哈夫曼树的构造和显示 （Haffman编码）----C语言

【问题描述】

    写出构造一棵哈夫曼树，并根据哈夫曼树求哈夫曼编码的算法。

【实验要求】

    用户给定若干个整数作为待编码字符的权值，程序建立哈夫曼树并输出各字符的哈夫曼编码。

 

【例】设权w={5， 29， 7， 8， 14， 23， 3，11}, n=8, 2n-1=15, 可构造出哈夫曼树如下图。其存储结构ht[]的初始状态如表1所示，终结状态如表2所示，所得各字符的哈夫曼编码如表3所示。

 

例题，Haffman编码示例：

（注：哈夫曼树编码不唯一；下面给出的编码和图中所示编码，二者等效）

##Haffman Code##
>>NUM = 5       Code: 0001
>>NUM = 29      Code: 10
>>NUM = 7       Code: 1110
>>NUM = 8       Code: 1111
>>NUM = 14      Code: 110
>>NUM = 23      Code: 01
>>NUM = 3       Code: 0000
>>NUM = 11      Code: 001

README

Author:YXP
e-mail:[email protected]
如有问题，请我联系~
转载请标明出处~

权值 w={5， 29， 7， 8， 14， 23， 3，11} （对应 element[8] ={...}）
数目 n=8 （对应 len = 8）
源代码，以上述数据为例。

源代码

mian.c文件

#include 
#include 

/*	
author:YXP
e-mail:[email protected]
如有问题，欢迎和我联系~
转载请标明出处~
*/

#define USED 1
#define UNUSED 0 
#define CHILDNUM 2

struct Node {
	int weight;
	int *child;/*存储孩子的位置*/
	int parent;/*存储父亲的位置*/
	int state;/*used = 1; Unsed = 0*/
	int level;/*当前点所在的层数*/
	int code;/*编码*/ 
};

struct Node** ini_Node_arr (int len,int* element);				/*初始化Haffman编码数数组*/ 
struct Node** Build_Haffman_tree (int* element,int len);		/*构建Haffman编码树*/ 
int Find_2min_position (int* store, struct Node** Arr,int len);	/*在Arr中，找到最小和次小的权值的位置*/
int Create_newNode (struct Node** Arr,int* store,int All_len);	/*创建新的Haffman编码树 节点*/ 
int Decode (struct Node** Arr,int len);							/*解码 Haffman树*/ 
int Print_Code (struct Node** Arr,int len);						/*打印待编码树的编码*/ 

int main(int argc, char *argv[]) {
	
	int len = 8;	/*待编码数 的个数*/ 
	int element[8] = {5,29,7,8,14,23,3,11};/*待编码数*/ 
	
	struct Node** Arr = Build_Haffman_tree (element,len);
	
	int i, All_len = (int)((len*(len+1)/2)+1);
	
//	for (i=0;iweight);
//		}
//	}
	
	printf ("##Haffman Code##");
	Decode (Arr,len);
	Print_Code (Arr,len);
		
	return 0;
}


struct Node** ini_Node_arr (int len,int* element)	/*初始化Haffman编码数数组*/ 
{
	int All_len = (int)((len*(len+1)/2)+1);
	struct Node** Arr = (struct Node**)malloc((All_len)*sizeof(struct Node*));
	int i;
	for (i = 0;ichild = NULL;
		Arr[i]->parent = -1;
		Arr[i]->level = 0;		
		Arr[i]->state = 0;
		Arr[i]->weight = element[i];
		Arr[i]->code = 0;
	}
	for (i = len;istate == UNUSED){
				if (min_p1 == -1){
					min_p1 = i;
				}else{
					if (Arr[i]->weight < Arr[min_p1]->weight){
					min_p2 = min_p1;
					min_p1 = i;					
					}else{
						if (min_p2 == -1){
							min_p2 = i;
						}else{
							if (Arr[i]->weight < Arr[min_p2]->weight){
								min_p2 = i;
							}
						}
					}											
				}
			}		
		}	
	}
	store[0] = min_p1;
	store[1] = min_p2;
	
	return 0;
}

int Create_newNode (struct Node** Arr,int* store,int All_len)	/*创建新的Haffman编码树 节点*/ 
{
	int child1 = store[0], child2 = store[1];
	int i = 0;
	
	while (Arr[i] != NULL){
		i++;
	}
	 
	Arr[i] = (struct Node*)malloc(sizeof(struct Node));
	
	Arr[i]->child = (int*)malloc(CHILDNUM*sizeof(int));
	Arr[i]->child[0] = child1;
	Arr[i]->child[1] = child2;
	
	Arr[child1]->state = USED;
	Arr[child1]->code = 0;/*左边*/
	Arr[child1]->parent = i;
	
	Arr[child2]->state = USED;
	Arr[child2]->code = 1;/*右边*/ 
	Arr[child2]->parent = i;
	
	Arr[i]->weight = Arr[child1]->weight + Arr[child2]->weight;
	Arr[i]->level ++;
	Arr[i]->state = 0;
	
	return 0;
}


int Decode (struct Node** Arr,int len)/*解码 Haffman树*/ 
{
	int temp_parent = -1,Total_parent = 0;
	while (Arr[Total_parent] != NULL){
		Total_parent++;
	}
	
	int i;
	for (i=0;iparent;
		while(temp_parent != (Total_parent-1)){
			Arr[i]->code = (Arr[i]->code)*2+Arr[temp_parent]->code;
			Arr[i]->level ++;
			temp_parent = Arr[temp_parent]->parent;
		}	
	}
	
	return 0; 
}


int Print_Code (struct Node** Arr,int len)	/*打印待编码树的编码*/ 
{
	int i;
	int temp,code;
	for (i=0;i>NUM = %d\t",Arr[i]->weight);
		temp = Arr[i]->level;
		code = Arr[i]->code;
		printf("Code: ");
		while (temp >= 0){
			printf ("%d",code%2);
			code = code/2;
			temp--;
		}
	}
	return 0;
}

运行结果

##Haffman Code##
>>NUM = 5       Code: 0001
>>NUM = 29      Code: 10
>>NUM = 7       Code: 1110
>>NUM = 8       Code: 1111
>>NUM = 14      Code: 110
>>NUM = 23      Code: 01
>>NUM = 3       Code: 0000
>>NUM = 11      Code: 001
--------------------------------