利用Python和C語言分別實現哈夫曼編碼

2022-07-14 14:01:18

1.C語言實現

1.1程式碼說明

a 建立雙向連結串列：

在建立哈夫曼樹的過程中，需要不斷對結點進行更改和刪除，所以選用雙向連結串列的結構更容易

'''C
#include <stdlib.h>
#include <stdio.h>
#include <windows.h>
 
 
//哈夫曼樹結構體，資料域儲存字元及其權重
typedef struct node
{
    char c;
    int weight;
    struct node *lchild, *rchild;
}Huffman, *Tree;
 
 
//雙向連結串列結構體，資料域儲存哈夫曼樹結點
typedef struct list
{
    Tree root;
    struct list *pre;
    struct list *next;
}List, *pList;
 
 
//建立雙向連結串列，返回頭結點指標
pList creatList()
{
    pList head = (pList)malloc(sizeof(List));
 
    pList temp1 = head;
    pList temp2 = (pList)malloc(sizeof(List));
    temp1->pre = NULL;
    temp1->next = temp2;
    temp1->root = (Tree)malloc(sizeof(Huffman));
    temp1->root->c = 'a';
    temp1->root->weight = 22;
    temp1->root->lchild = NULL;
    temp1->root->rchild = NULL;
    
 
    temp2->pre = temp1;
    temp1 = temp2;
    temp2 = (pList)malloc(sizeof(List));
    temp1->next = temp2;
    temp1->root = (Tree)malloc(sizeof(Huffman));
    temp1->root->c = 'b';
    temp1->root->weight = 5;
    temp1->root->lchild = NULL;
    temp1->root->rchild = NULL;
    
 
    temp2->pre = temp1;
    temp1 = temp2;
    temp2 = (pList)malloc(sizeof(List));
    temp1->next = temp2;
    temp1->root = (Tree)malloc(sizeof(Huffman));
    temp1->root->c = 'c';
    temp1->root->weight = 38;
    temp1->root->lchild = NULL;
    temp1->root->rchild = NULL;
 
    temp2->pre = temp1;
    temp1 = temp2;
    temp2 = (pList)malloc(sizeof(List));
    temp1->next = temp2;
    temp1->root = (Tree)malloc(sizeof(Huffman));
    temp1->root->c = 'd';
    temp1->root->weight = 9;
    temp1->root->lchild = NULL;
    temp1->root->rchild = NULL;
 
    temp2->pre = temp1;
    temp1 = temp2;
    temp2 = (pList)malloc(sizeof(List));
    temp1->next = temp2;
    temp1->root = (Tree)malloc(sizeof(Huffman));
    temp1->root->c = 'e';
    temp1->root->weight = 44;
    temp1->root->lchild = NULL;
    temp1->root->rchild = NULL;
 
    temp2->pre = temp1;
    temp1 = temp2;
    temp2 = (pList)malloc(sizeof(List));
    temp1->next = temp2;
    temp1->root = (Tree)malloc(sizeof(Huffman));
    temp1->root->c = 'f';
    temp1->root->weight = 12;
    temp1->root->lchild = NULL;
    temp1->root->rchild = NULL;
 
    temp2->pre = temp1;
    temp1 = temp2;
    temp1->next = NULL;
    temp1->root = (Tree)malloc(sizeof(Huffman));
    temp1->root->c = 'g';
    temp1->root->weight = 65;
    temp1->root->lchild = NULL;
    temp1->root->rchild = NULL;
 
    return head;                          
}

b建立棧結構：

解碼過程需要用到兩個棧，一個用來存放樹結點，一個用來存放碼0和1

'''C
#define STACK_INIT_SIZE 100   //棧初始開闢空間大小
#define STACK_INCREMENT 10    //棧追加空間大小
 
//字元棧結構體，存放編碼'0'和'1'
typedef struct {
    char *base;
    char *top;
    int size;
}charStack;
 
