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基于二叉树和数组实现限制长度的最优Huffman编码
详细介绍详见上篇博客:基于二叉树和双向链表实现限制长度的最优Huffman编码
基于数组和基于链表的实现方式在效率上有明显差别:
编码256个符号,符号权重为1...256,限制长度为16,循环编码1w次,Release模式下,基于链表的耗时为8972ms,基于数组的耗时为1793ms,速度是链表实现方式的5倍.
具体代码如下:
基于数组和基于链表的实现方式在效率上有明显差别:
编码256个符号,符号权重为1...256,限制长度为16,循环编码1w次,Release模式下,基于链表的耗时为8972ms,基于数组的耗时为1793ms,速度是链表实现方式的5倍.
具体代码如下:
//Reference:A fast algorithm for optimal length-limited Huffman codes.pdf,http://pan.baidu.com/s/1o6E19Bs //author:by Pan Yumin.2014-06-18 //with the method of BinaryTree and linked-list #include <stdio.h> #include <memory.h> #include <malloc.h> #define MaxSymbols 256 //the Maximum Number of Symbols #define MaxHuffLen 16 //the Limited Length typedef unsigned char boolean; #ifndef FALSE //in case these macros already exist #define FALSE 0 //values of boolean #endif #ifndef TRUE #define TRUE 1 #endif typedef struct __Node{ int width; int weight; int index; int depth; struct __Node *left; //left child struct __Node *right; //right child }Node; typedef struct __HuffTable{ unsigned int index; unsigned int len; unsigned int code; }HuffTable; //Test memory leak /*int g_malloc = 0,g_free = 0; void* my_malloc(int size){ g_malloc++; return malloc(size); } void my_free(void *ptr){ if(ptr){ g_free++; free(ptr); ptr = NULL; } } #define malloc my_malloc #define free my_free*/ //Get the smallest term in the diadic expansion of X int GetSmallestTerm(int X) { int N=0; while((X & 0x01) == 0){ X >>= 1; N++; } return 1<<N; } void RemoveNodeMark(Node *tree,unsigned char *Flag,int Symbols) { if(tree->left == NULL && tree->right == NULL){ Flag[tree->depth*Symbols+tree->index] = 0; //set the nodemark zero } if(tree->left){ RemoveNodeMark(tree->left,Flag,Symbols); } if(tree->right){ RemoveNodeMark(tree->right,Flag,Symbols); } } void PrintHuffCode(HuffTable Huffcode) { int i; for(i=Huffcode.len-1;i>=0;i--){ printf("%d",(Huffcode.code>>i) & 0x01); } } void GenerateHuffmanCode(HuffTable *HuffCode,unsigned char *Flag,int L,int Symbols,int *SortIndex) { char Code[17]; int Pre_L = 0; int i=0,j=0; unsigned int codes[MaxHuffLen+2]={0},rank[MaxHuffLen+1] = {0}; //rank: the number of symbols in every length //find the first code for(i=0;i<Symbols;i++){ for(j=0;j<L;j++){ HuffCode[i].len += Flag[j*Symbols+i]; } if(HuffCode[i].len != 0) rank[HuffCode[i].len]++; HuffCode[i].index = SortIndex[i]; } for(i=0;i<=L;i++){ codes[i+1] = (codes[i]+rank[i])<<1; rank[i] = 0; } //code for(i=0;i<Symbols;i++){ HuffCode[i].code = codes[HuffCode[i].len] + rank[HuffCode[i].len]++; } } float BitsPerSymbol(HuffTable *HuffCode,int *weight,int Symbols,int WeightSum) { float bitspersymbol = 0.0; int i; for(i=0;i<Symbols;i++){ bitspersymbol += (float)HuffCode[i].len*weight[i]; } return bitspersymbol/WeightSum; } //ascending order void FreqSort(int *Freq,int *SortIndex,int Symbols) { int i,j,tmp; for(i=0;i<Symbols;i++){ for(j=i+1;j<Symbols;j++){ if(Freq[i]>Freq[j]){ tmp = Freq[i]; Freq[i] = Freq[j]; Freq[j] = tmp; tmp = SortIndex[i]; SortIndex[i] = SortIndex[j]; SortIndex[j] = tmp; } } } } //ascending order, quick sort void QuickSort(int *arr, int *SortIndex,int startPos,int endPos) { int i,j,key,index; key=arr[startPos]; index = SortIndex[startPos]; i = startPos; j = endPos; while(i < j){ while(arr[j]>=key && i<j) --j; arr[i]=arr[j]; SortIndex[i] = SortIndex[j]; while(arr[i]<=key && i<j) ++i; arr[j]=arr[i]; SortIndex[j] = SortIndex[i]; } arr[i]=key; SortIndex[i] = index; if(i-1 > startPos) QuickSort(arr,SortIndex,startPos,i-1); if(endPos > i+1) QuickSort(arr,SortIndex,i+1,endPos); } int