信息论与编码

信息论与编码实验报告Huffman and Shannon coding学生姓名***学号***专业班级信息安全0701指导教师***学院***完成时间2009年4月一、实验目的1. 熟悉C/C++语言的上机环境，掌握C /C++语言的基本结构；2. 理解并掌握Huffman编码和Shannon编码；3. 能用C/C++实现这两个编码；4. 对N（N较小时）个数进行全排列。

三、详细设计1.Huffman编码#include<iostream.h>#include<stdio.h>#include<malloc.h>typedef struct node{node * lchild;node * rchild;char data;int weight;}* tree;struct elemtype{char ch;int weight;int code[10];};int N=0,m=0;void savetree(char *str){FILE *fp=fopen("1.txt","w");for(int i=0;i<m;i++){fputc(str[i],fp);}fclose(fp);}void createhuffman(tree& T,elemtype ** a,int n){ 二、实验内容1. 在VC6.0的环境下实现Huffman编码；2. 在VC6.0的环境下实现Shannon编码；3. 在VC6.0的环境下实现4个数的全排列。

int i=0,j,k1,k2;btree * b;btree q;b=(btree * )malloc(n*sizeof(tree));for(i=0;i<n;i++){b[i]=(bnode *)malloc(sizeof(node));b[i]->data=a[i]->ch;b[i]->weight=a[i]->weight;b[i]->lchild=b[i]->rchild=NULL;}for(i=1;i<n;i++){k1=-1;for(j=0;j<n;j++){if(b[j]!=NULL&&k1==-1){k1=j;continue;}if(b[j]!=NULL){k2=j;break;}}for(j=0;j<n;j++){if(b[j]!=NULL){if(b[j]->weight<=b[k1]->weight){k1=j;} } }if(k1==k2){for(j=0;j<n;j++){if(b[j]!=NULL&&j!=k1){k2=j;break;}} }for(j=0;j<n;j++){if(b[j]!=NULL&&j!=k1){if(b[j]->weight<=b[k2]->weight){k2=j;}} }q=(bnode *)malloc(sizeof(bnode));q->data='#';q->lchild=b[k1];q->rchild=b[k2];q->weight=b[k1]->weight+b[k2]->weight;b[k1]=q;b[k2]=NULL; }free(b);T=q; }void huffmancoding(btree T,int len,elemtype**codes){static int a[10];if(T!=NULL){if(T->lchild==NULL&&T->rchild==NULL){int i;printf("%c------",T->data);codes[N]=(elemtype *)malloc(sizeof(elemtype));codes[N]->ch=T->data;codes[N]->weight=0;for(i=0;i<10;i++)codes[N]->code[i]=2;for(i=0;i<len;i++){printf("%d",a[i]);codes[N]->code[i]=a[i]; }N++;printf("\n"); }else{a[len]=0;huffmancoding(T->lchild,len+1,codes);a[len]=1;huffmancoding(T->rchild,len+1,codes);} }}void initlize(char * str,btree & T,elemtype ** codes,char *s){int i=0,j,n=0,k=0,h;elemtype* a[20];for(j=0;j<20;j++)a[j]=NULL;while(str[i]!=0){for(j=0;j<i;j++){if(str[j]==str[i]){for(h=0;h<n;h++){if(a[h]->ch==str[j])break;}a[h]->weight++;break;}}if(j>=i){a[k]=(elemtype*)new(elemtype);a[k]->ch=str[i];a[ k]->weight=1;n++;k++;}i++;}cout<<n<<endl;createhuffman(T,a,n);cout<<endl;savetree(s);k=0;cout<<"所求哈夫曼编码表如下："<<endl; huffmancoding(T,k,codes);} void main(){btree t=NULL;elemtype* b[26];char str[100];char s[50];cout<<endl;cout<<"**哈夫曼编码程序**"<<endl;cout<<endl;cout<<"请输入要编码的字符串:"<<endl;cin>>str;initlize(str,t,b,s);cout<<endl;cout<<"*** Made by ZBF 2009/4/22 *** "<<endl;cout<<endl;}2.