.Add(hates[agatha,charles] == 1);
    solver.Add(hates[agatha,agatha] == 1);
    solver.Add(hates[agatha,butler] == 0);

    // The butler hates everyone not richer than Aunt Agatha.
    //    forall i in 0..2:
    //       (richer[i, agatha] = 0) => (hates[butler, i] = 1)
    for(int i = 0; i < n; i++) {
      solver.Add((richer[i,agatha] == 0)-(hates[butler,i] == 1)<=0);
    }

    // The butler hates everyone whom Agatha hates.
    //     forall i : 0..2:
    //         (hates[agatha, i] = 1) => (hates[butler, i] = 1)
    for(int i = 0; i < n; i++) {
      solver.Add((hates[agatha,i] == 1)-(hates[butler,i] == 1)<=0);
    }

    // Noone hates everyone.
    //     forall i in 0..2:
    //         (sum j in 0..2: hates[i,j]) <= 2
    for(int i = 0; i < n; i++) {
      solver.Add((from j in Enumerable.Range(0, n)
                  select hates[i,j]
                  ).ToArray().Sum() <= 2 );
    }


    // Who killed Agatha?
    solver.Add(the_victim == agatha);


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

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      Console.WriteLine("the_killer: " + the_killer.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();

  }

  /**
   *
   * 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.........

//.........这里部分代码省略.........

      // Another representation of Problem 1
      int[,] problem1 = {
        {8,8,0,9, 6},
        {7,1,1,1, 0},
        {2,1,7,2, 0},
        {6,6,6,6, 4},
        {1,1,1,1, 0},
        {3,2,1,3, 0},
        {7,6,6,2, 2},
        {9,3,1,2, 1},
        {0,0,0,0, 4},
        {2,2,2,2, 0},
        {3,3,3,3, 0},
        {5,5,5,5, 0},
        {8,1,9,3, 3},
        {8,0,9,6, 5},
        {7,7,7,7, 0},
        {9,9,9,9, 4},
        {7,7,5,6, 1},
        {6,8,5,5, 3},
        {9,8,8,1, 5},
        {5,5,3,1, 0}
      };

      for(int i = 0; i < problem1.GetLength(0); i++) {
        solver.Add( (from j in Enumerable.Range(0, 4)
                     select all[problem1[i,j]]
                     ).ToArray().Sum() == problem1[i,4] );
      }

      solver.Add(all[2]+all[5]+all[8]+all[1] == x);

    } else if (p == 3) {

      // Problem 2
      solver.Add(x8+x8+x0+x9 == 6);
      solver.Add(x7+x6+x6+x2 == 2);
      solver.Add(x9+x3+x1+x2 == 1);
      solver.Add(x8+x1+x9+x3 == 3);
      solver.Add(x8+x0+x9+x6 == 5);
      solver.Add(x7+x7+x5+x6 == 1);
      solver.Add(x6+x8+x5+x5 == 3);
      solver.Add(x9+x8+x8+x1 == 5);

      // The unknown
      solver.Add(x2+x5+x8+x1 == x);

    } else {

      // Another representation of Problem 2
      int[,] problem2 = {
        {8,8,0,9, 6},
        {7,6,6,2, 2},
        {9,3,1,2, 1},
        {8,1,9,3, 3},
        {8,0,9,6, 5},
        {7,7,5,6, 1},
        {6,8,5,5, 3},
        {9,8,8,1, 5}
      };

      for(int i = 0; i < problem2.GetLength(0); i++) {
        solver.Add( (from j in Enumerable.Range(0, 4)
                     select all[problem2[i,j]]
                     ).ToArray().Sum() == problem2[i,4] );
      }


      solver.Add(all[2]+all[5]+all[8]+all[1] == x);
    }



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


    solver.NewSearch(db);
    int c = 0;
    while (solver.NextSolution()) {
      Console.Write("x: {0}  x0..x9: ", x.Value());
      for(int i = 0; i < n; i++) {
        Console.Write(all[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.........
                        {22, 0, 15, 0, 0},
                        {23, 0, 1, 14, 11},
                        {0, 25, 0, 0, 12}};
      puzzle = puzzle3;

    } else if (model == 4) {
      // problem 2 (Practice)
      int[,] puzzle4 = {{0, 0, 0, 0, 14},
                        {0, 18, 12, 0, 0},
                        {0, 0, 17, 4, 5},
                        {0, 0, 7, 0, 0},
                        {9, 8, 25, 1, 0}};
      puzzle = puzzle4;

    } else if (model == 5) {
      // problem 3 (Beginner)
      int[,] puzzle5 = {{0, 26, 0, 0, 0, 18},
                        {0, 0, 27, 0, 0, 19},
                        {31, 23, 0, 0, 14, 0},
                        {0, 33, 8, 0, 15, 1},
                        {0, 0, 0, 5, 0, 0},
                        {35, 36, 0, 10, 0, 0}};
      puzzle = puzzle5;

    } else if (model == 6) {
      // Problem 15 (Intermediate)
      int[,] puzzle6 = {{64, 0, 0, 0, 0, 0, 0, 0},
                        {1, 63, 0, 59, 15, 57, 53, 0},
                        {0, 4, 0, 14, 0, 0, 0, 0},
                        {3, 0, 11, 0, 20, 19, 0, 50},
                        {0, 0, 0, 0, 22, 0, 48, 40},
                        {9, 0, 0, 32, 23, 0, 0, 41},
                        {27, 0, 0, 0, 36, 0, 46, 0},
                        {28, 30, 0, 35, 0, 0, 0, 0}};
      puzzle = puzzle6;
    }

    int r = puzzle.GetLength(0);
    int c = puzzle.GetLength(1);

