《C++实现数据结构》：二叉树

来源：互联网发布：江苏省人口普查数据编辑：程序博客网时间：2024/06/10 00:25

二叉树的定义以及性质在之前的博客里已经说过了，今天来用C++实现二叉树。提供先序遍历、中序遍历、后序遍历的递归和非递归的两种实现方式，也提供了层次遍历的用队列实现方式。详细的看代码学习吧，关键注释都有加上了。

————————————————————2017.4.4补充————————————————————
今天补充了反转二叉树的实现，提供递归和非递归两个版本。
————————————————————————————————————————————————

//// Created by huxijie on 17-3-20.// 二叉树#include <iostream>#include <stack>#include <queue>using namespace std;//二叉树结点类template <typename T>struct BTNode{    T elemet;    BTNode<T>* lChild,*rChild;    BTNode() {        lChild = rChild = NULL;    }    BTNode(const T& x,BTNode<T>* l, BTNode<T> *r) {        elemet = x;        lChild = l;        rChild = r;    }};//二叉树类template <typename T>class BinaryTree{private:    BTNode<T>* root;    void Clear(BTNode<T>* t);    void PreOrder(void (*Visit)(T &x),BTNode<T> *r);    void InOrder(void (*Visit)(T &x),BTNode<T> *r);    void PostOrder(void (*Visit)(T &x),BTNode<T> *r);    void LayerOrder(void (*Visit)(T &x), BTNode<T> *r);    int Size(BTNode<T>* r);    BTNode<T>* Copy(BTNode<T> *r);    BTNode<T>* InvertTree(BTNode<T> *root);public:    BinaryTree();    ~BinaryTree();    bool IsEmpty() const;    void Clear();               //移去所有结点,成为空二叉树    bool Root(T& x) const;      //若二叉树非空,则x为根的值,并返回true    //构造一棵二叉树,根的值为x,以left和right为左右子树    void MakeTree(const T& x,BinaryTree<T>& left,BinaryTree<T>& right);    void PreOrder(void (*Visit)(T &x));            //先序遍历    void InOrder(void (*Visit)(T &x));             //中序遍历    void PostOrder(void (*Visit)(T &x));           //后序遍历    void LayerOrder(void (*Visit)(T &x));          //层次遍历    int Size();                 //结点个数    BTNode<T>* Copy();          //二叉树的复制    void InvertTree();          //反转二叉树};template <typename T>BinaryTree<T>::BinaryTree() {    root = NULL;}template <typename T>BinaryTree<T>::~BinaryTree() {    Clear();}template <typename T>bool BinaryTree<T>::IsEmpty() const {    if (root == NULL) {        return true;    } else {        return false;    }}//递归实现清空二叉树template <typename T>void BinaryTree<T>::Clear(BTNode<T> *t) {    if (!t) {        return;    } else {        Clear(t->lChild);        Clear(t->rChild);        delete (t);        t = NULL;    }}template <typename T>void BinaryTree<T>::Clear() {    Clear(root);}template <typename T>bool BinaryTree<T>::Root(T &x) const {    if (IsEmpty()) {        return false;    }else {        x = root->elemet;        return true;    }}template <typename T>void BinaryTree<T>::MakeTree(const T &x, BinaryTree<T> &left, BinaryTree<T> &right) {    if (root || &left == &right) {    //若root不空则返回,若左右子树相同则返回,不构造树        return;    }    root = new BTNode<T>(x, left.root, right.root);    left.root = NULL;    right.root = NULL;}//访问元素的函数,作为参数传入遍历函数中template <typename T>void Visit(T &x) {    cout << x << " ";}////递归实现先序遍历//template <typename T>//void BinaryTree<T>::PreOrder(void (*Visit)(T &x),BTNode<T> *r) {//    if (r) {//        Visit(r->elemet);//        PreOrder(Visit, r->lChild);//        PreOrder(Visit, r->rChild);//    }//}//非递归实现先序遍历template <typename T>void BinaryTree<T>::PreOrder(void (*Visit)(T &x),BTNode<T> *r) {    if (r == NULL) {        return;    }    BTNode<T>* p = r;    stack<BTNode<T> *> mystack;    while (p != NULL || !mystack.empty()) {        //边遍历边打印,并存入栈中,以后需要通过这些结点进入右子树        while (p != NULL) {            Visit(p->elemet);            mystack.push(p);            p = p->lChild;        }        //当p为空时,说明根和左子树已经遍历完了,需要进入右子树了        if (!mystack.empty()) {            p = mystack.top();            mystack.pop();            p = p->rChild;        }    }}template <typename T>void BinaryTree<T>::PreOrder(void (*Visit)(T &)) {    PreOrder(Visit, root);}////递归实现中序遍历//template <typename T>//void BinaryTree<T>::InOrder(void (*Visit)(T &), BTNode<T> *r) {//    if (r) {//        InOrder(Visit, r->lChild);//        Visit(r->elemet);//        InOrder(Visit, r->rChild);//    }//}//非递归实现中序遍历template <typename T>void BinaryTree<T>::InOrder(void (*Visit)(T &), BTNode<T> *r) {    if (r == NULL) {        return;    }    