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  /** \author Jia Pan  */
  
  #ifndef FCL_HIERARCHY_TREE_H
  #define FCL_HIERARCHY_TREE_H
  
  #include <vector>
  #include <map>
  #include <functional>
  #include "fcl/BV/AABB.h"
  #include "fcl/broadphase/morton.h"
  
  namespace fcl
  {
  
  /// @brief dynamic AABB tree node
  template<typename BV>
  struct NodeBase
  {
    /// @brief the bounding volume for the node
    BV bv;
  
    /// @brief pointer to parent node
    NodeBase<BV>* parent;
  
    /// @brief whether is a leaf
    bool isLeaf() const { return (children[1] == NULL); }
  
    /// @brief whether is internal node
    bool isInternal() const { return !isLeaf(); }
  
    union
    {
      /// @brief for leaf node, children nodes
      NodeBase<BV>* children[2];
      void* data;
    };
  
    /// @brief morton code for current BV
    FCL_UINT32 code;
  
    NodeBase()
    {
      parent = NULL;
      children[0] = NULL;
      children[1] = NULL;
    }
  };
  
  
  /// @brief Compare two nodes accoording to the d-th dimension of node center
  template<typename BV>
  bool nodeBaseLess(NodeBase<BV>* a, NodeBase<BV>* b, int d)
  {
    if(a->bv.center()[d] < b->bv.center()[d]) return true;
    return false;
  }
  
  /// @brief select from node1 and node2 which is close to a given query. 0 for node1 and 1 for node2
  template<typename BV>
  size_t select(const NodeBase<BV>& query, const NodeBase<BV>& node1, const NodeBase<BV>& node2)
  {
    return 0;
  }
  
  template<>
  size_t select(const NodeBase<AABB>& node, const NodeBase<AABB>& node1, const NodeBase<AABB>& node2);
  
  /// @brief select from node1 and node2 which is close to a given query bounding volume. 0 for node1 and 1 for node2
  template<typename BV>
  size_t select(const BV& query, const NodeBase<BV>& node1, const NodeBase<BV>& node2)
  {
    return 0;
  }
  
  template<>
  size_t select(const AABB& query, const NodeBase<AABB>& node1, const NodeBase<AABB>& node2);
  
  
  /// @brief Class for hierarchy tree structure
  template<typename BV>
  class HierarchyTree
  {
    typedef NodeBase<BV> NodeType;
    typedef typename std::vector<NodeBase<BV>* >::iterator NodeVecIterator;
    typedef typename std::vector<NodeBase<BV>* >::const_iterator NodeVecConstIterator;
  
    struct SortByMorton
    {
      bool operator() (const NodeType* a, const NodeType* b) const
      {
        return a->code < b->code;
      }
    };
  
  public:
  
    /// @brief Create hierarchy tree with suitable setting.
    /// bu_threshold decides the height of tree node to start bottom-up construction / optimization;
    /// topdown_level decides different methods to construct tree in topdown manner.
    /// lower level method constructs tree with better quality but is slower.
    HierarchyTree(int bu_threshold_ = 16, int topdown_level_ = 0);
  
    ~HierarchyTree();
    
    /// @brief Initialize the tree by a set of leaves using algorithm with a given level.
    void init(std::vector<NodeType*>& leaves, int level = 0);
  
    /// @brief Insest a node
    NodeType* insert(const BV& bv, void* data);
  
    /// @brief Remove a leaf node
    void remove(NodeType* leaf);
  
    /// @brief Clear the tree 
    void clear();
  
    /// @brief Whether the tree is empty 
    bool empty() const;
  
    /// @brief update one leaf node 
    void update(NodeType* leaf, int lookahead_level = -1);
  
    /// @brief update the tree when the bounding volume of a given leaf has changed
    bool update(NodeType* leaf, const BV& bv);
  
