数据结构——普通树的定义与C++实现

github地址：https://github.com/lining91/NormalTree

实现了树的兄弟孩子表示法，插入新数据，查询某个数据，前序遍历，中序遍历，后序遍历。

相关概念：
每一棵树都有一个根节点。
每个节点可以有多个儿子节点，没有儿子的结点叫做叶子节点。
具有相同父亲的节点叫做兄弟节点。
对于任意一个节点ni，ni的深度为从根到ni的唯一路径的长。因此，根的深度是0。
ni的高是从ni到一片树叶的最长路径的长。因此叶子节点的高是0。一棵树的高等于它的根的高。
一棵树的深度等于它的最深的树叶的深度，该深度等于这棵树的高。

树的实现：
使用树的兄弟孩子表示法。
typedef struct STreeNode* pSTreeNode;

struct STreeNode
{
int nValue;
pSTreeNode pFirstChild;
pSTreeNode pNextBrother;

STreeNode(){    nValue = 0;    pFirstChild = NULL;    pNextBrother = NULL;}

};

其中pFirstChild(左孩子节点)表示第一个儿子节点，pNextBrother(右孩子节点)表示下一个兄弟节点。

一颗普通树表示如下：

使用兄弟孩子表示法表示如下：

树的遍历：
前序遍历（先根节点，后左孩子节点，再右孩子结点）
中序遍历（先左孩子结点，后根节点，再右孩子结点）
后序遍历（先做孩子节点，后右孩子结点，再根节点）

代码如下：

#include <iostream>using namespace std;typedef struct STreeNode* pSTreeNode;typedef int TreeDataType;struct STreeNode{    TreeDataType data;    pSTreeNode pFirstChild;    pSTreeNode pNextBrother;    STreeNode( TreeDataType Value )    {        data = Value;        pFirstChild = NULL;        pNextBrother = NULL;    }}; class CTree{public:    CTree();    CTree( TreeDataType Value );    ~CTree();public:    void Insert( TreeDataType parentValue, TreeDataType Value );    //  parentValue：该节点的父结点；Value：该节点的值    void InsertBrother( pSTreeNode pParentNode, TreeDataType Value );    pSTreeNode Search( pSTreeNode pNode, TreeDataType Value );    void Preorder( pSTreeNode pNode );      //  前序遍历    void Inorder( pSTreeNode pNode );       //  中序遍历    void postorder( pSTreeNode pNode );     //  后续遍历    void PrintNode( pSTreeNode pNode );    void FreeMemory( pSTreeNode pNode );    //  释放内存    public:    pSTreeNode pRoot;};CTree::CTree(){    pRoot = NULL;}CTree::CTree( TreeDataType Value ){    pRoot = new STreeNode( Value );    if ( pRoot == NULL )        return;}CTree::~CTree(){    if (pRoot == NULL )        return;    FreeMemory( pRoot );}void CTree::FreeMemory( pSTreeNode pNode ){    if ( pNode == NULL )        return;    if ( pNode->pFirstChild != NULL )        FreeMemory( pNode->pFirstChild );    if ( pNode->pNextBrother != NULL )        FreeMemory( pNode->pNextBrother );    delete pNode;    pNode = NULL;}void CTree::Insert( TreeDataType parentValue, TreeDataType Value ){    if ( pRoot == NULL )        return;    pSTreeNode pFindNode = Search( pRoot, parentValue );    if ( pFindNode == NULL )        return;    if ( pFindNode->pFirstChild == NULL )    {        pFindNode->pFirstChild = new STreeNode( Value );        return;    }    else    {        InsertBrother( pFindNode->pFirstChild, Value );        return;    }}void CTree::InsertBrother( pSTreeNode pBrotherNode, TreeDataType Value ){    if ( pBrotherNode->pNextBrother != NULL )        InsertBrother( pBrotherNode->pNextBrother, Value );    else    {        pBrotherNode->pNextBrother = new STreeNode( Value );        return;    }}pSTreeNode CTree::Search( pSTreeNode pNode, TreeDataType Value ){    if ( pNode == NULL )        return NULL;    if ( pNode->data == Value )        return pNode;    if ( pNode->pFirstChild == NULL && pNode->pNextBrother == NULL )        return NULL;    else    {        if ( pNode->pFirstChild != NULL )        {            pSTreeNode pNodeTemp = Search( pNode->pFirstChild, Value );            if ( pNodeTemp != NULL )                return pNodeTemp;            else            {                return Search( pNode->pNextBrother, Value );            }        }        else            return Search( pNode->pNextBrother, Value );    }}void CTree::Preorder( pSTreeNode pNode ){    if (pNode == NULL)        return;    cout << " " << pNode->data << " ";    Preorder( pNode->pFirstChild );    Preorder( pNode->pNextBrother );}void CTree::Inorder( pSTreeNode pNode ){    if ( pNode == NULL )        return;    Inorder( pNode->pFirstChild );    cout << " " << pNode->data << " ";    Inorder( pNode->pNextBrother );}void CTree::postorder( pSTreeNode pNode ){    if ( pNode == NULL )        return;    postorder( pNode->pFirstChild );    postorder( pNode->pNextBrother );    cout << " " << pNode->data << " ";}int main(){    CTree* pTree = new CTree( 1 );    if ( pTree == NULL )        return 0;    pTree->Insert( 1, 2 );    pTree->Insert( 1, 3 );    pTree->Insert( 1, 4 );    pTree->Insert( 1, 5 );    pTree->Insert( 1, 6 );    pTree->Insert( 1, 7 );    pTree->Insert( 4, 8 );    pTree->Insert( 5, 9 );    pTree->Insert( 5, 10 );    pTree->Insert( 6, 11 );    pTree->Insert( 6, 12 );    pTree->Insert( 6, 13 );    pTree->Insert( 10, 14 );    pTree->Insert( 10, 15 );    cout << "前序遍历：" << endl;    pTree->Preorder( pTree->pRoot );    cout << endl;    cout << "中序遍历：" << endl;    pTree->Inorder( pTree->pRoot );    cout << endl;    cout << "后序遍历：" << endl;    pTree->postorder( pTree->pRoot );    cout << endl;    delete pTree;    pTree = NULL;    system("pause");    return 1;}

运行结果如下：