哈夫曼樹編解碼
問題 B: DS_6.14 給定報文，哈弗曼編碼、譯碼(by Yan)
時間限制: 20 Sec 記憶體限制: 256 MB
提交: 303 解決: 218
[提交][狀態][討論版]
題目描述
已知某段通訊報文內容，對該報文進行哈弗曼編碼，並計算平均碼長。
(1)統計報文中各字元出現的頻度。(字符集範圍為52個英文字母，空格，英文句號。報文長度<=200)
(2)構造一棵哈弗曼樹，依次給出各字元編碼結果。
(3)給字串進行編碼。
(4)給編碼串進行譯碼。
(5)計算平均碼長。
規定：
(1)結點統計：以ASCII碼的順序依次排列，例如：空格，英文句號，大寫字母，小寫字母。
(2)構建哈弗曼樹時：左子樹根結點權值小於等於右子樹根結點權值。
(3)選擇的根節點權值相同時，前者構建為雙親的左孩子，後者為右孩子。
(4)生成編碼時：左分支標0，右分支標1。
輸入
第一部分：報文內容，以’#'結束。
第二部分：待譯碼的編碼串。
輸出
依次輸出報文編碼串、譯碼串、平均碼長，三者之間均以換行符間隔。
平均碼長，保留小數點2位。
樣例輸入
Data structure is the way of computer storage and organization data. A data structure is a collection of data elements that exist between one or more specific relationships.#
000111111110101111110100101010000110111100010011011000001110011110011100101011010011100001101111011001011010101011001101110010101011101011110110101000110001101001010101010001111000101001110111111101000001101010100000010111111110101110110011111101001111010111011100000011110101111000100110000111011000000111101011111101001010100001101111000100110110000011100111100111011111101110010100000100001001111000100111101011101110101010110011000000111101011111100010000100110111000111101010100111001010110111110101100010110001011110010101100110000001010000110001001111011101010111010011101010100011010111010101000001110100110111100111100011110110001111110011010000010000111110100111101011101100110110101111011111001000100
樣例輸出
000111111110101111110100101010000110111100010011011000001110011110011100101011010011100001101111011001011010101011001101110010101011101011110110101000110001101001010101010001111000101001110111111101000001101010100000010111111110101110110011111101001111010111011100000011110101111000100110000111011000000111101011111101001010100001101111000100110110000011100111100111011111101110010100000100001001111000100111101011101110101010110011000000111101011111100010000100110111000111101010100111001010110111110101100010110001011110010101100110000001010000110001001111011101010111010011101010100011010111010101000001110100110111100111100011110110001111110011010000010000111110100111101011101100110110101111011111001000100
Data structure is the way of computer storage and organization data. A data structure is a collection of data elements that exist between one or more specific relationships.
4.11
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#define LettersNum 6
#define TextCharTypeNum 54
typedef struct{//三叉連結串列的結點結構體定義
int weight;
int Parent;
int Lchild;
int Rchild;
}HFTreeNode;
void SelectTwoMinimumWeightNodes(HFTreeNode Tree[],int Range,int *Node1,int *Node2)//在哈夫曼樹陣列從第一個元素到第Range元素找出兩個不重複的權值最小的樹結點
{
int cmp = 998,i;
for(i=1;i<=Range;i++)
{
if(Tree[i].weight<cmp&&Tree[i].Parent==0)
{
cmp = Tree[i].weight;
*Node1 = i;
}
}
cmp = 998;
for(i=1;i<=Range;i++)
{
if((Tree[i].weight<cmp)&&Tree[i].Parent==0&&i!=*Node1)
{
cmp = Tree[i].weight;
*Node2 = i;
}
}
return;
}
void CreateHuffmanTree(HFTreeNode *Tree,int weights[],int LeafsNum)//由於大小固定哈夫曼樹的儲存採用靜態三叉連結串列自底而頂構建
{
int NodesNum = 2*LeafsNum-1;//整棵樹結點數
int i;
int Node1,Node2;
for(i=1;i<=LeafsNum;i++){Tree[i].weight = weights[i-1];Tree[i].Parent=Tree[i].Lchild=Tree[i].Rchild=0;}//初始前n個元素作為根基
for(i=LeafsNum+1;i<=NodesNum;i++){Tree[i].weight = Tree[i].Parent = Tree[i].Lchild = Tree[i].Rchild = 0;}
for(i=LeafsNum+1;i<=NodesNum;i++)
{
SelectTwoMinimumWeightNodes(Tree,i-1,&Node1,&Node2);
Tree[i].weight = Tree[Node1].weight+Tree[Node2].weight;//子母結點的連線
Tree[i].Lchild = Node1;
Tree[i].Rchild = Node2;
Tree[Node1].Parent = i;
Tree[Node2].Parent = i;
}
return;
}
void PrintTreeContent(HFTreeNode *Tree,int LeafsNum)
{
int i;
for(i = 1;i<=2*LeafsNum-1;i++)
{
printf("%d %d %d %d\n",Tree[i].weight,Tree[i].Parent,Tree[i].Lchild,Tree[i].Rchild);
}
return;
}
void SetBinaryCode(HFTreeNode *Tree,int WhichLetter,char **Aim)
{
int Codelength = 0,i=WhichLetter,j;
while(Tree[i].Parent!=0)
{
i = Tree[i].Parent;
Codelength++;
}
*Aim = (char*)malloc((Codelength+1)*sizeof(char));