    /// @brief update one leaf's bounding volume, with prediction 
    bool update(NodeType* leaf, const BV& bv, const Vec3f& vel, FCL_REAL margin);
  
    /// @brief update one leaf's bounding volume, with prediction 
    bool update(NodeType* leaf, const BV& bv, const Vec3f& vel);
  
    /// @brief get the max height of the tree
    size_t getMaxHeight() const;
  
    /// @brief get the max depth of the tree
    size_t getMaxDepth() const;
  
    /// @brief balance the tree from bottom 
    void balanceBottomup();
  
    /// @brief balance the tree from top 
    void balanceTopdown();
    
    /// @brief balance the tree in an incremental way 
    void balanceIncremental(int iterations);
    
    /// @brief refit the tree, i.e., when the leaf nodes' bounding volumes change, update the entire tree in a bottom-up manner
    void refit();
  
    /// @brief extract all the leaves of the tree 
    void extractLeaves(const NodeType* root, std::vector<NodeType*>& leaves) const;
  
    /// @brief number of leaves in the tree
    size_t size() const;
  
    /// @brief get the root of the tree
    NodeType* getRoot() const;
  
    NodeType*& getRoot();
  
    /// @brief print the tree in a recursive way
    void print(NodeType* root, int depth);
  
  private:
  
    /// @brief construct a tree for a set of leaves from bottom -- very heavy way 
    void bottomup(const NodeVecIterator lbeg, const NodeVecIterator lend);
  
    /// @brief construct a tree for a set of leaves from top 
    NodeType* topdown(const NodeVecIterator lbeg, const NodeVecIterator lend);
  
    /// @brief compute the maximum height of a subtree rooted from a given node
    size_t getMaxHeight(NodeType* node) const;
  
    /// @brief compute the maximum depth of a subtree rooted from a given node
    void getMaxDepth(NodeType* node, size_t depth, size_t& max_depth) const;
  
    /// @brief construct a tree from a list of nodes stored in [lbeg, lend) in a topdown manner.
    /// During construction, first compute the best split axis as the axis along with the longest AABB edge.
    /// Then compute the median of all nodes' center projection onto the axis and using it as the split threshold.
    NodeType* topdown_0(const NodeVecIterator lbeg, const NodeVecIterator lend);
  
    /// @brief construct a tree from a list of nodes stored in [lbeg, lend) in a topdown manner.
    /// During construction, first compute the best split thresholds for different axes as the average of all nodes' center.
    /// Then choose the split axis as the axis whose threshold can divide the nodes into two parts with almost similar size.
    /// This construction is more expensive then topdown_0, but also can provide tree with better quality.
    NodeType* topdown_1(const NodeVecIterator lbeg, const NodeVecIterator lend);
  
    /// @brief init tree from leaves in the topdown manner (topdown_0 or topdown_1)
    void init_0(std::vector<NodeType*>& leaves);
  
    /// @brief init tree from leaves using morton code. It uses morton_0, i.e., for nodes which is of depth more than the maximum bits of the morton code,
    /// we use bottomup method to construct the subtree, which is slow but can construct tree with high quality.
    void init_1(std::vector<NodeType*>& leaves);
  
    /// @brief init tree from leaves using morton code. It uses morton_0, i.e., for nodes which is of depth more than the maximum bits of the morton code,
    /// we split the leaves into two parts with the same size simply using the node index. 
    void init_2(std::vector<NodeType*>& leaves);
  
    /// @brief init tree from leaves using morton code. It uses morton_2, i.e., for all nodes, we simply divide the leaves into parts with the same size simply using the node index.
    void init_3(std::vector<NodeType*>& leaves);
    
    NodeType* mortonRecurse_0(const NodeVecIterator lbeg, const NodeVecIterator lend, const FCL_UINT32& split, int bits);
  
    NodeType* mortonRecurse_1(const NodeVecIterator lbeg, const NodeVecIterator lend, const FCL_UINT32& split, int bits);
  
