赫夫曼树的构建、编码、译码解析

假设在查找的过程中无法找到叶子节点，则报文有错误。

四、赫夫曼树构造、编码、译码代码例如以下

1、我们须要两个结构体，一个是赫夫曼树节点的结构体。还有一个是链表节点的结构体：

typedef struct Node
{
	int weight;
	key_type key;
	struct Node *lchild, *rchild;
}HFMNode,*HFMTree;
/*用于链表的结构体*/
typedef struct link_node
{
	HFMTree data;
	struct link_node *next;
}LNode,*Link;

void init_link(Link *head);//初始化链表
void insert_link(Link head, HFMTree hfm);//向链表中插入一个元素，并依照权重排序
int delete_link(Link head,HFMTree *hfm);//依次删除链表中的数据。成功返回1，失败返回0
/*创建赫夫曼树,str为keyword，w为相应的权重*/
int creat_hfmTree(HFMTree *root,char str[],int w[]);
/*获取赫夫曼编码表，存储在数组code中*/
void hfmTree_code(HFMTree head, int a,char code[]);
/*译码,译码结果存储在decode数组中,code输入的报文*/
int hfmTree_decode(HFMTree head,const char code[],char decode[]);
3、总体代码例如以下：

#include <iostream>
#include <assert.h>
typedef char key_type;
/*用于赫夫曼树的结构体*/

using namespace std;

typedef struct Node
{
	int weight;
	key_type key;
	struct Node *lchild, *rchild;
}HFMNode,*HFMTree;
/*用于链表的结构体*/
typedef struct link_node
{
	HFMTree data;
	struct link_node *next;
}LNode,*Link;
/*对链表的操作*/
void init_link(Link *head);//初始化链表
void insert_link(Link head, HFMTree hfm);//向链表中插入一个元素。并依照权重排序
int delete_link(Link head,HFMTree *hfm);//依次删除链表中的数据，成功返回1。失败返回0
/*创建赫夫曼树,str为keyword，w为相应的权重*/
int creat_hfmTree(HFMTree *root,char str[],int w[]);
/*获取赫夫曼编码表，存储在数组code中*/
void hfmTree_code(HFMTree head, int a,char code[]);
/*译码,译码结果存储在decode数组中,code输入的报文*/
int hfmTree_decode(HFMTree head,const char code[],char decode[]);
int main()
{
	HFMTree root;
	char str[] = "abcdefg";
	int w[] = { 12, 18, 36, 79,85,32,40};
	creat_hfmTree(&root, str, w);
	
	char code[1024] = { 0 };//用来存放编码表
	hfmTree_code(root, 1,code);
	cout <<"编码结果为："<<endl<< code << endl;
	
	char decode[90] = { 0 };
	hfmTree_decode(root, "00001100010010100111011", decode);
	cout <<"译码结果为："<<endl<< decode << endl;

}

void init_link(Link *head)
{
	(*head) = (Link)malloc(sizeof(LNode));
	(*head)->next = NULL;
	(*head)->data = NULL;
}

void insert_link(Link head, HFMTree hfm)
{
	assert(head != NULL);
	/*先构造链表节点*/
	Link temp = (Link)malloc(sizeof(LNode));
	temp->next = NULL;
	temp->data = hfm;

	while (head->next != NULL && head->next->data->weight < hfm->weight)
	{
		head = head->next;
	}
	if (head->next == NULL)
	{
		head->next = temp;
	}
	else
	{
		temp->next = head->next;
		head->next = temp;
	}
}

int delete_link(Link head, HFMTree *hfm)
{
	assert(head != NULL);
	if (head->next == NULL)
		return 0;
	Link temp = head->next;
	head->next = temp->next;

	*hfm = temp->data;

	free(temp);
	return 1;
}

int creat_hfmTree(HFMTree *root, char str[], int w[])
{
	int n = strlen(str);
	HFMTree temp;

	Link head;
	init_link(&head);
	/*构造节点，依照权重的递增顺序插入到链表中*/
	for (int i = 0; i < n;i++)
	{
		/*构造节点*/
		temp = (HFMTree)malloc(sizeof(HFMNode));
		
		temp->key = str[i];
		temp->weight = w[i];
		temp->lchild = NULL;
		temp->rchild = NULL;

		insert_link(head, temp);
	}
	if (head->next == NULL)//链表中没有元素
		return 0;
	/*从链表中取出两个最小的节点构造赫夫曼树*/
	HFMTree temp1, temp2, temp3;
	/*链表中存在1个元素则退出循环*/
	while ( delete_link(head,&temp1) && delete_link(head,&temp2) )
	{
		temp3 = (HFMTree)malloc(sizeof(HFMNode));

		temp3->weight = temp1->weight + temp2->weight;
		temp3->lchild = temp1;
		temp3->rchild = temp2;

		insert_link(head, temp3);
	}
	*root = temp1;
	return 1;
}

void hfmTree_code(HFMTree head, int a, char code[])
{
	static int i = 0;
	if (head != NULL)
	{
		if (head->lchild == NULL && head->rchild == NULL)//訪问到了叶子节点
		{
			code[i++] = head->key;
			code[i++] = ':';//在keyword后面加"："，其后面的"0"、"1"表示编码
			int count = 0;
			/*对a做处理。a最前面的1要舍去*/
			while (a > 1)
			{
				if (a % 2 == 0)
					code[i++] = '0';
				else
					code[i++] = '1';
				a = a>>1;
				count++;
			}
			/*对字符串反转，这样才和我们的赫夫曼编码一直*/
			strrev( code + i - count);
			/*keyword之间的编码用空格分开*/
			code[i++] = ' ';
		}
		hfmTree_code(head->lchild, a * 2, code);
		hfmTree_code(head->rchild, a * 2 + 1, code);
	}
}

int hfmTree_decode(HFMTree head, const char code[], char decode[])
{
	assert(head != NULL);
	HFMTree root = head,pre;
	int i = 0;
	int j = 0;
	
	while (code[i] == '0' || code[i] == '1')
	{
		if (code[i] == '0')
			head = head->lchild;
		else
			head = head->rchild;
		if (head->rchild == NULL )//訪问到了叶子节点
		{
			decode[j] = head->key;
			j++;
			head = root;
		}
		i++;
	}
	if (code[i] != '\0')//没有訪问到叶子节点
	{
		cout << "报文错误" << endl;
		return 0;
	}
	return 1;
}