C++模板实现哈夫曼树

       

哈夫曼树（霍夫曼树）又称为最优树.

1、路径和路径长度

在一棵树中，从一个结点往下可以达到的孩子或孙子结点之间的通路，称为路径。通路中分支的数目称为路径长度。若规定根结点的层数为1，则从根结点到第L层结点的路径长

度为L-1。

2、结点的权及带权路径长度

若将树中结点赋给一个有着某种含义的数值，则这个数值称为该结点的权。结点的带权路径长度为：从根结点到该结点之间的路径长度与该结点的权的乘积。

3、树的带权路径长度

给定n个权值作为n个叶子结点，构造一棵二叉树，若带权路径长度达到最小，称这样的二叉树为最优二叉树，也称为哈夫曼树(Huffman Tree)。哈夫曼树是带权路径长度最短的树，权值较大的结点离根较近。

BinTreeNode.h

template<typename Type> class BinaryTree;template<typename Type> void Huffman(Type *, int, BinaryTree<Type> &);template<typename Type> class BinTreeNode{public:friend class BinaryTree<Type>;    friend void Huffman<Type>(Type *, int, BinaryTree<Type> &);BinTreeNode():m_pleft(NULL),m_pright(NULL){}BinTreeNode(Type item,BinTreeNode<Type> *left=NULL,BinTreeNode<Type> *right=NULL):m_data(item),m_pleft(left),m_pright(right){}void Destroy(){//destroy the tree with the root of the nodeif(this!=NULL){this->m_pleft->Destroy();this->m_pright->Destroy();delete this;}}    Type GetData(){        return m_data;    }    BinTreeNode<Type> *Copy(const BinTreeNode<Type> *copy);//copy the nodeprivate:BinTreeNode<Type> *m_pleft,*m_pright;Type m_data;};template<typename Type> BinTreeNode<Type>* BinTreeNode<Type>::Copy(const BinTreeNode<Type> *copy){if(copy==NULL){return NULL;}BinTreeNode<Type> *temp=new BinTreeNode<Type>(copy->m_data);temp->m_pleft=Copy(copy->m_pleft);temp->m_pright=Copy(copy->m_pright);return temp;}

BinaryTree.h

#include "BinTreeNode.h"template<typename Type> void Huffman(Type *, int, BinaryTree<Type> &);template<typename Type> class BinaryTree{public:        BinaryTree(BinaryTree<Type> &bt1, BinaryTree<Type> &bt2){        m_proot = new BinTreeNode<Type>(bt1.m_proot->m_data             + bt2.m_proot->m_data, bt1.m_proot, bt2.m_proot);    }    BinaryTree(Type item){        m_proot = new BinTreeNode<Type>(item);    }    BinaryTree(const BinaryTree<Type> &copy){        this->m_proot = copy.m_proot;    }    BinaryTree(){        m_proot = NULL;    }    void Destroy(){        m_proot->Destroy();    }    ~BinaryTree(){//        m_proot->Destroy();    }        BinaryTree<Type>& operator=(BinaryTree<Type> copy);//evaluate node    friend void Huffman<Type>(Type *, int, BinaryTree<Type> &);    friend bool operator < <Type>(BinaryTree<Type> &l, BinaryTree<Type> & r);    friend bool operator > <Type>(BinaryTree<Type> &l, BinaryTree<Type> & r);    friend bool operator <= <Type>(BinaryTree<Type> &l, BinaryTree<Type> & r);    friend ostream& operator<< <Type>(ostream& ,BinaryTree<Type>&);//output the dataprivate:BinTreeNode<Type> *m_proot;    void Print(BinTreeNode<Type> *start,int n=0);//print the tree with the root of start};template<typename Type> bool operator <(BinaryTree<Type> &l, BinaryTree<Type> &r){    return l.m_proot->GetData() < r.m_proot->GetData();}template<typename Type> bool operator >(BinaryTree<Type> &l, BinaryTree<Type> &r){    return l.m_proot->GetData() > r.m_proot->GetData();}template<typename Type> bool operator <=(BinaryTree<Type> &l, BinaryTree<Type> &r){    return l.m_proot->GetData() <= r.m_proot->GetData();}template<typename Type> void BinaryTree<Type>::Print(BinTreeNode<Type> *start, int n){if(start==NULL){for(int i=0;i<n;i++){cout<<"     ";}cout<<"NULL"<<endl;return;}Print(start->m_pright,n+1);//print the right subtreefor(int i=0;i<n;i++){//print blanks with the height of the nodecout<<"     ";}if(n>=0){cout<<start->m_data<<"--->"<<endl;//print the node}Print(start->m_pleft,n+1);//print the left subtree}template<typename Type> ostream& operator<<(ostream& os,BinaryTree<Type>& out){out.Print(out.m_proot);return os;}template<typename Type> BinaryTree<Type>& BinaryTree<Type>::operator=(BinaryTree<Type> copy){m_proot=m_proot->Copy(copy.m_proot);    return *this;}