    NodeType* mortonRecurse_2(const NodeVecIterator lbeg, const NodeVecIterator lend);
  
    /// @brief update one leaf node's bounding volume 
    void update_(NodeType* leaf, const BV& bv);
  
    /// @brief sort node n and its parent according to their memory position 
    NodeType* sort(NodeType* n, NodeType*& r);
    
    /// @brief Insert a leaf node and also update its ancestors 
    void insertLeaf(NodeType* root, NodeType* leaf);
  
    /// @brief Remove a leaf. The leaf node itself is not deleted yet, but all the unnecessary internal nodes are deleted.
    /// return the node with the smallest depth and is influenced by the remove operation 
    NodeType* removeLeaf(NodeType* leaf);
  
    /// @brief Delete all internal nodes and return all leaves nodes with given depth from root 
    void fetchLeaves(NodeType* root, std::vector<NodeType*>& leaves, int depth = -1);
  
    static size_t indexOf(NodeType* node);
  
    /// @brief create one node (leaf or internal)  
    NodeType* createNode(NodeType* parent, 
                         const BV& bv,
                         void* data);
  
    NodeType* createNode(NodeType* parent,
                         const BV& bv1,
                         const BV& bv2,
                         void* data);
    
    NodeType* createNode(NodeType* parent,
                         void* data);
  
    void deleteNode(NodeType* node);
  
    void recurseDeleteNode(NodeType* node);
  
    void recurseRefit(NodeType* node);
  
    static BV bounds(const std::vector<NodeType*>& leaves);
  
    static BV bounds(const NodeVecIterator lbeg, const NodeVecIterator lend);
  
  protected:
    NodeType* root_node;
  
    size_t n_leaves;
  
    unsigned int opath;
  
    /// This is a one NodeType cache, the reason is that we need to remove a node and then add it again frequently. 
    NodeType* free_node; 
  
    int max_lookahead_level;
    
  public:
    /// @brief decide which topdown algorithm to use
    int topdown_level;
  
    /// @brief decide the depth to use expensive bottom-up algorithm
    int bu_threshold;
  };
  
  
  template<>
  bool HierarchyTree<AABB>::update(NodeBase<AABB>* leaf, const AABB& bv_, const Vec3f& vel, FCL_REAL margin);
  
  template<>
  bool HierarchyTree<AABB>::update(NodeBase<AABB>* leaf, const AABB& bv_, const Vec3f& vel);
  
  
  namespace implementation_array
  {
  
  template<typename BV>
  struct NodeBase
  {
    BV bv;
  
    union
    {
      size_t parent;
      size_t next;
    };
    
    union
    {
      size_t children[2];
      void* data;
    };
  
    FCL_UINT32 code;
    
    bool isLeaf() const { return (children[1] == (size_t)(-1)); }
    bool isInternal() const { return !isLeaf(); }
  };
   
  
  
  /// @brief Functor comparing two nodes
  template<typename BV>
  struct nodeBaseLess
  {
    nodeBaseLess(const NodeBase<BV>* nodes_, size_t d_) : nodes(nodes_),
                                                          d(d_)
    {}
  
    bool operator() (size_t i, size_t j) const
    {
      if(nodes[i].bv.center()[d] < nodes[j].bv.center()[d])
        return true;
      return false;
    }
  
  private:
  
    /// @brief the nodes array
    const NodeBase<BV>* nodes;
    
    /// @brief the dimension to compare
    size_t d;
  };
  
  
  /// @brief select the node from node1 and node2 which is close to the query-th node in the nodes. 0 for node1 and 1 for node2.
  template<typename BV> 
  size_t select(size_t query, size_t node1, size_t node2, NodeBase<BV>* nodes)
  {
    return 0;
  }
  
  template<>
  size_t select(size_t query, size_t node1, size_t node2, NodeBase<AABB>* nodes);
  
