/*
Name: 赫夫曼編碼
Copyright: 始發(fā)于goal00001111的專欄；允許自由轉(zhuǎn)載，但必須注明作者和出處
Author: goal00001111
Date: 16-12-08 21:16
Description: 赫夫曼編碼
本程序?qū)崿F(xiàn)了使用赫夫曼編碼壓縮數(shù)據(jù)；輸入一串字符串sourceCode——為方便理解，暫時(shí)要求字符串只包含大寫(xiě)字母和空格，如果你愿意，
很容易就可以推廣到所有的字符——計(jì)算出字符串中各個(gè)字母的權(quán)重，然后對(duì)其進(jìn)行赫夫曼編碼，輸出赫夫曼樹(shù)。
將赫夫曼樹(shù)的葉子結(jié)點(diǎn)存儲(chǔ)到有序二叉樹(shù)中，輸出原字符串經(jīng)壓縮后得到的用'0'和'1'表示的新字符串destCode；
然后利用赫夫曼樹(shù)將字符串destCode進(jìn)行譯碼，得到目標(biāo)字符串objCode，比較objCode和sourceCode，發(fā)現(xiàn)完全一樣！
編碼譯碼成功！
最后銷毀有序二叉樹(shù)和赫夫曼樹(shù)。
本程序的一個(gè)亮點(diǎn)是使用了二叉堆來(lái)存儲(chǔ)需要合并的赫夫曼樹(shù)結(jié)點(diǎn)，這樣在求最小值時(shí)時(shí)間復(fù)雜度可以降低到log(n)。
另外關(guān)于赫夫曼編碼的詳細(xì)內(nèi)容請(qǐng)參考維基百科： http://zh.wikipedia.org/wiki/%E5%93%88%E5%A4%AB%E6%9B%BC%E7%BC%96%E7%A0%81
和數(shù)據(jù)結(jié)構(gòu)自考網(wǎng)：http://student.zjzk.cn/course_ware/data_structure/web/shu/shu6.6.2.1.htm
關(guān)于二叉堆的詳細(xì)內(nèi)容請(qǐng)參考百度百科：http://baike.baidu.com/view/668854.html
*/
#include<iostream>
using namespace std;
typedef char ElemType;
typedef struct sNode
{
double weight;
ElemType data;
} *Source;
typedef struct hNode
{
double weight;
ElemType data;
int lc, rc;
} *HuffmanTree;
typedef struct cNode
{
ElemType data;
string str;
struct cNode *lc, *rc;
} *Btree;
HuffmanTree CreateHuffmanTree(const Source w, int n);//創(chuàng)建一棵赫夫曼樹(shù)
void BuildHeap(HuffmanTree t, int n); //構(gòu)造一個(gè)二叉堆；小頂堆
void PercDown(HuffmanTree t, int pos, int n);//構(gòu)造二叉堆的功能子函數(shù)
void DeleteMin(HuffmanTree t, int len); //刪除二叉堆的根，并通過(guò)上移使得新得到的序列仍為二叉堆
void InsertHfNode(HuffmanTree t, int len, struct hNode x); //把x插入到原長(zhǎng)度為len的二叉堆
void Preorder(HuffmanTree t, int p); //先序遍歷赫夫曼樹(shù)
void Postorder(Btree & t, HuffmanTree a, int n); //后序遍歷赫夫曼樹(shù)，并記錄葉子結(jié)點(diǎn)編碼
bool InsertBtNode(Btree & t, Btree s); //向一個(gè)二叉排序樹(shù)t中插入一個(gè)結(jié)點(diǎn)s
void Inorder(Btree t); //中序遍歷二叉排序樹(shù)
Btree Search(Btree p, ElemType data); //查找值為data的結(jié)點(diǎn)的遞歸算法
string Coding(string s, Btree t); //利用記錄了葉子結(jié)點(diǎn)編碼的排序二叉樹(shù)，對(duì)sourceCode進(jìn)行編碼，返回編碼后的字符串
string Decode(string s, HuffmanTree hT); //利用赫夫曼樹(shù)對(duì)destCode進(jìn)行解碼
void DestroyBTree(Btree & t); //銷毀一棵二叉排序樹(shù)
void DestroyHfmanTree(HuffmanTree & t, int n); //銷毀一棵赫夫曼樹(shù)
int main()
{
string sourceCode;
getline(cin, sourceCode, '\n');
int n = sourceCode.size();
const int MAX = 27; //原碼由26個(gè)大寫(xiě)字母加空格組成
Source w = new struct sNode[MAX];
//讀取各個(gè)字母并初始化權(quán)重
w[MAX-1].data = ' ';
w[MAX-1].weight = 0;
for (int i=MAX-2; i>=0; i--)
{
w[i].data = 'A' + i;
w[i].weight = 0;
}
//讀取各個(gè)字母的權(quán)重
for (int i=0; i<n; i++)
{
if (sourceCode[i] == ' ')
w[26].weight++;
else
w[sourceCode[i]-'A'].weight++;
}
//獲取出現(xiàn)了的大寫(xiě)字母和空格
n = 0;
for (int i=0; i<MAX; i++)
{
if (w[i].weight > 0)
w[n++] = w[i];
}
// //直接輸入原碼和權(quán)重
// for (int i=0; i<n; i++)
// {
