huffman

哈夫曼樹又稱最優二叉樹，是帶權路徑最短的樹，可以用來構造最優編碼，用於信息傳遞，數據壓縮等方面，是一種應用廣泛的二叉樹。

哈夫曼算法的實現

（1）存儲結構

哈夫曼樹是一種二叉樹，其有自己的存儲特點，可以採用靜態三叉鏈表來實現。對於每個節點，它的存儲信息應包含自身的權值，雙親信息，以及左右孩子的信息。因此可以設計成如下所示的三叉鏈表結點結構。

weight------parent------Lchild------Rchild

類型定義如下

struct huffman {
	char n;
	int weight;
	struct huffman *next;
	struct huffman *LChlid,*RChlid,*Parent;
};

（2）哈夫曼算法的實現

對於一串字符串，我們可以統計出串中每個字符出現的次數，以此來表示它們的權值，統計完後把他們的權值依次排序，然後把第一個和第二個進行求和，並且申請空間來存儲該節點的信息，該你結點就是權值最小的兩個節點的雙親節點，這兩個結點就是新申請結點的孩子結點，然後將新結點和後續的結點根據權值的大小放到合適的位置；再找出權值最小的兩個結點，直到把權值最大的兩個結點處理完畢。至此，把所有的字符根據權值大小存儲到相應結點中。這樣，huffman樹就創建完畢了。

<pre name="code" class="java">

<pre name="code" class="java">#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#define FULL 100
struct huffman {
	char n;
	int weight;
	char *code;
	struct huffman *next;
	struct huffman *LChlid,*RChlid,*Parent;
};
struct stack {							
	int cnt;
	struct huffman *top;
};	
int sum = 0;
char string [FULL] = "";							//存儲字符串 
struct huffman *create(){
	struct huffman *Head;
	struct huffman *New,*End;	
	char str [FULL] = "";							//存儲不同字符 
	int w[FULL];								//存儲權值 
	int i,j;
	int n = 0;
	for(i = 0;i<FULL;i++){
		w[i] = 0;
	}
	printf("Please Input expressions\n");
	gets(string);
	for(i = 0;i<strlen(string);i++){
		for(j = 0;j<i;j++){
			if(string[i] == str[j]){
				break;
			} 
		}
		if(i == j){
			str[n] = string[i];
			w[n]++;
			n++;
		}else{
			w[j]++;
		}
	}
	New = End = (struct huffman *)malloc(sizeof(struct huffman));
	New->n = str[sum];
	New->weight = w[sum];
	while(1){
		sum++;
		if(sum == 1){
			New->next = NULL;
			Head = New;
			End = New;
			New->LChlid = NULL;
			New->RChlid = NULL;
		}
		else{
			New->next = NULL;
			End->next = New;
			End = New;
			New->LChlid = NULL;
			New->RChlid = NULL;
		}
		if(sum == n){
			break;
		}
		New = (struct huffman *)malloc(sizeof(struct huffman));
		New->n = str[sum];
		New->weight = w[sum];
	}
	return Head;
}
print(struct huffman *p){
	while(p !=NULL){
		if(p->LChlid == NULL && p->RChlid == NULL){
			printf("%c\t",p->n);
		}else{
			printf("*\t");
		}
		printf("%d\n",p->weight);
		p = p->next;
	}
}
sort(struct huffman *New){
	int j;
	char k;
	struct huffman *End;
	if(New->next != NULL){
		while(New->next!=NULL){
			End = New->next;
			while(End!=NULL){
				if(New->weight>End->weight){
					j = New->weight;
					New->weight = End->weight;
					End->weight = j;
	
					k = New->n;
					New->n = End->n;
					End->n = k;
				}
				End = End->next;
			}
			New = New->next;
		}
	}
}
struct huffman *findLocal(struct huffman *LChlid,struct huffman *RChlid,int weight){
	char k[FULL];
	struct huffman *p,*q;
	struct huffman *t = (struct huffman *)malloc(sizeof(struct huffman));
	t->weight = weight;
	t->LChlid = LChlid;
	t->RChlid = RChlid;
	LChlid->Parent = RChlid->Parent = t;
	t->Parent = NULL; 
	p = RChlid;
	q = p->next;
	while(q != NULL){
		if(t->weight > q->weight && q->next == NULL){
			q->next = t;.
			t->next = NULL;
			break;
		} else if(p->weight >= t->weight && p == RChlid) {
			RChlid->next = t;
			t->next = q;
			break;
		} else if(t->weight >= p->weight && t->weight <= q->weight){
			p->next = t;
			t->next = q;
			break;
		} else{
			p = q;
			q = q->next;
		}
	}
	if(q == NULL){
		p->next = t;
		t->next = NULL;
	}
	return RChlid->next;
}	
huffmanCode(struct huffman *p,int n){
	struct huffman *q,*s;
	char *cd = p->code = (char*)malloc(n * sizeof(char));
	int i,start = n-1;
	cd[n-1] = 0;
	s = q = p;
	p = p->Parent;
	while(p != NULL){
		start--;
		if(q == p->LChlid){
			cd[start] = '0';
		} else{
			cd[start] = '1';
		}
		q = p;
		p = p->Parent;
	}
	printf("%c\t",s->n);
	printf("%d\t",s->weight);
	for(i = 0;i < n-1;i++){
		printf("%c",cd[i]);
	}
	printf("\n");
}
main(){
	struct huffman *Head;
	struct huffman *p,*q;
	struct huffman *s,*t;
	struct stack temp;
	char *cd;
	char code[FULL] = "";
	int size = 0;
	int weight; 					
	int i = 0,j; 
	Head = p = create();
	q = p->next;
	if(q == NULL){
		print(p);
		return 0;
	}
	sort(p);
	weight = p->weight + q->weight;
	while(1){
		p = findLocal(p,q,weight);
		if(p->next != NULL){
			q = p->next;
			weight = p->weight + q->weight;
		} else{
			break;
		}
	}
	t = p;
	print(Head);
	s = p = Head;
	printf("字符\t權值\t編碼\n");
	while(p != NULL){
		if(p->LChlid == NULL && p->RChlid == NULL){
			while(s != NULL){
				s = s->Parent;
				i++;
			}
			huffmanCode(p,i);
			size++;
			i = 0;
		}
		p = p->next;
		s = p;
	}
	printf("所有字符編碼爲：\n");
	p = Head;
	for(i = 0;i<strlen(string);i++){
		while(1){
			if(p->LChlid == NULL && p->RChlid == NULL && string[i] == p->n){
				printf("%s",p->code);
				strcat(code,p->code);
				break;
			}
			p = p->next;
		}
		p = Head;
	}
	printf("\n");
	printf("對應的字符串爲：\n");
	s = t;
	i = 0;
	while(i != strlen(code)){
		if(code[i] == '0'){
			t = t->LChlid;
		} else{
			t = t->RChlid;
		}
		if(t->LChlid == NULL && t->RChlid == NULL){
			printf("%c",t->n);
			t = s;
		}
		i ++;
	}
}