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赫夫曼樹： 如果有n個權值{w1,w2,w3....},試構造一棵具有n個葉子節點的二叉樹，每一個葉子節點帶權為wi。則當中帶權路徑長度最小的二叉樹稱為最優二叉樹或者叫赫夫曼樹。 構造赫夫曼樹： 如果有n個權值，則構造出的赫夫曼樹有n個葉子節點，n個權值分別設置為w1，w2,....wn,則赫夫曼樹的構造規則為： 1.將w1,w2...看成是有n棵樹的森林； 2.在森林中選擇兩個根節點的權值最小的樹合並，作為一棵新樹的左右子樹，且新樹的根節點權值為其左右子樹根節點權值之和； 3.從森林中刪除選取的兩棵樹，並將新樹增加森林。 4.反復2、3步，直到森林中僅僅剩一棵樹為止。該樹即為所求得的赫夫曼樹。
實現： 以數組形式存儲赫夫曼樹節點，節點形態：

/**************************************************
構造赫夫曼樹
by Rowandjj
2014/6/2
**************************************************/
#include<IOSTREAM>
using namespace std;

#define UINT_MAX 0xffffffff

typedef struct _BITREE_//二叉樹
{
    int data;//存放節點的圈中
    struct _BITREE_ *lChild;
    struct _BITREE_ *rChild;
}Bitree,*pBitree;

typedef struct _HUFFMANTREE_//赫夫曼樹
{
    unsigned int weight;
    unsigned int parent;
    unsigned int lChild;
    unsigned int rChild;
}HuffmanTree,*pHuffmanTree;

int iCount = 0;//葉子節點數
int iIndex = 1;//索引

//-----------------------------------------

void CreateBiTree(pBitree* pBitreeTemp);//創建二叉樹
void CreatreArray(pHuffmanTree& pHuffmanTreeTemp,pBitree pBitreeTemp);//將二叉樹每一個節點的值作為權放進赫夫曼樹中
pHuffmanTree InitHuffmanTree();//初始化赫夫曼樹，
void CreateHuffmanTree(pHuffmanTree& pHuffmanTreeTemp);//創建赫夫曼樹
int GetNode(pHuffmanTree& pHuffmanTreeTemp,int i);//獲取赫夫曼樹中位置0-i中值最小的節點的索引
void SelectNode(pHuffmanTree& pHuffmanTreeTemp,int i,int *m,int *n);//選擇赫夫曼樹數組中值最小的兩個節點的索引（不包括已有父節點的節點）
void DestroyTree(pBitree* pBitreeTemp);
void DestroyHuffmanTree(pHuffmanTree& pHuffmanTreeTemp);
int main()
{
    int i;
    //創建二叉樹
    pBitree pBitreeTemp;
    CreateBiTree(&pBitreeTemp);
    //初始化赫夫曼樹
    pHuffmanTree pHuffmanTreeTemp = InitHuffmanTree();

    //初始化赫夫曼樹的葉子節點的權
    CreatreArray(pHuffmanTreeTemp,pBitreeTemp);
    for(i = 1; i <= iCount ; i++)
    {
        cout<<pHuffmanTreeTemp[i].weight<<" ";
    }
    cout<<endl;
    //創建赫夫曼樹
    CreateHuffmanTree(pHuffmanTreeTemp);
    for(i = 1; i <= 2*iCount-1 ; i++)
    {
        cout<<pHuffmanTreeTemp[i].weight<<" ";
    }
    cout<<endl;

    DestroyTree(&pBitreeTemp);
    DestroyHuffmanTree(pHuffmanTreeTemp);
    return 0;
}

void CreateBiTree(pBitree* pBitreeTemp)
{
    int data;
    cin>>data;
    if(data == -1)
    {
        return;
    }
    *pBitreeTemp = (pBitree)malloc(sizeof(Bitree));
    if(*pBitreeTemp == NULL)
    {
        return;
    }
    (*pBitreeTemp)->data = data;
    (*pBitreeTemp)->lChild = NULL;
    (*pBitreeTemp)->rChild = NULL;