MinHeap.h

template<typename Type> class MinHeap{public:MinHeap(Type heap[],int n);//initialize heap by a array~MinHeap(){delete[] m_pheap;}public:    bool Insert(const Type item);    bool DeleteMin(Type &first);private:void Adjust(const int start, const int end);//adjust the elements from start to endprivate:const int m_nMaxSize;Type *m_pheap;int m_ncurrentsize;};template<typename Type> void MinHeap<Type>::Adjust(const int start, const int end){int i = start,j = i*2+1;Type temp=m_pheap[i];while(j <= end){if(j<end && m_pheap[j]>m_pheap[j+1]){j++;}if(temp <= m_pheap[j]){break;}else{m_pheap[i] = m_pheap[j];i = j;j = 2*i+1;}}m_pheap[i] = temp;}template<typename Type> MinHeap<Type>::MinHeap(Type heap[], int n):m_nMaxSize(n){m_pheap = new Type[m_nMaxSize];for(int i=0; i<n; i++){m_pheap[i] = heap[i];}m_ncurrentsize = n;int pos=(n-2)/2;//Find the last tree which has more than one element;while(pos>=0){Adjust(pos, n-1);pos--;}}template<typename Type> bool MinHeap<Type>::DeleteMin(Type &first){    first = m_pheap[0];    m_pheap[0] = m_pheap[m_ncurrentsize-1];    m_ncurrentsize--;    Adjust(0, m_ncurrentsize-1);    return 1;}template<typename Type> bool MinHeap<Type>::Insert(const Type item){if(m_ncurrentsize == m_nMaxSize){cerr<<"Heap Full!"<<endl;return 0;}m_pheap[m_ncurrentsize] = item;int j = m_ncurrentsize, i = (j-1)/2;Type temp = m_pheap[j];while(j > 0){if(m_pheap[i] <= temp){break;}else{m_pheap[j] = m_pheap[i];j = i;i = (j-1)/2;}}m_pheap[j] = temp;m_ncurrentsize++;return 1;}

Huffman.h

#include "BinaryTree.h"#include "MinHeap.h"template<typename Type> void Huffman(Type *elements, int n, BinaryTree<Type> &tree){    BinaryTree<Type> first, second;    BinaryTree<Type> node[20];    for (int i=0; i<n; i++){        node[i].m_proot = new BinTreeNode<Type>(elements[i]);    }    MinHeap<BinaryTree<Type> > heap(node, n);    for (int i=0; i<n-1; i++){        heap.DeleteMin(first);        heap.DeleteMin(second);                //using the first and the second minimize element create new tree        if (first.m_proot->GetData() == second.m_proot->GetData()){            tree = *(new BinaryTree<Type>(second, first));        }        else {            tree = *(new BinaryTree<Type>(first, second));        }        heap.Insert(tree);    }}

Main.cpp

#include <iostream>using namespace std;#include "Huffman.h"int main(){    BinaryTree<int> tree;    int init[10]={3,6,0,2,8,4,9,1,5,7};    Huffman(init,10,tree);    cout << tree;    tree.Destroy();    return 0;}