  /// @brief select the node from node1 and node2 which is close to the query AABB. 0 for node1 and 1 for node2.
  template<typename BV>
  size_t select(const BV& query, size_t node1, size_t node2, NodeBase<BV>* nodes)
  {
    return 0;
  }
  
  template<>
  size_t select(const AABB& query, size_t node1, size_t node2, NodeBase<AABB>* nodes);
  
  /// @brief Class for hierarchy tree structure
  template<typename BV>
  class HierarchyTree
  {
    typedef NodeBase<BV> NodeType;
    
    struct SortByMorton
    {
      bool operator() (size_t a, size_t b) const
      {
        if((a != NULL_NODE) && (b != NULL_NODE))
          return nodes[a].code < nodes[b].code;
        else if(a == NULL_NODE)
          return split < nodes[b].code;
        else if(b == NULL_NODE)
          return nodes[a].code < split;
  
        return false;
      }
  
      NodeType* nodes;
      FCL_UINT32 split;
    };
  
  public:
    /// @brief Create hierarchy tree with suitable setting.
    /// bu_threshold decides the height of tree node to start bottom-up construction / optimization;
    /// topdown_level decides different methods to construct tree in topdown manner.
    /// lower level method constructs tree with better quality but is slower.
    HierarchyTree(int bu_threshold_ = 16, int topdown_level_ = 0);
  
    ~HierarchyTree();
  
    /// @brief Initialize the tree by a set of leaves using algorithm with a given level.
    void init(NodeType* leaves, int n_leaves_, int level = 0);
  
    /// @brief Initialize the tree by a set of leaves using algorithm with a given level.
    size_t insert(const BV& bv, void* data);
  
    /// @brief Remove a leaf node
    void remove(size_t leaf);
  
    /// @brief Clear the tree 
    void clear();
  
    /// @brief Whether the tree is empty 
    bool empty() const;
   
    /// @brief update one leaf node 
    void update(size_t leaf, int lookahead_level = -1);
  
    /// @brief update the tree when the bounding volume of a given leaf has changed
    bool update(size_t leaf, const BV& bv);
  
    /// @brief update one leaf's bounding volume, with prediction 
    bool update(size_t leaf, const BV& bv, const Vec3f& vel, FCL_REAL margin);
  
    /// @brief update one leaf's bounding volume, with prediction 
    bool update(size_t leaf, const BV& bv, const Vec3f& vel);
  
    /// @brief get the max height of the tree
    size_t getMaxHeight() const;
  
    /// @brief get the max depth of the tree
    size_t getMaxDepth() const;
  
    /// @brief balance the tree from bottom 
    void balanceBottomup();
  
    /// @brief balance the tree from top 
    void balanceTopdown();
  
    /// @brief balance the tree in an incremental way 
    void balanceIncremental(int iterations);
  
    /// @brief refit the tree, i.e., when the leaf nodes' bounding volumes change, update the entire tree in a bottom-up manner
    void refit();
  
    /// @brief extract all the leaves of the tree 
    void extractLeaves(size_t root, NodeType*& leaves) const;
  
    /// @brief number of leaves in the tree
    size_t size() const;
  
    /// @brief get the root of the tree
    size_t getRoot() const;
  
    /// @brief get the pointer to the nodes array
    NodeType* getNodes() const;
  
    /// @brief print the tree in a recursive way
    void print(size_t root, int depth);
  
  private:
  
    /// @brief construct a tree for a set of leaves from bottom -- very heavy way 
    void bottomup(size_t* lbeg, size_t* lend);
    
    /// @brief construct a tree for a set of leaves from top 
    size_t topdown(size_t* lbeg, size_t* lend);
  
    /// @brief compute the maximum height of a subtree rooted from a given node
    size_t getMaxHeight(size_t node) const;
  
    /// @brief compute the maximum depth of a subtree rooted from a given node
    void getMaxDepth(size_t node, size_t depth, size_t& max_depth) const;
  