 
//棧初始化
charStack charStackInit()
{
    charStack s;
    s.base = (char *)malloc(sizeof(char)*STACK_INIT_SIZE);
    s.top = s.base;
    s.size = STACK_INIT_SIZE;
    return s;
}
 
//入棧
void charPush(charStack *s, char e)
{
    if(s->top - s->base >= s->size)
    {
        s->size += STACK_INCREMENT;
        s->base = realloc(s->base, sizeof(char)*s->size);
    }
    *s->top = e;
    s->top++;
}
 
//出棧
char charPop(charStack *s)
{
    if(s->top != s->base)
    {
        s->top--;
        return *s->top;
    }
    return -1;
}
 
//得到棧頂元素，但不出棧
char charGetTop(charStack *s)
{
    s->top--;
    char temp = *s->top;
    s->top++;
    return temp;
}
 
//棧結構體，存放哈夫曼樹結點
typedef struct 
{
    Huffman *base;
    Huffman *top;
    int size;
}BiStack;
 
//棧初始化
BiStack stackInit()
{
    BiStack s;
    s.base = (Huffman *)malloc(sizeof(Huffman)*STACK_INIT_SIZE);
    s.top = s.base;
    s.size =STACK_INIT_SIZE;
    return s;
}
 
//入棧
void push(BiStack *s, Huffman e)
{
    if(s->top - s->base >= s->size)
    {
        s->size += STACK_INCREMENT;
        s->base = (Huffman *)realloc(s->base, sizeof(Huffman)*s->size);
    }
    *s->top = e;
    s->top++;
}
 
//出棧
Huffman pop(BiStack *s)
{
    Huffman temp;
    s->top--;
    temp = *s->top;
    return temp;
}
 
//得到棧頂元素，但不出棧
Huffman getTop(BiStack s)
{
    Huffman temp;
    s.top--;
    temp = *s.top;
    return temp;
}
 
char stack[7][10];             //記錄a~g的編碼
//遍歷棧，得到字元c的編碼
void traverseStack(charStack s, char c)
{
    int index = c - 'a'; 
    int i = 0;
    while(s.base != s.top)
    {
        stack[index][i] = *s.base;
        i++;
        s.base++;
    }
}

c 建立哈夫曼樹：

'''C
//通過雙向連結串列建立哈夫曼樹，返回根結點指標
Tree creatHuffman(pList head)
{
    pList list1 = NULL;
    pList list2 = NULL;
    pList index = NULL;
    Tree root = NULL;
    while(head->next != NULL)   //連結串列只剩一個結點時迴圈結束，此結點資料域即為哈夫曼樹的根結點
    {
        list1 = head;
        list2 = head->next;
        index = list2->next;
        root = (Tree)malloc(sizeof(Huffman));
        while(index != NULL)    //找到連結串列中權重最小的兩個結點list1,list2
        {
            if(list1->root->weight > index->root->weight || list2->root->weight > index->root->weight)
            {
                if(list1->root->weight > list2->root->weight) list1 = index;
                else list2 = index;
            }
            index = index->next;
        }
        //list1和list2設為新結點的左右孩子
        if(list2->root->weight > list1->root->weight)
        {
            root->lchild = list1->root;
            root->rchild = list2->root;
        }
        else
        {
            root->lchild = list2->root;
            root->rchild = list1->root;
        }
        //新結點字元統一設為空格，權重設為list1與list2權重之和
        root->c = ' ';
        root->weight = list1->root->weight + list2->root->weight;
        //list1資料域替換成新結點，並刪除list2
        list1->root = root;
        list2->pre->next = list2->next;
        if(list2->next != NULL)
            list2->next->pre = list2->pre;    
    }
    return head->root;
}

d編碼：

'''C
char stack[7][10];             //記錄a~g的編碼
//遍歷棧，得到字元c的編碼
void traverseStack(charStack s, char c)
{
    int index = c - 'a'; 
    int i = 0;
    while(s.base != s.top)
    {
        stack[index][i] = *s.base;
        i++;
        s.base++;
    }
}
 
