数据结构-树-二叉树的基本操作(递归和非递归遍历，深度)

1.需求

• 递归实现层序、先序、中序、后序遍历
• 非递归实现层序、先序、中序、后序遍历
• 求树的深度

2.实现代码

#include<iostream>
#include<cstring>
#include<string>
#include<queue>
#include<stack>
using namespace std;

typedef struct BiTNode
{   char data;   //使用字符串来建树
    struct BiTNode *lchild,*rchild;
}BiTNode,*BiTree;

//建树
void Create(BiTree &T)
{//例子ABD##E##CF###
    char ch;
    cin>>ch;
    if(ch=='#')
        T=NULL;  //递归结束
    else{
        T=new BiTNode;
        T->data=ch;
        Create(T->lchild); //递归建左子树
        Create(T->rchild); //递归建右子树
    }
}

//层序遍历
void levleorder(BiTree T)
{
    queue<BiTree> B;  //队列辅助遍历
    cout<<"层序遍历：";
    BiTree front;
    if(T==NULL) return;
    B.push(T);
    while(!B.empty())
    {
        front=B.front();
        B.pop();
        if(front->lchild)
            B.push(front->lchild); //左孩子不为空，左孩子进入队列
        if(front->rchild)
            B.push(front->rchild); //右孩子不为空，右孩子进入队列
        cout<<front->data<<"->";
    }
    cout<<endl;
}

//递归前序遍历
void PreOrderTraverse(BiTree T)
{
    if(T==NULL)
    {
        cout<<"#"<<"->";
        return ;
    }else{
        cout<<T->data<<"->"; //访问根节点
        PreOrderTraverse(T->lchild);
        PreOrderTraverse(T->rchild);
    }
}

//非递归前序遍历
void PreOrderLoop(BiTree T)
{
    stack<BiTree> s;
    BiTree cur,top;
    cur=T;
    while(cur!=NULL||!s.empty())
    {
        while(cur!=NULL)
        {
            cout<<cur->data<<"->";
            s.push(cur);
            cur=cur->lchild;
        }

        top=s.top();
        s.pop();

        cur=top->rchild;
    }
}

//递归中序遍历
void InOrderTraverse(BiTree T)
{
    if(T==NULL)
    {
        cout<<"#"<<"->";
        return;
    }else{
        InOrderTraverse(T->lchild);
        cout<<T->data<<"->";
        InOrderTraverse(T->rchild);
    }
}

//非递归中序遍历
void InOrderLoop(BiTree T)
{
    stack<BiTree>s;
    BiTree cur;
    cur=T;
    while(cur!=NULL||!s.empty())
    {
        while(cur!=NULL)
        {
            s.push(cur);
            cur=cur->lchild;
        }

        cur=s.top();
        s.pop();
        cout<<cur->data<<"->";

        cur=cur->rchild;
    }
}

//后序递归遍历
void PostOrderTraverse(BiTree T)
{
    if(T==NULL){
        cout<<"#"<<"->";
    }else{
        PostOrderTraverse(T->lchild);
        PostOrderTraverse(T->rchild);
        cout<<T->data<<"->";
    }
}

//后序非递归遍历
void PostOrderLoop(BiTree T)
{
    stack<BiTree> s;
    BiTree cur ,top,last=NULL;
    cur=T;
    while(cur!=NULL||!s.empty())
    {
        while(cur!=NULL)
        {
            s.push(cur);
            cur=cur->lchild;
        }

        top=s.top();
        if(top->rchild==NULL||top->rchild==last){
            s.pop();
            cout<<top->data<<"->";
            last=top;
        }else{
            cur=top->rchild;
        }
    }
}

//求树的深度
int TreeDeep(BiTree T)
{
    int deep=0;
    if(T)
    {
        int leftdeep=TreeDeep(T->lchild);
        int rightdeep=TreeDeep(T->rchild);
        deep=leftdeep>=rightdeep?leftdeep+1:rightdeep+1;
    }
    return deep;
}

int NodeCount(BiTree T){
  if(T == NULL ) return 0;
  else return NodeCount(T->lchild)+NodeCount(T->rchild)+1;
}

int main()
{
    //建树
    BiTree t;
    cout<<"请输入建树序列：";
    Create(t);

    //层序遍历
    levleorder(t);

    //递归前序遍历
    cout<<"递归前序遍历：";
    PreOrderTraverse(t);
    cout<<endl;

    //非递归前序遍历
    cout<<"非递归前序遍历：";
    PreOrderLoop(t);
    cout<<endl;

    //递归中序遍历
    cout<<"递归中序遍历：";
    InOrderTraverse(t);
    cout<<endl;

    //非递归中序遍历
    cout<<"非递归中序遍历：";
    InOrderLoop(t);
    cout<<endl;

    //递归后序遍历
    cout<<"递归后序遍历：";
    PostOrderTraverse(t);
    cout<<endl;

    //非递归后续遍历
    cout<<"非递归后序遍历：";
    PostOrderLoop(t);
    cout<<endl;

    //树的深度
    int d=TreeDeep(t);
    cout<<"树的深度："<<d<<endl;

    //树的结点个数
    int n=NodeCount(t);
    cout<<"树的结点个数："<<n<<endl;
    return 0;

}

3.运行结果