红黑树实施

Question

这是我对红黑树类的实现，它具有嵌套类Position，Node，Binary Search Tree，RBI等等：

    #include <iostream>

using namespace std;

template <typename Key, typename Element>
class RBTree : public BinarySearchTree<Key, Element, RBItem<Key,Element> > {
protected:                      // local types
  typedef RBItem<Key, Element>      Item;       // a tree node item
  typedef BinarySearchTree<Key, Element, Item>  BST;    // base search tree
  typedef BST::BTPosition       BTPosition; // a tree position
public:                         // public types
  typedef BST::Position         Position;   // a position
protected:                      // local utilities
  Color color(const BTPosition& p) const {      // get position's color
    if (T.isExternal(p)) return BLACK;          // externals are black
    return p.element().color();
  }
  bool isRed(const BTPosition& p) const         // is p red?
    { return color(p) == RED; }
  bool isBlack(const BTPosition& p) const       // is p black?
    { return color(p) == BLACK; }
  void setRed(const BTPosition& p)          // make p red 
    { if (T.isInternal(p)) p.element().setColor(RED); }
  void setBlack(const BTPosition& p)            // make p black
    { if (T.isInternal(p)) p.element().setColor(BLACK); }
  void setColor(const BTPosition& p, Color color)   // set p's color
    { if (T.isInternal(p)) p.element().setColor(color); }
  bool hasTwoExternalChildren(const BTPosition& p) const // 2 external children?
    { return (T.isExternal(T.leftChild(p)) &&
              T.isExternal(T.rightChild(p))); }
  bool hasRedChild(const BTPosition& p) const       // does p have red child?
    { return (isRed(T.leftChild(p)) || isRed(T.rightChild(p))); }
  // ... (other utilities omitted)
template <typename Key, typename Element>
class Item {                    // a (key, element) pair
private:
  Key       _key;               // key value
  Element   _elem;              // element
public:
  Item(const Key& k = Key(), const Element& e = Element())
    : _key(k), _elem(e) { }         // constructor
  const Key& key() const            // gets the key (read only)
    { return _key; }
  Element& element()                // gets the element
    { return _elem; }
  const Element& element() const        // gets the element (read only)
    { return _elem; }
  void setKey(const Key& k)         // sets the key value
    { _key = k; }
  void setElement(const Element& e)     // sets the element
    { _elem = e; }
};
template <typename Key, typename Element,
            typename BSTItem = Item<Key, Element> >
class BinarySearchTree {
protected:                      // local types
  typedef BinaryTree<BSTItem>::Position BTPosition; // a tree position
public:                         // public types
    class Position {                                      // a Position
  private:
    BTPosition btPos;                   // position of node
  public:
    Position(const BTPosition &p) : btPos(p) { }    // constructor
    Element& element()                  // get element
      { return btPos.element().element(); }
    const Key& key() const              // get key (read only)
      { return btPos.element().key(); }
    bool isNull() const                 // a null position?
      { return btPos.isNull(); }
  };
protected:                      // member data
  BinaryTree<BSTItem> T;                // the binary tree
protected:                      // local utilities
  Key key(const BTPosition& p) const            // get position's key
    { return p.element().key(); }
                            // set a node's item
  void setItem(const BTPosition& p, const BSTItem& i) const {
    p.element().setKey(i.key());
    p.element().setElement(i.element());
  }
public:
  BinarySearchTree() : T() { }              // constructor
  int size() const                  // size
    { return (T.size() - 1) / 2; }          // number of internals
  bool isEmpty() const
    { return size() == 0; }
  // ... (insert find, insert, and remove functions here)
};

enum Color {RED, BLACK};                // item colors
template <typename Key, typename Element>
class RBItem : public Item<Key,Element> {       // a RBTree item
private:
  Color col;                        // node color
public:
  RBItem(const Key& k = Key(),
     const Element& e = Element(), Color c = RED)   // constructor
      : Item<Key,Element>(k, e), col(c) { }
  Color color() const { return col; }           // get color
  void setColor(Color c) { col = c; }           // set color
};
public:
  RBTree() : BST() { }                  // constructor
  // ... (insert insertItem() and removeElement() here)

public:
  void insertItem(const Key& k, const Element& e) { // insert (key,element)
    BTPosition z = inserter(k, e);          // insert in base tree
    if (T.isRoot(z))
      setBlack(z);                  // root is always black
    else 
      remedyDoubleRed(z);               // rebalance if needed
  }
protected:
  void remedyDoubleRed(const BTPosition& z) {       // fix double-red z
    BTPosition v = T.parent(z);             // v is z's parent
    if (T.isRoot(v) || isBlack(v)) return;      // v is black, all ok
                                // z, v are double-red
    if (isBlack(T.sibling(v)))  {           // Case 1: restructuring
      v = T.restructure(z);
      setBlack(v);                  // top vertex now black
      setRed(T.leftChild(v)); setRed(T.rightChild(v));  // children are red
    }  
    else  {                     // Case 2: recoloring
      setBlack(v);                  // make v black
      setBlack(T.sibling(v));               // ..and its sibling
      BTPosition u = T.parent(v);           // u is v's parent
      if (T.isRoot(u)) return;
      setRed(u);                    // make u red
      remedyDoubleRed(u);               // may need to fix u now
    }
  }
public:
  void removeElement(const Key& k)          // remove using key
      throw(NonexistentElementException) {
    BTPosition u = finder(k, T.root());         // find the node
    if (u.isNull())                 // not found?
      throw NonexistentElementException("Remove nonexistent element");
    BTPosition r = remover(u);              // remove u
    if (T.isRoot(r) || isRed(r) || wasParentRed(r))
      setBlack(r);                  // fix by color change
    else                        // r, parent both black
      remedyDoubleBlack(r);             // fix double-black r
  }
protected:
  void remedyDoubleBlack(const BTPosition& r) {     // fix double-black r
    BTPosition x, y, z;
    x = T.parent(r);
    y = T.sibling(r);
    if (isBlack(y))  {
      if (hasRedChild(y))  {                // Case 1: restructuring
        z = redChild(y);
        Color oldColor = color(x);          // save top vertex color
        z = T.restructure(z);               // restructure x,y,z
        setColor(z, oldColor);       setBlack(r);   // fix colors
        setBlack(T.leftChild(z));    setBlack(T.rightChild(z));
      }
      else {                        // Case 2: recoloring
        setBlack(r); setRed(y);             // r=black, y=red
        if (isBlack(x) && !T.isRoot(x))
    remedyDoubleBlack(x);               // fix double-black x
        setBlack(x);
      }
    }
    else {                      // Case 3: adjustment
      if (y == T.rightChild(x))   z = T.rightChild(y);  // z is the grandchild
      else            z = T.leftChild(y);   // ...on same side as y
      T.restructure(z);                 // restructure x,y,z
      setBlack(y); setRed(x);               // y=black, x=red
      remedyDoubleBlack(r);             // fix by Case 1 or 2
    }
  }
};



int main()
{
    return 0;
}

这是编译器发现的问题，任何人都可以解释模板的错误吗？

hm3.cpp:6:39: error: expected template-name before ‘<’ token
hm3.cpp:6:39: error: expected ‘{’ before ‘<’ token
hm3.cpp:6:39: error: expected unqualified-id before ‘<’ token

Answer 1

缺少一些代码，这里是完整的代码集：http://cpp.datastructures.net/source/ch09.html（来自“C ++中的数据结构和算法”一书）