// cin >> w[i].weight >> w[i].data;
// }
for (int i=0; i<n; i++)
{
cout << w[i].weight << " " << w[i].data << endl;
}
HuffmanTree hT = CreateHuffmanTree(w, n);//構(gòu)造赫夫曼樹(shù)
// for (int i=1; i<2*n; i++)
// cout << hT[i].weight << " ";
// cout << endl;
//先序遍歷赫夫曼樹(shù)，并輸出結(jié)點(diǎn)權(quán)重和葉子結(jié)點(diǎn)的data
Preorder(hT, 1);
cout << endl;
//后序遍歷赫夫曼樹(shù)，并記錄葉子結(jié)點(diǎn)編碼
Btree bT = NULL;
Postorder(bT, hT, n);
//中序遍歷記錄了葉子結(jié)點(diǎn)編碼的排序二叉樹(shù)
Inorder(bT);
//利用記錄了葉子結(jié)點(diǎn)編碼的排序二叉樹(shù)，對(duì)sourceCode進(jìn)行編碼
string destCode = Coding(sourceCode, bT);
cout << destCode << endl;
//利用赫夫曼樹(shù)對(duì)destCode進(jìn)行解碼
string objCode = Decode(destCode, hT);
cout << objCode << endl;
DestroyBTree(bT); //銷毀二叉排序樹(shù)
//Inorder(bT); //再輸出試試看
DestroyHfmanTree(hT, n); //銷毀赫夫曼樹(shù)
//Preorder(hT, 1); //再輸出試試看
system("pause");
return 0;
}
//創(chuàng)建一棵赫夫曼樹(shù)
HuffmanTree CreateHuffmanTree(const Source w, int n)
{
HuffmanTree hT = new struct hNode[2*n]; //第一個(gè)結(jié)點(diǎn)不用
for (int i=0; i<n; i++)
{
hT[i+1].data = w[i].data;
hT[i+1].weight = w[i].weight;
hT[i+1].lc = hT[i+1].rc = 0;
}
BuildHeap(hT, n);//構(gòu)造一個(gè)二叉堆；小頂堆
struct hNode add;
int left = n;
int right = n;
while (left > 1)
{
hT[++right] = hT[1];
add.weight = hT[1].weight;
add.lc = right; //存儲(chǔ)左孩子下標(biāo)
DeleteMin(hT, left--);
hT[left+1] = hT[1];
add.weight += hT[1].weight;
add.rc = left+1; //存儲(chǔ)右孩子下標(biāo)
DeleteMin(hT, left--);
InsertHfNode(hT, ++left, add);
//for (int i=1; i<=right; i++)
// cout << hT[i].weight << " ";
// cout << endl;
// system("pause");
}
return hT;
}
//構(gòu)造一個(gè)二叉堆；小頂堆
void BuildHeap(HuffmanTree t, int len)
{
for (int i=len/2; i>0; i--)
{
PercDown(t, i, len);
}
}
//構(gòu)造二叉堆的功能子函數(shù)
void PercDown(HuffmanTree t, int pos, int len)
{
int child;
struct hNode min = t[pos];
while (pos * 2 <= len)
{
child = pos * 2;
if (child != len && t[child+1].weight < t[child].weight)
child++;
if (min.weight > t[child].weight)
t[pos] = t[child];
else
break;
pos = child;
}
t[pos] = min;
}
//刪除二叉堆的根，并通過(guò)上移使得新得到的序列仍為二叉堆
void DeleteMin(HuffmanTree t, int len)
{
struct hNode last = t[len--];//二叉堆的最后一個(gè)元素
int child, pos = 1;
while (pos * 2 <= len) //把二叉堆的某些元素往前移，使得新得到的序列仍為二叉堆
{
child = pos * 2;
if (child != len && t[child+1].weight < t[child].weight) //若i有右兒子，且右兒子小于左兒子，c指向右兒子
child++;
if (last.weight > t[child].weight) //若i的小兒子小于二叉堆的最后一個(gè)元素，把其移到i的位置
t[pos] = t[child];
else
break;
pos = child;
}
t[pos] = last; //把二叉堆的最后一個(gè)元素放到適當(dāng)?shù)目瘴唬藭r(shí)得到的序列仍為二叉堆
}
//把x插入到原長(zhǎng)度為len的二叉堆
void InsertHfNode(HuffmanTree t, int len, struct hNode x)
{
int i;
for (i=len; i/2>0 && t[i/2].weight>x.weight; i/=2)
t[i] = t[i/2];
t[i] = x;
}
//后序遍歷赫夫曼樹(shù)，并記錄葉子結(jié)點(diǎn)編碼
void Postorder(Btree & t, HuffmanTree a, int n)
{
int *stack = new int[n];
int *tag = new int[n];
char *buf = new char[n];
bool flag = true;