GenLenLimitedOptHuffCode(int *Freq,int Symbols) { int i,j; unsigned char *Flag = NULL; //record the state of the node unsigned int rank[MaxHuffLen]; Node *tree = NULL, *base = NULL, *left = NULL, *right = NULL; Node *start = NULL, *end = NULL, *Last = NULL; //start:the first(min weight) node of 2*r,end:the last(max weight) node of 2*r,Last:the last node of array. Node *node = NULL; HuffTable HuffCode[MaxSymbols]; float bitspersymbols = 0.0; int WeightSum = 0; int SortIndex[MaxSymbols]; int X = (Symbols-1)<<MaxHuffLen; //avoid float calculation int minwidth,r,weight; int r_Num = 0; if(Symbols > (1<<MaxHuffLen)){ printf("Symbols > (1<<MaxHuffLen)\n"); return -1; } for(i=0;i<MaxSymbols;i++){ SortIndex[i] = i; } //FreqSort(Freq,SortIndex,Symbols); //sort QuickSort(Freq,SortIndex,0,Symbols-1); //sort for(i=0;i<Symbols;i++){ WeightSum += Freq[i]; } tree = (Node *)malloc(Symbols*MaxHuffLen*2*sizeof(Node)); memset(tree,0,Symbols*MaxHuffLen*2*sizeof(Node)); //2: for the optimize Flag = (unsigned char*)malloc(MaxHuffLen*Symbols*sizeof(unsigned char)); memset(Flag,0x01,MaxHuffLen*Symbols*sizeof(unsigned char)); //mark every node 1 memset(HuffCode,0,sizeof(HuffCode)); for(i=0;i<MaxHuffLen;i++){ for(j=0;j<Symbols;j++){ tree[i*Symbols+j].depth = i; tree[i*Symbols+j].index = j; tree[i*Symbols+j].width = 1<<i; //avoid float calculation tree[i*Symbols+j].weight = Freq[j]; } } //start code base = tree; Last = tree+MaxHuffLen*Symbols-1; while(X>0){ minwidth = GetSmallestTerm(X); r = base->width; if(r > minwidth){ //there is no optimal solution. return -2; } else if(r == minwidth){ X -= minwidth; base++; }else{ //merge the smallest width and insert it into the original array if(r < (1<<(MaxHuffLen-1))){ start = base+1; r_Num = 1; //find start and end while(start->width < 2*r && start <= Last){ r_Num++; start++; } end = start; while(end->width == 2*r && end <= Last){ end++; } end--; //move back the (>=2*r)width node node = Last; r_Num = r_Num/2; while(node >= start){ *(node+r_Num) = *node; node--; } //package and merge node = start; start = start + r_Num; end = end + r_Num; for(i=0;i<r_Num;i++){ left = base; base++; right = base; base++; weight = left->weight + right->weight; while(start <= end && start->weight <= weight){ *node = *start; start++; node++; } node->weight = weight; node->width = 2*r; node->left = left; node->right = right; node++; } if(base->width == r){ //if r_Num is odd,remove the last r(width) Node. RemoveNodeMark(base,Flag,Symbols); base++; } Last += r_Num; }else{ //r >= (1<<(MaxHuffLen-1)) while(base->width == r){ left = base; weight = base->weight; if((*(base+1)).width == r){ base++; right = base; weight += base->weight; base++; Last++; Last->weight = weight; Last->width = 2*r; Last->left = left; Last->right = right; }else{ RemoveNodeMark(base,Flag,Symbols); base++; } } } } } //output the HuffCode GenerateHuffmanCode(HuffCode,Flag,MaxHuffLen,Symbols,SortIndex); //print HuffCode for(i=0;i<Symbols;i++){ printf("%03d weight:%04d Code:",HuffCode[i].index,Freq[i]); PrintHuffCode(HuffCode[i]); printf("\tCodeLen:%02d",HuffCode[i].len); printf("\n"); } bitspersymbols = BitsPerSymbol(HuffCode,Freq,Symbols,WeightSum); printf("average code length:%f bits/symbol.\n",bitspersymbols); free(tree); tree = NULL; free(Flag); Flag = NULL; return 0; } #include <time.h> int main() { // int Freq[MaxSymbols] = {1,25,3,4,9,6,4,6,26,15,234,4578}; //weight is not zero. int Freq[MaxSymbols] = {10,6,2,1,1}; //weight is not zero. GenLenLimitedOptHuffCode(Freq,5); //5,12 return 0; }输出结果如下所示:
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