    Console.WriteLine();
    Console.WriteLine("----- Solving problem {0} -----", model);
    Console.WriteLine();

    PrintMatrix(puzzle);

    //
    // Decision variables
    //
    IntVar[] positions = solver.MakeIntVarArray(r*c, 0, r * c - 1, "p");


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

    //
    // Fill in the clues
    //
    for(int i = 0; i < r; i++) {
      for(int j = 0; j < c; j++) {
        if (puzzle[i,j] > 0) {
          solver.Add(positions[puzzle[i,j] - 1] == i * c + j);
        }
      }
    }

    // Consecutive numbers much touch each other in the grid.
    // We use an allowed assignment constraint to model it.
    IntTupleSet close_tuples = BuildPairs(r, c);
    for(int k = 1; k < r * c - 1; k++) {
      IntVar[] tmp = new IntVar[] {positions[k], positions[k + 1]};
      solver.Add(tmp.AllowedAssignments(close_tuples));
    }


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

    solver.NewSearch(db);

    int num_solution = 0;
    while (solver.NextSolution()) {
      num_solution++;
      PrintOneSolution(positions, r, c, num_solution);
    }

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

    solver.EndSearch();

  }

//.........这里部分代码省略.........
  {

    Solver solver = new Solver("KenKen2");

    // size of matrix
    int n = 6;
    IEnumerable<int> RANGE = Enumerable.Range(0, n);

    // For a better view of the problem, see
    //  http://en.wikipedia.org/wiki/File:KenKenProblem.svg

    // hints
    //  sum, the hints
    // Note: this is 1-based
    int[][] problem =
      {
        new int[] { 11,  1,1, 2,1},
        new int[] {  2,  1,2, 1,3},
        new int[] { 20,  1,4, 2,4},
        new int[] {  6,  1,5, 1,6, 2,6, 3,6},
        new int[] {  3,  2,2, 2,3},
        new int[] {  3,  2,5, 3,5},
        new int[] {240,  3,1, 3,2, 4,1, 4,2},
        new int[] {  6,  3,3, 3,4},
        new int[] {  6,  4,3, 5,3},
        new int[] {  7,  4,4, 5,4, 5,5},
        new int[] { 30,  4,5, 4,6},
        new int[] {  6,  5,1, 5,2},
        new int[] {  9,  5,6, 6,6},
        new int[] {  8,  6,1, 6,2, 6,3},
        new int[] {  2,  6,4, 6,5}
      };


    int num_p = problem.GetLength(0); // Number of segments

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

    //
    // Constraints
    //

    //
    //  alldifferent rows and columns
    foreach(int i in RANGE) {
      // rows
      solver.Add( (from j in RANGE select x[i,j]).ToArray().AllDifferent());

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

    }


    // Calculate the segments
    for(int i = 0; i < num_p; i++) {

      int[] segment = problem[i];

      // Remove the sum from the segment
      int len = segment.Length-1;
      int[] s2 = new int[len];
      Array.Copy(segment, 1, s2, 0, len);

      // sum this segment
      calc(solver, s2, x, segment[0]);

    }

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

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
          Console.Write(x[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.........
      // size of crew
      IntVar[] tmp = new IntVar[num_persons];
      for(int p = 0; p < num_persons; p++) {
        tmp[p] = crew[f,p];
      }
      solver.Add(tmp.Sum() == required_crew[f,0]);

      // attributes and requirements
      for(int a = 0; a < 5; a++) {
        IntVar[] tmp2 = new IntVar[num_persons];
        for(int p = 0; p < num_persons; p++) {
          tmp2[p] = (crew[f,p]*attributes[p,a]).Var();
        }
        solver.Add(tmp2.Sum() >= required_crew[f,a+1]);
      }
    }

    // after a flight, break for at least two flights
    for(int f = 0; f < num_flights - 2; f++) {
      for(int i = 0; i < num_persons; i++) {
        solver.Add(crew[f,i] + crew[f+1,i] + crew[f+2,i] <= 1);
      }
    }

    // extra contraint: all must work at least two of the flights
    /*
    for(int p = 0; p < num_persons; p++) {
      IntVar[] tmp = new IntVar[num_flights];
      for(int f = 0; f < num_flights; f++) {
        tmp[f] = crew[f,p];
      }
      solver.Add(tmp.Sum() >= 2);
    }
    */


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

    if (minimize > 0) {
      OptimizeVar obj = num_working.Minimize(1);
      solver.NewSearch(db, obj);
    } else {
      solver.NewSearch(db);
    }

    int num_solutions = 0;
    while (solver.NextSolution()) {
      num_solutions++;
      Console.WriteLine("Solution #{0}", num_solutions);
      Console.WriteLine("Number working: {0}", num_working.Value());

      for(int f = 0; f < num_flights; f++) {
        for(int p = 0; p < num_persons; p++) {
          Console.Write(crew[f,p].Value() + " ");
        }
        Console.WriteLine();
      }
      Console.WriteLine("\nFlights: ");
      for(int f = 0; f < num_flights; f++) {
        Console.Write("Flight #{0}: ", f);
        for(int p = 0; p < num_persons; p++) {
          if (crew[f, p].Value() == 1) {
            Console.Write(names[p] + " ");
          }
        }
        Console.WriteLine();
      }

      Console.WriteLine("\nCrew:");
      for(int p = 0; p < num_persons; p++) {
        Console.Write("{0,-10}", names[p]);
        for(int f = 0; f < num_flights; f++) {
          if (crew[f,p].Value() == 1) {
            Console.Write(f + " ");
          }
        }
        Console.WriteLine();
      }

      Console.WriteLine();

      if (num_solutions >= sols) {
        break;
      }

    }

    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();

  }