/** Meek's rule R3. If a--b, a--c, a--d, c-->b, c-->b, then orient a-->b. */
  public static boolean meekR3(Graph graph, Knowledge knowledge) {

    List<Node> nodes = graph.getNodes();
    boolean changed = false;

    for (Node a : nodes) {
      List<Node> adjacentNodes = graph.getAdjacentNodes(a);

      if (adjacentNodes.size() < 3) {
        continue;
      }

      for (Node b : adjacentNodes) {
        List<Node> otherAdjacents = new LinkedList<Node>(adjacentNodes);
        otherAdjacents.remove(b);

        if (!graph.isUndirectedFromTo(a, b)) {
          continue;
        }

        ChoiceGenerator cg = new ChoiceGenerator(otherAdjacents.size(), 2);
        int[] combination;

        while ((combination = cg.next()) != null) {
          Node c = otherAdjacents.get(combination[0]);
          Node d = otherAdjacents.get(combination[1]);

          if (graph.isAdjacentTo(c, d)) {
            continue;
          }

          if (!graph.isUndirectedFromTo(a, c)) {
            continue;
          }

          if (!graph.isUndirectedFromTo(a, d)) {
            continue;
          }

          if (graph.isDirectedFromTo(c, b) && graph.isDirectedFromTo(d, b)) {
            if (isArrowpointAllowed(a, b, knowledge)) {
              graph.setEndpoint(a, b, Endpoint.ARROW);
              TetradLogger.getInstance()
                  .edgeOriented(SearchLogUtils.edgeOrientedMsg("Meek R3", graph.getEdge(a, b)));
              changed = true;
              break;
            }
          }
        }
      }
    }

    return changed;
  }
  /** If */
  public static boolean meekR2(Graph graph, Knowledge knowledge) {
    List<Node> nodes = graph.getNodes();
    boolean changed = false;

    for (Node a : nodes) {
      List<Node> adjacentNodes = graph.getAdjacentNodes(a);

      if (adjacentNodes.size() < 2) {
        continue;
      }

      ChoiceGenerator cg = new ChoiceGenerator(adjacentNodes.size(), 2);
      int[] combination;

      while ((combination = cg.next()) != null) {
        Node b = adjacentNodes.get(combination[0]);
        Node c = adjacentNodes.get(combination[1]);

        if (graph.isDirectedFromTo(b, a)
            && graph.isDirectedFromTo(a, c)
            && graph.isUndirectedFromTo(b, c)) {
          if (isArrowpointAllowed(b, c, knowledge)) {
            graph.setEndpoint(b, c, Endpoint.ARROW);
            TetradLogger.getInstance()
                .edgeOriented(SearchLogUtils.edgeOrientedMsg("Meek R2", graph.getEdge(b, c)));
          }
        } else if (graph.isDirectedFromTo(c, a)
            && graph.isDirectedFromTo(a, b)
            && graph.isUndirectedFromTo(c, b)) {
          if (isArrowpointAllowed(c, b, knowledge)) {
            graph.setEndpoint(c, b, Endpoint.ARROW);
            TetradLogger.getInstance()
                .edgeOriented(SearchLogUtils.edgeOrientedMsg("Meek R2", graph.getEdge(c, b)));
          }
        }
      }
    }

    return changed;
  }