 
//通過哈夫曼樹編碼
void encodeHuffman(Tree T)
{  
    BiStack bs = stackInit();
    charStack cs = charStackInit();
    Huffman root = *T;  
    Tree temp = NULL;
    push(&bs, root);      //根結點入棧
    while(bs.top != bs.base)      //棧空表示遍歷結束
    {
        root = getTop(bs);
        temp = root.lchild;       //先存取左孩子
        while(temp != NULL)       //左孩子不為空
        {
            //將結點左孩子設為空，代表已存取其左孩子
            root.lchild = NULL;
            pop(&bs);            
            push(&bs, root);
            //左孩子入棧
            root = *temp;
            temp = root.lchild;
            push(&bs, root);
            //'0'入字元棧
            charPush(&cs, '0');
        }
        temp = root.rchild;     //後存取右孩子     
        while(temp == NULL)     //右孩子為空，代表左右孩子均已存取，結點可以出棧 
        {
            //結點出棧
            root = pop(&bs);
            //尋到葉子結點，可以得到結點中字元的編碼
            if(root.c != ' ')
                traverseStack(cs, root.c);
            charPop(&cs);       //字元棧出棧
            if(bs.top == bs.base) break;    //根結點出棧，遍歷結束
            //檢視上一級結點是否存取完左右孩子  
            root = getTop(bs);
            temp = root.rchild;           
        }
        if(bs.top != bs.base)
        {
            //將結點右孩子設為空，代表已存取其右孩子
            root.rchild = NULL;       
            pop(&bs);
            push(&bs, root);
            //右孩子入棧
            root = *temp;      
            push(&bs, root);
            //'1'入字元棧
            charPush(&cs, '1');
        }    
    }
}

e解碼：

'''C
char decode[100];   //記錄解碼得到的字串
//通過哈夫曼樹解碼
void decodeHuffman(Tree T, char *code)
{
    int cnt = 0;
    Tree root;
    while(*code != '')                  //01編碼字串讀完，解碼結束
    {
        root = T;
        while(root->lchild != NULL)       //找到葉子結點
        {
            if(*code != '')
            {
                if(*code == '0')
                    root = root->lchild;
                else
                    root = root->rchild;
                code++;
            }
            else break;
        }
        decode[cnt] = root->c;             //葉子結點存放的字元即為解碼得到的字元
        cnt++;
    }
}

f主函數：

'''C
void main()
{
    pList pl = creatList();
    printf("字元的權重如下n");
    for(pList l = pl; l->next != NULL; l = l->next)
        printf("字元%c的權重是 %dn", l->root->c, l->root->weight);
    Tree T = creatHuffman(pl);
    encodeHuffman(T);
    printf("nn字元編碼結果如下n");
    for(int i = 0; i < 7; i++)
        printf("%c : %sn", i+'a', stack[i]);
    char code[100];
    printf("nn請輸入編碼：n");
    scanf("%s", code);
    printf("解碼結果如下：n");
    decodeHuffman(T, code);
    printf("%sn", decode);
    printf("nn");
    system("date /T");
    system("TIME /T");
    system("pause");
    exit(0); 
}

1.2執行結果

2.Python實現

2.1程式碼說明

a建立哈夫曼樹：

#coding=gbk
 
import datetime
import time
from pip._vendor.distlib.compat import raw_input
 
#哈夫曼樹結點類
class Huffman:
    def __init__(self, c, weight):
        self.c = c
        self.weight = weight
        self.lchild = None
        self.rchild = None
    
    #建立結點左右孩子    
    def creat(self, lchild, rchild):
        self.lchild = lchild
        self.rchild = rchild
 
#建立列表        
def creatList():
    list = []
    list.append(Huffman('a', 22))
    list.append(Huffman('b', 5))
    list.append(Huffman('c', 38))
    list.append(Huffman('d', 9))
    list.append(Huffman('e', 44))
    list.append(Huffman('f', 12))
    list.append(Huffman('g', 65))
    return list
 