    /// @brief construct a tree from a list of nodes stored in [lbeg, lend) in a topdown manner.
    /// During construction, first compute the best split axis as the axis along with the longest AABB edge.
    /// Then compute the median of all nodes' center projection onto the axis and using it as the split threshold.
    size_t topdown_0(size_t* lbeg, size_t* lend);
  
    /// @brief construct a tree from a list of nodes stored in [lbeg, lend) in a topdown manner.
    /// During construction, first compute the best split thresholds for different axes as the average of all nodes' center.
    /// Then choose the split axis as the axis whose threshold can divide the nodes into two parts with almost similar size.
    /// This construction is more expensive then topdown_0, but also can provide tree with better quality.
    size_t topdown_1(size_t* lbeg, size_t* lend);
  
    /// @brief init tree from leaves in the topdown manner (topdown_0 or topdown_1)
    void init_0(NodeType* leaves, int n_leaves_);
  
    /// @brief init tree from leaves using morton code. It uses morton_0, i.e., for nodes which is of depth more than the maximum bits of the morton code,
    /// we use bottomup method to construct the subtree, which is slow but can construct tree with high quality.
    void init_1(NodeType* leaves, int n_leaves_);
  
    /// @brief init tree from leaves using morton code. It uses morton_0, i.e., for nodes which is of depth more than the maximum bits of the morton code,
    /// we split the leaves into two parts with the same size simply using the node index. 
    void init_2(NodeType* leaves, int n_leaves_);
  
    /// @brief init tree from leaves using morton code. It uses morton_2, i.e., for all nodes, we simply divide the leaves into parts with the same size simply using the node index.
    void init_3(NodeType* leaves, int n_leaves_);
  
    size_t mortonRecurse_0(size_t* lbeg, size_t* lend, const FCL_UINT32& split, int bits);
  
    size_t mortonRecurse_1(size_t* lbeg, size_t* lend, const FCL_UINT32& split, int bits);
  
    size_t mortonRecurse_2(size_t* lbeg, size_t* lend);
  
    /// @brief update one leaf node's bounding volume 
    void update_(size_t leaf, const BV& bv);
  
    /// @brief Insert a leaf node and also update its ancestors 
    void insertLeaf(size_t root, size_t leaf);
  
    /// @brief Remove a leaf. The leaf node itself is not deleted yet, but all the unnecessary internal nodes are deleted.
    /// return the node with the smallest depth and is influenced by the remove operation 
    size_t removeLeaf(size_t leaf);
  
    /// @brief Delete all internal nodes and return all leaves nodes with given depth from root 
    void fetchLeaves(size_t root, NodeType*& leaves, int depth = -1);
  
    size_t indexOf(size_t node);
  
    size_t allocateNode();
  
    /// @brief create one node (leaf or internal)
    size_t createNode(size_t parent, 
                      const BV& bv1,
                      const BV& bv2,
                      void* data);
  
    size_t createNode(size_t parent,
                      const BV& bv, 
                      void* data);
  
    size_t createNode(size_t parent,
                      void* data);
  
    void deleteNode(size_t node);
  
    void recurseRefit(size_t node);
  
  protected:
    size_t root_node;
    NodeType* nodes;
    size_t n_nodes;
    size_t n_nodes_alloc;
    
    size_t n_leaves;
    size_t freelist;
    unsigned int opath;
  
    int max_lookahead_level;
  
  public:
    /// @brief decide which topdown algorithm to use
    int topdown_level;
  
    /// @brief decide the depth to use expensive bottom-up algorithm
    int bu_threshold;
  
  public:
    static const size_t NULL_NODE = -1;
  };
  
  template<typename BV>
  const size_t HierarchyTree<BV>::NULL_NODE;
  
  }
  
  }
  
  
  #include "fcl/broadphase/hierarchy_tree.hxx"
  
  
  #endif
  