数据结构之二叉树的遍历

二叉树的遍历分为前序遍历，中序遍历，后序遍历，层序遍历，在本文中，前三种由递归实现，层序遍历由队列实现。

#include "stdio.h"#include "stdlib.h"#include "windows.h"typedef struct Node{    char data;    struct Node *Left;    struct Node *Right;    struct Node *Next;}BT;typedef struct { /* 链队列结构 */    BT *rear; /* 指向队尾结点 */    BT *front; /* 指向队头结点 */} LinkQueue;//入队LinkQueue* AddQuee(LinkQueue *PtrL,BT* item){    BT *node;    node=PtrL->rear;    if (PtrL->front==NULL)    {        BT *q=(BT*)malloc(sizeof(BT));        q->Left=item->Left;        q->Right=item->Right;        q->Next=NULL;        q->data=item->data;        PtrL->front=q;        PtrL->rear=q;        return PtrL;    }    else    {        BT *q=(BT*)malloc(sizeof(BT));        q->Next=NULL;        q->Left=item->Left;        q->Right=item->Right;        q->data=item->data;        node->Next=q;        PtrL->rear=q;        return PtrL;    }}//出队BT* DeleteQ ( LinkQueue *PtrQ ){    BT *firstNode;    //BT* NodeItem;    if (PtrQ->front==NULL)    {        printf("queue is empty");        return NULL;    }    firstNode=PtrQ->front;    if (PtrQ->front==PtrQ->rear)    {        PtrQ->front=PtrQ->rear=NULL;    }else    {        PtrQ->front=PtrQ->front->Next;    }    //NodeItem->data=firstNode->data;    //free(firstNode);    return firstNode;}//判断是否为空int isempty(LinkQueue *PtrL){    if (PtrL->rear==NULL)    {        return 1;    }else    {        return 0;    }}BT *CreateBiTree(){    char ch;    BT *T;    printf("please enter tree node:");    scanf("%c",&ch);    if (ch=='#')    {        T=NULL;    }else    {        T=(BT*)malloc(sizeof(BT));        T->data=ch;        T->Left=CreateBiTree();        T->Right=CreateBiTree();    }    return T;}//先序遍历void PreOrderTraversal( BT* tree){    if (tree)    {        printf("%c ",tree->data);        PreOrderTraversal(tree->Left);        PreOrderTraversal(tree->Right);    }}//中序遍历void InOrderTraversal(BT* tree){    if (tree)    {        PreOrderTraversal(tree->Left);        printf("%c ",tree->data);        PreOrderTraversal(tree->Right);    }}//后序遍历void PostOderTraversal(BT *tree){    if (tree)    {        PostOderTraversal(tree->Left);        PostOderTraversal(tree->Right);        printf("%c ",tree->data);    }}//层序遍历void LevelOrderTraversal(BT *tree){    BT *bt;    LinkQueue *q=(LinkQueue*)malloc(sizeof(LinkQueue));    q->front=NULL;    q->rear=NULL;    if (!tree)    {        return;    }    AddQuee(q,tree);    while(isempty(q)==0)    {        bt=DeleteQ(q);        printf("%c ",bt->data);        if (bt->Left) AddQuee(q,bt->Left);        if (bt->Right) AddQuee(q,bt->Right);    }}int PostOrderGetHeight( BT* tree ){    int HL, HR, MaxH;    if( tree ) {        HL = PostOrderGetHeight(tree->Left); /*求左子树的深度*/        HR = PostOrderGetHeight(tree->Right); /*求右子树的深度*/        MaxH =(HL> HR)? HL : HR;/*取左右子树较大的深度*/        return ( MaxH + 1 ); /*返回树的深度*/    }    else return 0; /* 空树深度为0 */}void main(){    BT *t;    int a;    t=CreateBiTree();    printf("\n1.PreOrderTraversal\n");    printf("2.MidOrderTraversal\n");    printf("3.PostOrderTraversal\n");    printf("4.EXIT\n");    printf("5.LevelOrderTraversal\n");    printf("6.show the hieght of the tree");    while (1)    {        printf("please enter your order:");        scanf("%d",&a);        switch (a)        {        case 1:            PreOrderTraversal(t);            break;        case 2:            InOrderTraversal(t);            break;        case 3:            PostOderTraversal(t);            break;        case 4:            exit(0);            break;        case 5:            LevelOrderTraversal(t);            break;        case 6:            printf("%d",PostOrderGetHeight(t));            break;        default:            break;        }    }}