BTNode<T> *p = r;    stack<BTNode<T>*> mystack;    while (p != NULL || !mystack.empty()) {        //一直遍历到最后一棵左子树,边遍历边保存根结点到栈中        while (p != NULL) {            mystack.push(p);            p = p->lChild;        }        //当p为空时,说明已经到达最后一棵左子树了,这时需要出栈了        if (!mystack.empty()) {            p = mystack.top();            mystack.pop();            Visit(p->elemet);            //进入右子树,开始新的一轮左子树遍历            p = p->rChild;        }    }}template <typename T>void BinaryTree<T>::InOrder(void (*Visit)(T &)) {    InOrder(Visit, root);}////递归实现后序遍历//template <typename T>//void BinaryTree<T>::PostOrder(void (*Visit)(T &), BTNode<T> *r) {//    if (r) {//        PostOrder(Visit, r->lChild);//        PostOrder(Visit, r->rChild);//        Visit(r->elemet);//    }//}//非递归实现后序遍历template <typename T>void BinaryTree<T>::PostOrder(void (*Visit)(T &), BTNode<T> *r) {    if (r == NULL) {        return;    }    stack<BTNode<T>*> mystack;    BTNode<T>* pCur = r;        //当前访问结点    BTNode<T>* pLast = NULL;    //上次访问结点    //一直遍历到最后一棵左子树,边遍历边保存根结点到栈中    while (pCur != NULL) {        mystack.push(pCur);        pCur = pCur->lChild;    }    //已经遍历到最后一棵左子树了,接下来从栈中取结点    while (!mystack.empty()) {        pCur = mystack.top();        mystack.pop();        //一个根结点被访问的前提是：无右子树或者右子树已被访问过        if (pCur->rChild == NULL || pCur->rChild == pLast) {            Visit(pCur->elemet);            //修改最近被访问的结点            pLast = pCur;        } else { //先进入右子树            mystack.push(pCur);     //根结点重新入栈            pCur = pCur->rChild;    //进入右子树            while (pCur != NULL) {  //开始在右子树中一直遍历到最后一棵左子树                mystack.push(pCur);                pCur = pCur->lChild;            }        }    }}template <typename T>void BinaryTree<T>::PostOrder(void (*Visit)(T &)) {    PostOrder(Visit, root);}//用队列实现层次遍历template <typename T>void BinaryTree<T>::LayerOrder(void (*Visit)(T &x),BTNode<T> *r) {    if (!r) {        return;    }    queue<BTNode<T>*> myqueue;    BTNode<T> *p = r;    while (p != NULL || !myqueue.empty()) {        if (p != NULL) {            Visit(p->elemet);            myqueue.push(p->lChild);            myqueue.push(p->rChild);        }        p = myqueue.front();        myqueue.pop();    }}template <typename T>void BinaryTree<T>::LayerOrder(void (*Visit)(T &)) {    LayerOrder(Visit, root);}//递归实现求结点总数template <typename T>int BinaryTree<T>::Size(BTNode<T> *r) {    if (!r) {        return 0;    } else {        return Size(r->lChild) + Size(r->rChild) + 1;    }}template <typename T>int BinaryTree<T>::Size() {    return Size(root);}//递归实现复制二叉树template <typename T>BTNode<T>* BinaryTree<T>::Copy(BTNode<T> *r) {    if (!this) {        return NULL;    } else {        BTNode<T> *p = new BTNode<T>(r->elemet);        p->lChild = Copy(r->lChild);        p->rChild = Copy(r->rChild);        return p;    }}template <typename T>BTNode<T>* BinaryTree<T>::Copy() {    return Copy(root);}////递归实现反转二叉树//template <typename T>//BTNode<T>* BinaryTree<T>::InvertTree(BTNode<T> *root) {//    if (NULL == root) {//        return NULL;//    }////    root->lChild = InvertTree(root->lChild);    //对左子树进行反转//    root->rChild = InvertTree(root->rChild);    //对右子树进行反转////    //将左右子树的根结点进行交换//    BTNode<T> *tmp = root->lChild;//    root->lChild = root->rChild;//    root->rChild = tmp;//}//非递归实现反转二叉树template <typename T>BTNode<T>* BinaryTree<T>::InvertTree(BTNode<T> *root) {    if (NULL == root) {        return NULL;    }    queue<BTNode<T>*> myqueue;    myqueue.push(root);         //先将根结点入队    BTNode<T> *tmp = NULL;    BTNode<T> *tmpLeft = NULL;    while (!myqueue.empty()) {        tmp = myqueue.front();        myqueue.pop();        tmpLeft = tmp->lChild;      //交换左右孩子        tmp->lChild = tmp->rChild;        tmp->rChild = tmpLeft;        if (tmp->lChild != NULL) {  //交换后左孩子入队            myqueue.push(tmp->lChild);        }        if (tmp->rChild != NULL) {  //交换后右孩子入队            myqueue.push(tmp->rChild);        }    }}//反转二叉树template <typename T>void BinaryTree<T>::InvertTree() {    InvertTree(root);}