int top = -1;
int p = 1;
while (a[p].lc > 0 || top >= 0)
{
while (a[p].lc > 0) //先一直尋找左孩子
{
flag = true; //此時(shí)p指向的是新葉子（未輸出過(guò)的葉子）
stack[++top] = p; //結(jié)點(diǎn)入棧
p = a[p].lc;
tag[top] = 0; //表示右孩子沒(méi)有被訪問(wèn)
buf[top] = '0'; //左孩子標(biāo)記'0'
}
if (flag) //如果p指向的是新葉子
{
//cout << a[p].data << " : "; //輸出葉子結(jié)點(diǎn)
// for (int i=0; i<=top; i++)
// cout << buf[i];
// cout << endl;
Btree s = new struct cNode;
s->data = a[p].data;
for (int i=0; i<=top; i++)
s->str += buf[i];
s->lc = s->rc = NULL;
if (!(InsertBtNode(t, s))) //插入一個(gè)結(jié)點(diǎn)s
delete s;
}
if (top >= 0) //所有左孩子處理完畢后
{
if (tag[top] == 0) //如果右孩子沒(méi)有被訪問(wèn)
{
flag = true; //此時(shí)p指向的是新葉子（未輸出過(guò)的葉子）
p = stack[top]; //讀取棧頂元素，但不退棧 ，因?yàn)橐容敵銎溆液⒆咏Y(jié)點(diǎn)
p = a[p].rc;
tag[top] = 1; //表示右孩子被訪問(wèn)，下次直接退棧
buf[top] = '1'; //右孩子標(biāo)記'1'
}
else //棧頂元素出棧
{
flag = false; //此時(shí)p指向的是舊葉子（已輸出過(guò)的葉子），不再輸出
top--;
}
}
}
}
//先序遍歷赫夫曼樹(shù)
void Preorder(HuffmanTree t, int p)
{
if (t == NULL)
return;
if (t[p].lc > 0)
{
cout << t[p].weight << endl;
Preorder(t, t[p].lc); //遍歷左子樹(shù)
Preorder(t, t[p].rc); //遍歷右子樹(shù)
}
else
cout << t[p].weight << " " << t[p].data << endl;
}
//向一個(gè)二叉排序樹(shù)t中插入一個(gè)結(jié)點(diǎn)s
bool InsertBtNode(Btree & t, Btree s)
{
if (t == NULL)
{
t = s;
return true;
}
else if (t->data > s->data) //把s所指結(jié)點(diǎn)插入到左子樹(shù)中
return InsertBtNode(t->lc, s);
else if (t->data < s->data) //把s所指結(jié)點(diǎn)插入到右子樹(shù)中
return InsertBtNode(t->rc, s);
else //若s->data等于b的根結(jié)點(diǎn)的數(shù)據(jù)域之值，則什么也不做
return false;
}
//中序遍歷二叉排序樹(shù)
void Inorder(Btree t)
{
if (t)
{
Inorder(t->lc); //遍歷左子樹(shù)
cout << t->data << " : " << t->str << endl; //輸出該結(jié)點(diǎn)
Inorder(t->rc); //遍歷右子樹(shù)
}
}
//查找值為data的結(jié)點(diǎn)的遞歸算法
Btree Search(Btree p, ElemType data)
{
if (p == NULL || p->data == data) //空樹(shù)或找到結(jié)點(diǎn)
return p;
if (p->data > data)
return Search(p->lc, data); //在左孩子中尋找
else
return Search(p->rc, data); //在右孩子中尋找
}
//利用記錄了葉子結(jié)點(diǎn)編碼的排序二叉樹(shù)，對(duì)sourceCode進(jìn)行編碼，返回編碼后的字符串
string Coding(string s, Btree t)
{
Btree p = NULL;
string dest;
for (int i=0; i<s.size(); i++)
{
p = Search(t, s[i]);
if (p != NULL)
{
dest += p->str;
//dest += ' ';
}
}
return dest;
}
//利用赫夫曼樹(shù)對(duì)destCode進(jìn)行解碼
string Decode(string s, HuffmanTree hT)
{
string dest;
int p = 1;
int i = 0;
while (i < s.size())
{
while (hT[p].lc > 0)//非葉子結(jié)點(diǎn)
{
if (s[i++] == '0')
p = hT[p].lc; //向左結(jié)點(diǎn)前進(jìn)
else
p = hT[p].rc; //向右結(jié)點(diǎn)前進(jìn)
}
dest += hT[p].data; //存儲(chǔ)葉子結(jié)點(diǎn)
p = 1;
}
return dest;
}
//銷毀一棵二叉排序樹(shù)
void DestroyBTree(Btree & t)
{
if (t != NULL)
{
DestroyBTree(t->lc);
DestroyBTree(t->rc);
delete t;
t = NULL;
}
}
//銷毀一棵赫夫曼樹(shù)
void DestroyHfmanTree(HuffmanTree & t, int n)
{
for (int i=n-1; i>=0; i--)
{
delete &t[i];
}
t = NULL;
}