i = WhichLetter;
for(j=Codelength-1;j>=0;j--)
{
if(Tree[Tree[i].Parent].Lchild==i)
{
(*Aim)[j] = '0';
i = Tree[i].Parent;
}
else if(Tree[Tree[i].Parent].Rchild==i)
{
(*Aim)[j] = '1';
i = Tree[i].Parent;
}
}
(*Aim)[Codelength]='\0';
return;
}
void PrintLetterCorrespondingCodes(char *Codes[],int CodesSize,char ValidLetters[])
{
int i;
for(i=0;i<CodesSize;i++)
{
printf("%c:%s\n",ValidLetters[i],Codes[i]);
}
return;
}
void Encode(char *Aim,char *Codes[],int CodesSize,char ValidLetters[])//字母轉為01串
{
int i,j;
for(i=0;i<strlen(Aim);i++)
{
for(j=0;j<CodesSize;j++)
{
if(Aim[i]==ValidLetters[j]){printf("%s",Codes[j]);break;}
}
}
return;
}
void Decode(char *Aim,char *Codes[],int CodesSize,char ValidLetters[])//01串轉為字母
{//0010000100111101測試資料
int i,j,k,maxCodeLength=0,maxcmp,check,flag,AimLen;
for(i=0;i<CodesSize;i++)if(strlen(Codes[i])>maxCodeLength)maxCodeLength = strlen(Codes[i]);
//printf("最長碼長度%d\n",maxCodeLength);
AimLen = strlen(Aim);
//printf("二進位制串長度%d\n",AimLen);
i=0;
while(i<AimLen)
{
flag = 0;
maxcmp = 0;
for(k=0;k<CodesSize;k++)
{
j = 0;
for(check=i;check<i+maxCodeLength&&check<AimLen;check++)
{
if(Aim[check]!=Codes[k][check-i])break;
else j++;
}
if(j>maxcmp)
{
maxcmp = j;
flag = k;
}
}
printf("%c",ValidLetters[flag]);
i+=strlen(Codes[flag]);
//printf("此段譯碼長度%d\n",strlen(Codes[flag]));
}
return;
}
void CountTextCharNums(int *TextCharWeights,char Text[])
{
int i;
for(i=0;i<TextCharTypeNum;i++)
{
TextCharWeights[i]=0;
}
for(i=0;i<strlen(Text);i++)
{
if(Text[i]==' ')TextCharWeights[TextCharTypeNum-2]++;
else if(Text[i]=='.')TextCharWeights[TextCharTypeNum-1]++;
else if(Text[i]>='A'&&Text[i]<='Z')TextCharWeights[Text[i]-'A']++;
else if(Text[i]>='a'&&Text[i]<='z')TextCharWeights[Text[i]-'a'+(TextCharTypeNum-2)/2]++;
}
return;
}
float ComputeAverageBinStrLength(char *Codes[],int CodesSize)
{
unsigned i;
float result,Sum=0;
for(i=0;i<CodesSize;i++)
{
Sum += strlen(Codes[i]);
}
result = Sum/(float)CodesSize;
return result;
}
int GetValidWeightsNum(int weights[])
{
int i,Num=0;
for(i=0;i<TextCharTypeNum;i++)
{
if(weights[i]>0)Num++;
}
return Num;
}
void CopytoNewWeightsArr(int *NewWeights,int OldWeights[],char *ValidLetters,int ValidWeights,char TextChar[])
{
int i,k=0;
for(i=0;i<ValidWeights;i++)
{
NewWeights[i] = 0;
}
for(i=0;i<TextCharTypeNum;i++)
{
if(OldWeights[i]>0&&k<ValidWeights)
{
NewWeights[k] = OldWeights[i];
ValidLetters[k] = TextChar[i];
k++;
}
}
return;
}
int main()
{
int i;
char TextChar[TextCharTypeNum];
for(i=0;i<TextCharTypeNum;i++)
{
if(i<(TextCharTypeNum-2)/2)TextChar[i]='A'+i;
else if(i<TextCharTypeNum-2)TextChar[i]='a'+i-(TextCharTypeNum-2)/2;
else if(i==TextCharTypeNum-2)TextChar[i]=' ';
else if(i==TextCharTypeNum-1)TextChar[i]='.';
//printf("%c",TextChar[i]);
}
char Text[200],buf;
for(i=0;i<200;i++)Text[i]='\0';
i=0;
while(i<200)//給Text賦值
{
buf = getchar();
if(buf=='\n')continue;
else if(buf=='#')break;
else Text[i++]=buf;
}
int TextCharWeights[TextCharTypeNum];//未縮減前的weights陣列
int ValidWeights;//weight不為零的字元數量
CountTextCharNums(TextCharWeights,Text);//統計Text裡所有字元數量
ValidWeights = GetValidWeightsNum(TextCharWeights);
int Weights[ValidWeights];//僅有非零weight的weights陣列
char ValidLetters[ValidWeights];
char *Codes[ValidWeights];
CopytoNewWeightsArr(Weights,TextCharWeights,ValidLetters,ValidWeights,TextChar);
HFTreeNode HFTree[ValidWeights*2];
CreateHuffmanTree(HFTree,Weights,ValidWeights);
//PrintTreeContent(HFTree,TextCharTypeNum);
for(i=0;i<ValidWeights;i++)SetBinaryCode(HFTree,i+1,&Codes[i]);
PrintLetterCorrespondingCodes(Codes,ValidWeights,ValidLetters);
Encode(Text,Codes,ValidWeights,ValidLetters);
printf("\n");
char BinStr[3000];
i=0;
getchar();
while(i<3000)
{
buf = getchar();
if(buf=='1'||buf=='0')BinStr[i++]=buf;
else {BinStr[i++]='\0';break;}
}
//printf("\n%s\n",BinStr);
Decode(BinStr,Codes,ValidWeights,ValidLetters);
printf("\n%.2f\n",ComputeAverageBinStrLength(Codes,ValidWeights));
return 0;
}