#通過列表建立哈夫曼樹，返回樹的根結點
def creatHuffman(list):
    while len(list) > 1:               #列表只剩一個結點時迴圈結束，此結點即為哈夫曼樹的根結點
        i = 0
        j = 1
        k = 2
        while k < len(list):           #找到列表中權重最小的兩個結點list1,list2          
            if list[i].weight > list[k].weight or list[j].weight > list[k].weight:
                if list[i].weight > list[j].weight:
                    i = k
                else:
                    j = k
            k += 1       
        root = Huffman(' ', list[i].weight + list[j].weight) #新結點字元統一設為空格，權重設為list1與list2權重之和   
        if list[i].weight < list[j].weight:                  #list1和list2設為新結點的左右孩子
            root.creat(list[i], list[j])
        else:
            root.creat(list[j], list[i])
        #list1資料域替換成新結點，並刪除list2
        list[i] = root
        list.remove(list[j])
    return list[0]

b編碼：

#通過哈夫曼樹編碼
def encodeHuffman(T):
    code = [[], [], [], [], [], [], []]
    #列表實現棧結構
    treeStack = []
    codeStack = []
    treeStack.append(T)
    while treeStack != []:        #棧空代表遍歷結束
        root = treeStack[-1]
        temp = root.lchild
        while temp != None:
            #將結點左孩子設為空，代表已存取其左孩子
            root.lchild = None        
            #左孩子入棧          
            treeStack.append(temp)         
            root = temp
            temp = root.lchild
            #0入編碼棧
            codeStack.append(0)
        temp = root.rchild            #後存取右孩子
        while temp == None:           #右孩子為空，代表左右孩子均已存取，結點可以出棧
            root = treeStack.pop()           #結點出棧
            #尋到葉子結點，可以得到結點中字元的編碼
            if root.c != ' ':
                codeTemp = codeStack.copy()
                code[ord(root.c) - 97] = codeTemp     
            if treeStack == []:    #根結點出棧，遍歷結束
                break
            codeStack.pop()        #編碼棧出棧
            #檢視上一級結點是否存取完左右孩子
            root = treeStack[-1]
            temp = root.rchild
        if treeStack != []:
            treeStack.append(temp)     #右孩子入棧
            root.rchild = None         #將結點右孩子設為空，代表已存取其右孩子
            codeStack.append(1)        #1入編碼棧
    return code

c解碼：

#通過哈夫曼樹解碼
def decodeHuffman(T, strCode):
    decode = []
    index = 0
    while index < len(strCode):        #01編碼字串讀完，解碼結束
        root = T
        while root.lchild != None:     #找到葉子結點
            if index < len(strCode):
                if strCode[index] == '0':
                    root = root.lchild
                else:
                    root = root.rchild
                index += 1
            else:
                break
        decode.append(root.c)           #葉子結點存放的字元即為解碼得到的字元
    return decode

d主函數：

if __name__ == '__main__':
    list = creatList()
    print("字元的權重如下")
    for i in range(len(list)):
        print("字元{}的權重為: {}".format(chr(i+97), list[i].weight))
    T = creatHuffman(list)
    code = encodeHuffman(T)
    print("n字元編碼結果如下")
    for i in range(len(code)):
        print(chr(i+97), end=' : ')
        for j in range(len(code[i])):
            print(code[i][j], end='')
        print("")
    strCode = input("n請輸入編碼：n")
    #哈夫曼樹在編碼時被破壞，必須重建哈夫曼樹
    list = creatList()
    T = creatHuffman(list)
    decode = decodeHuffman(T, strCode)
    print("解碼結果如下：")
    for i in range(len(decode)):
        print(decode[i], end='')
    print("nn")
    datetime = datetime.datetime.now()
    print(datetime.strftime("%Y-%m-%dn%H:%M:%S"))
    input("Press Enter to exit…")

2.2執行結果

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