哈夫曼樹是路徑長度加權(quán)的最短樹,它可用于構(gòu)造信息傳輸、數(shù)據(jù)壓縮等的最優(yōu)編碼,今天武林技術(shù)頻道小編來為大家介紹C++實(shí)現(xiàn)哈夫曼樹簡單創(chuàng)建與遍歷的方法,大家一定不要錯(cuò)過哦。
據(jù)此構(gòu)造出最優(yōu)樹算法如下:
哈夫曼算法:
1. 將n個(gè)權(quán)值分別為w1,w2,w3,....wn-1,wn的節(jié)點(diǎn)按權(quán)值遞增排序,將每個(gè)權(quán)值作為一棵二叉樹。構(gòu)成n棵二叉樹森林F={T1,T2,T3,T4,...Tn},其中每個(gè)二叉樹都只有一個(gè)權(quán)值,其左右字?jǐn)?shù)為空
2. 在森林F中選取根節(jié)點(diǎn)權(quán)值最小二叉樹,作為左右字?jǐn)?shù)構(gòu)成一棵新的二叉樹,并使得新的二叉樹的根節(jié)點(diǎn)為
其左右字?jǐn)?shù)權(quán)值之和,其中葉子都是最初的樹
3. 在森林F中刪除這兩棵樹,同時(shí)將新得到的二叉樹代替這兩個(gè)樹加入到森林F中,因此森林中二叉樹的個(gè)數(shù)比以前少一顆
4. 對(duì)新的森林重復(fù)2和3,知道森林中只有一棵樹位置,這棵樹就是哈夫曼樹.
#include <iostream>using namespace std;#define LEAFNUM 10 //葉子節(jié)點(diǎn)數(shù),也就是權(quán)值樹#define HUFNUM 2*LEAFNUM#define MAXWEIGHT 999.9//*********存儲(chǔ)結(jié)構(gòu)***********class HufTree;//***** Node**********class NODE{private: char Data; //節(jié)點(diǎn)的數(shù)據(jù)域 double Weight; //節(jié)點(diǎn)的權(quán)值域 int Lchild,Rchild,Parent; //節(jié)點(diǎn)的左孩子右孩子及雙親域public: NODE() //構(gòu)造函數(shù) { Data = '/0'; Weight = 0; Lchild = -1; Rchild = -1; Parent = -1; //給節(jié)點(diǎn)的數(shù)據(jù)初始化 } int Re_L(){return Lchild;} int Re_R(){return Rchild;} char Re_Data(){return Data;} double Re_Weight(){return Weight;} friend class HufTree; //聲明友元};//Node//********HufTree類**********class HufTree{private: int NodeNum; NODE HufArry[HUFNUM];public: HufTree(){NodeNum = 0;} void SetHuf(int,double,char); //設(shè)置權(quán)值與數(shù)據(jù)域 void CreatHuf(); //創(chuàng)建哈夫曼樹 void SelectMin(int,int&,int&); //查找哈夫曼樹種兩個(gè)權(quán)值最小的樹 void Find_Root_and_Print(); //查找樹根節(jié)點(diǎn)位置 void PrintHuf(int); //遍歷哈夫曼樹};//huftree void HufTree::SetHuf(int i,double wei,char ch){ HufArry[i].Data = ch; HufArry[i].Weight = wei;}void HufTree::CreatHuf(){ cout<<"每次查詢兩個(gè)最小樹的位置:"<<endl; for(int i = LEAFNUM; i < HUFNUM - 1; i++) { int p1 = 0; int p2 = 0; SelectMin(i,p1,p2); //找出當(dāng)前樹種權(quán)值最小的兩顆樹 cout<<p1<<" < - > "<<p2<<endl; HufArry[p1].Parent = i; //設(shè)置兩顆最小樹的雙親 HufArry[p2].Parent = i; HufArry[i].Lchild = p1; //設(shè)置這棵3節(jié)點(diǎn)的樹的根的權(quán)值以及孩子 HufArry[i].Rchild = p2; HufArry[i].Weight = HufArry[p1].Weight + HufArry[p2].Weight; } cout<<"************************"<<endl;}void HufTree::SelectMin(int i,int &p1,int &p2){ int least1 = MAXWEIGHT; int least2 = MAXWEIGHT; for(int j = 0; j < i; j++) { if(HufArry[j].Parent == -1) { if(HufArry[j].Weight < least1) { least2 = least1; least1 = HufArry[j].Weight; p2 = p1; p1 = j; } else { if(HufArry[j].Weight < least2) { least2 = HufArry[j].Weight; p2 = j; } } } }}void HufTree::Find_Root_and_Print(){ int root; for(int i = 0; i < HUFNUM - 1; i++) { if(HufArry[i].Parent == -1) { root = i; break; } } PrintHuf(root);}void HufTree::PrintHuf(int position){ if(NodeNum == LEAFNUM) { return; } else { if(HufArry[position].Data != '/0') //如果是葉子節(jié)點(diǎn) { cout<<"權(quán)值:"<<HufArry[position].Weight<<"<-> 數(shù)據(jù):"<<HufArry[position].Data<<" 此節(jié)點(diǎn)為葉子"<<endl; NodeNum = NodeNum + 1; } else { cout<<"權(quán)值:"<<HufArry[position].Weight<<" 此節(jié)點(diǎn)無數(shù)據(jù)域,不是葉子"<<endl; PrintHuf(HufArry[position].Lchild); PrintHuf(HufArry[position].Rchild); } } }int main(){ HufTree Tree; cout<<"請輸入"<<LEAFNUM<<"對(duì)(權(quán)值,數(shù)據(jù)):"<<endl; double wei; char ch; for(int i = 0; i < LEAFNUM; i++) { cin>>wei; cin>>ch; Tree.SetHuf(i,wei,ch); } Tree.CreatHuf(); //創(chuàng)建哈夫曼樹 Tree.Find_Root_and_Print(); //遍歷哈夫曼樹 return 0;}武林技術(shù)頻道小編在上文為大家分享了C++實(shí)現(xiàn)哈夫曼樹簡單創(chuàng)建與遍歷的方法,如果我們要學(xué)習(xí)編程知識(shí),一定不能錯(cuò)過武林技術(shù)頻道哦!新聞熱點(diǎn)
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