香农编码#include<iostream.h>#include<math.h>#include<iomanip.h>#include<stdlib.h>class T{public:T() {}~T();void Create();void Coutpxj();void Coutk();void Coutz();void Print();protected:int n;double *p;double *pxj;int *k;double *mz;};T::~T(){ delete p;delete pxj;delete k;delete mz;}void T::Coutpxj(){for(int i=1;i<n;i++){ pxj[i]=0;for(int j=0;j<i;j++)pxj[i]+=p[j];}}void T::Coutk(){for(int i=0;i<n;i++){double d=(-1)*(log(p[i])/log(2));if(d-(int)d>0) k[i]=(int)d+1;else k[i]=(int)d;}}void T::Create(){cout<<"请输入信号个数:";cin>>n;p=new double[n];cout<<"分别输入这"<<n<<"个概率:\n"; for(int i=0;i<n;i++) cin>>p[i];pxj=new double[n];k=new int[n];mz=new double[n];double sum=0.0;for(i=0;i<n;i++) sum+=p[i];if(sum!=1.0) throw 1;else{for(i=0;i<n;i++){int k=i;for(int j=i+1;j<n;j++)if(p[k]<p[j]) k=j;double m=p[i];p[i]=p[k];p[k]=m;}}}void T::Print(){cout<<"其香农编码如下："; cout<<endl;cout<<"Xi"<<setw(8)<<"概率"<<setw(8)<<"概率和"<<setw(8)<<"码长"<<setw(8)<<"编码"<<endl;for(int i=0;i<n;i++){ cout<<"X"<<i+1<<setw(8)<<setprecision(2)<<p[i]<<setw(8)<<setprecision(2)<<pxj[i]<<setw(8)<<k[i]<<" ";mz[i]=pxj[i];for(int j=0;j<k[i];j++){if(2*mz[i]-1>=0){ cout<<1;mz[i]=2*mz[i]-1;}else{cout<<0;mz[i]=2*mz[i];} }cout<<endl;}double K=0.0,H=0.0,Y;for(i=0;i<n;i++){K+=(double)p[i]*k[i];H+=(-1)*p[i]*(log10(p[i])/log10(2.0));}Y=H/K;cout<<"Average length:"<<K<<endl;cout<<"H(S):"<<H<<endl;cout<<"Coding efficiency:"<<Y<<endl;}void main(){ T t;int e;try{ cout<<endl;cout<<"***香农编码程序***";cout<<endl;cout<<endl;t.Create();t.Coutpxj();t.Coutk();t.Print();cout<<endl;cout<<" ***Made by ZBF 2009/4/22***";cout<<endl;cout<<endl;}catch(int e){if(e==1) cout<<"ERROR!";}}3.4个数的全排列#include <stdio.h>#define N 7int Arrange(int* p, int num, int a,int &j);int main(){int p[N],n,c,j=20;printf("\n**输出n个元素的全排列程序**\n"); printf("\n请输入元素个数n（小于7）:");scanf("%d", &n);printf("\n");c = Arrange(p, n, 0,j);printf("\n\n%d个元素的全排列个数为%d\n\n", n,c); printf("\t********* Made by ZBF 2009/4/22\n"); return 0;}int Arrange(int* p, int num, int a,int &j){int c = 0;if (a == num){ for (int i = 0; i < num; i++){printf("%d", p[i]);}if(j%2==0){printf("+");j--;}else{printf("-");j--;}printf("\t\t");c = 1;}else{ for (int i = 1; i <= num; i++){ bool b = false;for (int m = 0; m< a; m++){if (p[m] == i){b = true;break;}}if (!b){ p[a] = i;c += Arrange(p, num, a + 1,j);}}}return c;}四.程序结果截图五、心得体会随着科学技术发展的日新日异，当今计算机应用在生活中可以说得是无处不在。