最后的测试用例如下，构造的二叉树结构（左图）以及反转后的二叉树（右图）是：
这里写图片描述

这里写图片描述

int main() {    BinaryTree<char> a, b, x, y, z; //都是空二叉树    char e;    x.MakeTree('A', a, b);    y.MakeTree('B', a, b);    z.MakeTree('C', x, y);    x.MakeTree('D', a, b);    y.MakeTree('E', x, b);    x.MakeTree('F', y, z);    cout<<"先序遍历：";    x.PreOrder(Visit);    cout<<endl;    cout<<"中序遍历：";    x.InOrder(Visit);    cout<<endl;    cout<<"后序遍历：";    x.PostOrder(Visit);    cout<<endl;    cout<<"层次遍历：";    x.LayerOrder(Visit);    cout<<endl;    cout<<"结点个数：";    cout << x.Size()<<endl;    cout<<"反转二叉树......"<<endl;    x.InvertTree();    cout<<"先序遍历：";    x.PreOrder(Visit);    cout<<endl;    cout<<"中序遍历：";    x.InOrder(Visit);    cout<<endl;    cout<<"后序遍历：";    x.PostOrder(Visit);    cout<<endl;    cout<<"层次遍历：";    x.LayerOrder(Visit);    cout<<endl;    return 0;}

运行结果是：

先序遍历：F E D C A B 中序遍历：D E F A C B 后序遍历：D E A B C F 层次遍历：F E C D A B 结点个数：6反转二叉树......先序遍历：F C B A E D 中序遍历：B C A F E D 后序遍历：B A C D E F 层次遍历：F C E B A D Process finished with exit code 0

0 0