C++二叉树实验

Posted 2023-02-17 康小庄

1.以下图的二叉树为例，设计程序完成对二叉树的基本操作

运行结果如图所示：

2.自行设计一个算法，以二叉树为存储结构，统计二叉树的叶子结点个数，并将叶子节点依次输出

#include <stdio.h>
#include <malloc.h>

#define MaxSize 100
typedef char ElemType;

typedef struct node 
    //数据元素
    ElemType data;
    //指向左孩子
    struct node *lchild;
    //指向右孩子
    struct node *rchild;
 BTNode;

//由str串创建二叉链
void CreateBTNode(BTNode *&b, char *str) 
    BTNode *St[MaxSize], *p = NULL;
    int top = -1, k, j = 0;
    char ch;
    b = NULL;                //建立的二叉树初始时为空
    ch = str[j];
    while (ch != '\\0')    //str未扫描完时循环
    
        switch (ch) 
            case '(':
                top++;
                St[top] = p;
                k = 1;
                break;        //为左结点
            case ')':
                top--;
                break;
            case ',':
                k = 2;
                break;                        //为右结点
            default:
                p = (BTNode *) malloc(sizeof(BTNode));
                p->data = ch;
                p->lchild = p->rchild = NULL;
                if (b == NULL)                    //p指向二叉树的根结点
                    b = p;
                else                            //已建立二叉树根结点
                
                    switch (k) 
                        case 1:
                            St[top]->lchild = p;
                            break;
                        case 2:
                            St[top]->rchild = p;
                            break;
                    
                
        
        j++;
        ch = str[j];
    


//以广义表法输出二叉树
void DispBTNode(BTNode *b) 
    if (b != NULL) 
        printf("%c", b->data);
        if (b->lchild != NULL || b->rchild != NULL) 
            printf("(");
            DispBTNode(b->lchild);
            if (b->rchild != NULL) printf(",");
            DispBTNode(b->rchild);
            printf(")");
        
    


//求二叉树b的结点个数
int Nodes(BTNode *b) 
    int num1, num2;
    if (b == NULL) 
        return 0;
        // b为叶子节点
     else if (b->lchild == NULL && b->rchild == NULL) 
        return 1;
     else 
        num1 = Nodes(b->lchild);
        num2 = Nodes(b->rchild);
        return (num1 + num2 + 1);
    



//求二叉树b的叶子结点个数
int LeafNodes(BTNode *b) 
    int num1, num2;
    if (b == NULL) 
        return 0;
        // b为叶子节点
     else if (b->lchild == NULL && b->rchild == NULL) 
        return 1;
     else 
        num1 = LeafNodes(b->lchild);
        num2 = LeafNodes(b->rchild);
        return (num1 + num2);
    



//求二叉树b的深度
int BTNodeDepth(BTNode *b) 
    int lchilddep, rchilddep;
    if (b == NULL) 
        return 0;
     else 
        lchilddep = BTNodeDepth(b->lchild);
        rchilddep = BTNodeDepth(b->rchild);
        return lchilddep > rchilddep ? (lchilddep + 1) : (rchilddep + 1);
    



//先序遍历的递归算法
void PreOrder(BTNode *b) 
    if (b->data == NULL) 
        return;
    
    // 输出根结点
    printf("%c ", b->data);
    // 遍历左子树
    if (b->lchild != NULL) 
        PreOrder(b->lchild);
    
    // 遍历右子树
    if (b->rchild != NULL) 
        PreOrder(b->rchild);
    


//中序遍历的递归算法
void InOrder(BTNode *b) 
    if (b->data == NULL) 
        return;
    
    // 遍历左子树
    if (b->lchild != NULL) 
        InOrder(b->lchild);
    
    // 输出根结点
    printf("%c ", b->data);
    // 遍历右子树
    if (b->rchild != NULL) 
        InOrder(b->rchild);
    



//后序遍历的递归算法
void PostOrder(BTNode *b) 
    if (b->data == NULL) 
        return;
    
    // 遍历左子树
    if (b->lchild != NULL) 
        PostOrder(b->lchild);
    
    // 遍历右子树
    if (b->rchild != NULL) 
        PostOrder(b->rchild);
    
    // 输出根结点
    printf("%c ", b->data);


//层次遍历算法
void TravLevel(BTNode *b) 
    //定义循环队列
    BTNode *Qu[MaxSize];
    //定义队首和队尾指针
    int front, rear;
    //置队列为空队列
    front = rear = 0;
    if (b != NULL)
        printf("%c ", b->data);
    //结点指针进入队列
    rear++;
    Qu[rear] = b;
    //队列不为空
    while (rear != front) 
        front = (front + 1) % MaxSize;
        //队头出队列
        b = Qu[front];
        //输出左孩子,并入队列
        if (b->lchild != NULL) 
            printf("%c ", b->lchild->data);
            rear = (rear + 1) % MaxSize;
            Qu[rear] = b->lchild;
        
        //输出右孩子,并入队列
        if (b->rchild != NULL) 
            printf("%c ", b->rchild->data);
            rear = (rear + 1) % MaxSize;
            Qu[rear] = b->rchild;
        
    
    printf("\\n");



void AllPath(BTNode *b, ElemType path[], int pathlen) 
    int i;
    if (b != NULL) 
        //*b为叶子结点
        if (b->lchild == NULL && b->rchild == NULL) 
            printf("%c到根结点路径: %c ", b->data, b->data);
            for (i = pathlen - 1; i >= 0; i--) 
                printf("%c ", path[i]);
            
            printf("\\n");
         else 
            //将当前结点放入路径中
            path[pathlen] = b->data;
            //路径长度增1
            pathlen++;
            //递归扫描左子树
            AllPath(b->lchild, path, pathlen);
            //递归扫描右子树
            AllPath(b->rchild, path, pathlen);
            //恢复环境
            pathlen--;
        
    


int main() 
    BTNode *b;
    ElemType path[MaxSize];
    CreateBTNode(b, "A(B(D,E(H(J,K(L,M(,N))))),C(F,G(,I)))");
    printf(" 二叉树b: ");
    DispBTNode(b);
    printf("\\n\\n");

    //在此处调用相关函数，输出二叉树b的结点个数;
    printf("二叉树b的结点个数：%d", Nodes(b));
    printf("\\n");
    //在此处调用相关函数，输出二叉树b的叶子结点个数;
    printf("二叉树b的叶子结点个数：%d", LeafNodes(b));
    printf("\\n");
    //在此处调用相关函数，输出二叉树b的深度;
    printf("二叉树b的深度：%d", BTNodeDepth(b));
    printf("\\n\\n");

    //参照运行结果图，在此处调用先序遍历函数;
    printf("先序遍历序列: ");
    PreOrder(b);
    printf("\\n");
    //参照运行结果图，在此处调用中序遍历函数;
    printf("中序遍历序列: ");
    InOrder(b);
    printf("\\n");
    //参照运行结果图，在此处调用后序遍历函数;
    printf("后序遍历序列: ");
    PostOrder(b);
    printf("\\n");
    printf("层次遍历序列: ");
    TravLevel(b);
    printf("\\n");

    printf("叶子结点路径: \\n");
    AllPath(b, path, 0);
    printf("\\n");

运行截图