Huffman树的建立(c++实现)

    Huffman 编码是应用很广泛的一种文本压缩编码方式。它的原理就是用不等长的编码来表示不同出现频率的字符。出现频率高的字符，就用比较短的编码来表示，出现频率低的，就是较长的编码来表示。

      Huffman编码是一种前缀编码方式，所谓前缀编码，即，在编码集合中，没有任何一个编码是另一个编码的前缀。

      使用Huffman编码的时候，一般要生成对应文本的编码集合（Huffman树），然后再将文本的每个字符相应都转成压缩码。解码时也要依赖于对应的Huffman树。

      其建立的过程其实运用了贪婪算法的思想, 每次从可用的二叉树中选出权重最小的两棵.

      以下代码是Huffman树的建立:

 

template<class T> class Huffman { friend BinaryTree<int> HuffmanTree(T [], int); public: operator T () const {return weight;} public: BinaryTree<int> tree; T weight; }; template <class T> BinaryTree<int> HuffmanTree(T a[], int n) { //根据权重数组a[1->n] 构造霍夫曼树 //创建一个单节点树的数组 Huffman<T> *w = new Huffman<T> [n+1]; BinaryTree<int> z, zero; for (int i = 1; i <= n; i++) { z.MakeTree(i, zero, zero); w[i].weight = a[i]; w[i].tree = z; } //把数组变成一个最小堆 MinHeap<Huffman<T> > H(1); H.Initialize(w,n,n); //将堆中的树不断合并 Huffman<T> x, y; for (int i = 1; i < n; i++) { H.DeleteMin(x); H.DeleteMin(y); z.MakeTree(0, x.tree, y.tree); x.weight += y.weight; x.tree = z; H.Insert(x); } H.DeleteMin(x); //得到霍夫曼树 H.Deactivate(); delete [] w; return x.tree; }

 

队列:

 

template <class T> class Node { friend LinkedStack<T>; friend LinkedQueue<T>; private: T data; Node<T> *link; }; template<class T> class LinkedQueue { public: LinkedQueue() {front = rear = 0;} ~LinkedQueue(); bool IsEmpty() const {return ((front) ? false : true);} bool IsFull() const; T First() const; // 返回第一个元素 T Last() const; // 返回最后一个元素 LinkedQueue<T>& Add(const T& x); LinkedQueue<T>& Delete(T& x); private: Node<T> *front; // 指向第一个节点 Node<T> *rear; // 指向最后一个节点 }; template<class T> LinkedQueue<T>::~LinkedQueue() { Node<T> *next; while (front) { next = front->link; delete front; front = next; } } template<class T> bool LinkedQueue<T>::IsFull() const { // 判断队列是否已满 Node<T> *p; try { p = new Node<T>; delete p; return false; } catch (NoMem) { return true; } } template<class T> T LinkedQueue<T>::First() const { if (IsEmpty()) throw OutOfBounds(); return front->data; } template<class T> T LinkedQueue<T>::Last() const { if (IsEmpty()) throw OutOfBounds(); return rear->data; } template<class T> LinkedQueue<T>& LinkedQueue<T>::Add(const T& x) { Node<T> *p = new Node<T>; p->data = x; p->link = 0; // 在队列尾部添加新节点 if (front) rear->link = p; else front = p; rear = p; return *this; } template<class T> LinkedQueue<T>& LinkedQueue<T>::Delete(T& x) { if (IsEmpty()) throw OutOfBounds(); x = front->data; // 删除第一个节点 Node<T> *p = front; front = front->link; delete p; return *this; }

 

 

二叉树:

 

template <class T> class BinaryTreeNode { friend BinaryTree<T>; friend BSTree<T,int>; friend DBSTree<T,int>; public: BinaryTreeNode() {LeftChild = RightChild = 0;} BinaryTreeNode(const T& e){data = e; LeftChild = RightChild = 0;} BinaryTreeNode(const T& e, BinaryTreeNode *l,BinaryTreeNode *r) {data = e; LeftChild = l; RightChild = r;} private: T data; BinaryTreeNode<T> *LeftChild, // 左子树 *RightChild; // 右子树 }; template<class T> class BinaryTree { friend BSTree<T,int>; friend DBSTree<T,int>; public: BinaryTree() {root = 0;}; ~BinaryTree(){}; bool IsEmpty() const {return ((root) ? false : true);} bool Root(T& x) const; void MakeTree(const T& element, BinaryTree<T>& left, BinaryTree<T>& right); void BreakTree(T& element, BinaryTree<T>& left, BinaryTree<T>& right); void PreOrder(void(*Visit)(BinaryTreeNode<T> *u)) {PreOrder(Visit, root);} void InOrder(void(*Visit)(BinaryTreeNode<T> *u)) {InOrder(Visit, root);} void PostOrder(void(*Visit)(BinaryTreeNode<T> *u)) {PostOrder(Visit, root);} void LevelOrder(void(*Visit)(BinaryTreeNode<T> *u)); void PreOutput() {PreOrder(Output, root); cout << endl;} void InOutput() {InOrder(Output, root); cout << endl;} void PostOutput() {PostOrder(Output, root); cout << endl;} void LevelOutput() {LevelOrder(Output); cout << endl;} void Delete() {PostOrder(Free, root); root = 0;} int Height() const {return Height(root);} int Size(){_count = 0; PreOrder(Add1, root); return _count;} private: BinaryTreeNode<T> *root; void PreOrder(void(*Visit)(BinaryTreeNode<T> *u), BinaryTreeNode<T> *t); void InOrder(void(*Visit)(BinaryTreeNode<T> *u), BinaryTreeNode<T> *t); void PostOrder(void(*Visit)(BinaryTreeNode<T> *u), BinaryTreeNode<T> *t); static void Free(BinaryTreeNode<T> *t) {delete t;} static void Output(BinaryTreeNode<T> *t) {cout << t->data << ' ';} static void Add1(BinaryTreeNode<T> *t) {_count++;} int Height(BinaryTreeNode<T> *t) const; }; template<class T> bool BinaryTree<T>::Root(T& x) const { if (root) { x = root->data; return true; } else { // 没有根节点 return false; } } template<class T> void BinaryTree<T>::MakeTree(const T& element, BinaryTree<T>& left, BinaryTree<T>& right) { //将left, right 和 element合并成一棵新树,left,right和this必须是不同的树 root = new BinaryTreeNode<T>(element, left.root, right.root); // 阻止访问left和right left.root = right.root = 0; } template<class T> void BinaryTree<T>::BreakTree(T& element, BinaryTree<T>& left, BinaryTree<T>& right) { if (!root) throw BadInput(); //分解树 element = root->data; left.root = root->LeftChild; right.root = root->RightChild; delete root; root = 0; } template<class T> void BinaryTree<T>::PreOrder( void(*Visit)(BinaryTreeNode<T> *u), BinaryTreeNode<T> *t) { if(t) { Visit(t); PreOrder(Visit, t->LeftChild); PreOrder(Visit, t->RightChild); } } template <class T> void BinaryTree<T>::InOrder(void(*Visit)(BinaryTreeNode<T> *u), BinaryTreeNode<T> *t) { if(t) { InOrder(Visit, t->LeftChild); Visit(t); InOrder(Visit, t->RightChild); } } template <class T> void BinaryTree<T>::PostOrder(void(*Visit)(BinaryTreeNode<T> *u),BinaryTreeNode<T> *t) { if(t) { PostOrder(Visit, t->LeftChild); PostOrder(Visit, t->RightChild); Visit(t); } } template <class T> void BinaryTree<T>::LevelOrder(void(*Visit)(BinaryTreeNode<T> *u)) { LinkedQueue<BinaryTreeNode<T>*> Q; BinaryTreeNode<T> *t; t = root; while (t) { Visit(t); if (t->LeftChild) Q.Add(t->LeftChild); if (t->RightChild) Q.Add(t->RightChild); try { Q.Delete(t); } catch(OutOfBounds) { return; } } } template <class T> int BinaryTree<T>::Height(BinaryTreeNode<T> *t) const { if(!t) return 0; int hl = Height(t->LeftChild); int hr = Height(t->RightChild); if(hl > hr) return ++hl; else return ++hr; }