    CreateBiTree(&(*pBitreeTemp)->lChild);
    CreateBiTree(&(*pBitreeTemp)->rChild);

    iCount++;
}
pHuffmanTree InitHuffmanTree()
{
    int num = 2*iCount - 1;//赫夫曼樹的節點總數為：葉子節點數*2-1
    pHuffmanTree pTemp = (pHuffmanTree)malloc(sizeof(HuffmanTree)*(num+1));//0位不存
    if(pTemp == NULL)
    {
        return NULL;
    }
    for(int i = 0; i <= num; i++)
    {
        pTemp[i].lChild = 0;
        pTemp[i].rChild = 0;
        pTemp[i].parent = 0;
        pTemp[i].weight = 0;
    }
    return pTemp;
}
void CreatreArray(pHuffmanTree& pHuffmanTreeTemp,pBitree pBitreeTemp)
{
    if(pBitreeTemp == NULL || pHuffmanTreeTemp == NULL)
    {
        return;
    }
    pHuffmanTreeTemp[iIndex].weight = pBitreeTemp->data;
    iIndex++;
    CreatreArray(pHuffmanTreeTemp,pBitreeTemp->lChild);
    CreatreArray(pHuffmanTreeTemp,pBitreeTemp->rChild);
}
int GetNode(pHuffmanTree& pHuffmanTreeTemp,int i)
{
    int min = UINT_MAX;
    int flag;
    for(int j = 1; j <= i; j++)
    {
        if(pHuffmanTreeTemp[j].weight < min && pHuffmanTreeTemp[j].parent == 0)//已有父節點的不算
        {
            min = pHuffmanTreeTemp[j].weight;
            flag = j;
        }
    }
    pHuffmanTreeTemp[flag].parent = 1;//防止兩次調用獲取的索引同樣
    return flag;
}
void SelectNode(pHuffmanTree& pHuffmanTreeTemp,int i,int *m,int *n)//m為序號小的那個
{
    *m = GetNode(pHuffmanTreeTemp,i);
    *n = GetNode(pHuffmanTreeTemp,i);

    int t;
    if(*m > *n)
    {
        t = *m;
        *m = *n;
        *n = t;
    }
}

void CreateHuffmanTree(pHuffmanTree& pHuffmanTreeTemp)
{
    if(pHuffmanTreeTemp == NULL)
    {
        return;
    }
    int m = 0,n = 0;
    for(int i = iCount+1;i <= 2*iCount-1; i++)
    {
        SelectNode(pHuffmanTreeTemp,i-1,&m,&n);
        pHuffmanTreeTemp[m].parent = pHuffmanTreeTemp[n].parent = i;
        //構造兩個最小權重的節點的父節點
        pHuffmanTreeTemp[i].lChild = m;
        pHuffmanTreeTemp[i].rChild = n;
        pHuffmanTreeTemp[i].weight = pHuffmanTreeTemp[m].weight+pHuffmanTreeTemp[n].weight;
    }

}

void DestroyTree(pBitree* pBitreeTemp)
{
    if(*pBitreeTemp == NULL)
    {
        return;
    }
    if((*pBitreeTemp)->lChild)
    {
        DestroyTree(&(*pBitreeTemp)->lChild);
    }
    if((*pBitreeTemp)->rChild)
    {
        DestroyTree(&(*pBitreeTemp)->rChild);
    }
    free(*pBitreeTemp);
    *pBitreeTemp = NULL;
}

void DestroyHuffmanTree(pHuffmanTree& pHuffmanTreeTemp)
{
    if(pHuffmanTreeTemp)
    {
        free(pHuffmanTreeTemp);
    }
    pHuffmanTreeTemp = NULL;
}

測試： 圖解構造過程： 1.首先將二叉樹中的節點所有存到代表赫夫曼樹的數組中。其余位置為0:
2.循環遍歷該數組。每次找到最小權重的兩個節點。之和作為其父節點的權重

3.循環一遍後。便得到赫夫曼樹：

由二叉樹構造赫夫曼樹