运行结果

C++实现二叉树的遍历

#include "iostream"#include "stack"#include "queue"using namespace std;//二叉树结点typedef struct BiTNode{    //数据    char data;    //左右孩子指针    struct BiTNode *lchild,*rchild;}BiTNode,*BiTree;//按先序序列创建二叉树int CreateBiTree(BiTree &T){    char data;    //按先序次序输入二叉树中结点的值（一个字符），‘#’表示空树    scanf("%c",&data);    if(data == '#'){        T = NULL;    }    else{        T = (BiTree)malloc(sizeof(BiTNode));        //生成根结点        T->data = data;        //构造左子树        CreateBiTree(T->lchild);        //构造右子树        CreateBiTree(T->rchild);    }    return 0;}//输出void Visit(BiTree T){    if(T->data != '#'){        printf("%c ",T->data);    }}//先序遍历void PreOrder(BiTree T){    if(T != NULL){        //访问根节点        Visit(T);        //访问左子结点        PreOrder(T->lchild);        //访问右子结点        PreOrder(T->rchild);    }}//中序遍历  void InOrder(BiTree T){      if(T != NULL){          //访问左子结点          InOrder(T->lchild);          //访问根节点          Visit(T);          //访问右子结点          InOrder(T->rchild);      }  }  //后序遍历void PostOrder(BiTree T){    if(T != NULL){        //访问左子结点        PostOrder(T->lchild);        //访问右子结点        PostOrder(T->rchild);        //访问根节点        Visit(T);    }}/* 先序遍历(非递归)   思路：访问T->data后，将T入栈，遍历左子树；遍历完左子树返回时，栈顶元素应为T，出栈，再先序遍历T的右子树。*/void PreOrder2(BiTree T){    stack<BiTree> stack;    //p是遍历指针    BiTree p = T;    //栈不空或者p不空时循环    while(p || !stack.empty()){        if(p != NULL){            //存入栈中            stack.push(p);            //访问根节点            printf("%c ",p->data);            //遍历左子树            p = p->lchild;        }        else{            //退栈            p = stack.top();            stack.pop();            //访问右子树            p = p->rchild;        }    }//while}/* 中序遍历(非递归)   思路：T是要遍历树的根指针，中序遍历要求在遍历完左子树后，访问根，再遍历右子树。         先将T入栈，遍历左子树；遍历完左子树返回时，栈顶元素应为T，出栈，访问T->data，再中序遍历T的右子树。*/void InOrder2(BiTree T){    stack<BiTree> stack;    //p是遍历指针    BiTree p = T;    //栈不空或者p不空时循环    while(p || !stack.empty()){        if(p != NULL){            //存入栈中            stack.push(p);            //遍历左子树            p = p->lchild;        }        else{            //退栈，访问根节点            p = stack.top();            printf("%c ",p->data);            stack.pop();            //访问右子树            p = p->rchild;        }    }//while}//后序遍历(非递归)typedef struct BiTNodePost{    BiTree biTree;    char tag;}BiTNodePost,*BiTreePost;void PostOrder2(BiTree T){    stack<BiTreePost> stack;    //p是遍历指针    BiTree p = T;    BiTreePost BT;    //栈不空或者p不空时循环    while(p != NULL || !stack.empty()){        //遍历左子树        while(p != NULL){            BT = (BiTreePost)malloc(sizeof(BiTNodePost));            BT->biTree = p;            //访问过左子树            BT->tag = 'L';            stack.push(BT);            p = p->lchild;        }        //左右子树访问完毕访问根节点        while(!stack.empty() && (stack.top())->tag == 'R'){            BT = stack.top();            //退栈            stack.pop();            BT->biTree;            printf("%c ",BT->biTree->data);        }        //遍历右子树        if(!stack.empty()){            BT = stack.top();            //访问过右子树            BT->tag = 'R';            p = BT->biTree;            p = p->rchild;        }    }//while}//层次遍历void LevelOrder(BiTree T){    BiTree p = T;    //队列    queue<BiTree> queue;    //根节点入队    queue.push(p);    //队列不空循环    while(!queue.empty()){        //对头元素出队        p = queue.front();        //访问p指向的结点        printf("%c ",p->data);        //退出队列        queue.pop();        //左子树不空，将左子树入队        if(p->lchild != NULL){            queue.push(p->lchild);        }        //右子树不空，将右子树入队        if(p->rchild != NULL){            queue.push(p->rchild);        }    }}int main(){    BiTree T;    CreateBiTree(T);    printf("先序遍历：\n");    PreOrder(T);    printf("\n");    printf("先序遍历(非递归)：\n");    PreOrder2(T);    printf("\n");    printf("中序遍历：\n");    InOrder(T);    printf("\n");    printf("中序遍历(非递归)：\n");    InOrder2(T);    printf("\n");    printf("后序遍历：\n");    PostOrder(T);    printf("\n");    printf("后序遍历(非递归)：\n");    PostOrder2(T);    printf("\n");    printf("层次遍历：\n");    LevelOrder(T);    printf("\n");    system("pause");    return 0;}