二叉树的计数

二叉树的遍历也常常用来对二叉树进行计数。

#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>
#define MAXSIZE 100
typedef char ElemType;
typedef struct Node
{
    ElemType data;
    struct Node *lchild;
    struct Node *rchild;
}*BitTree,BitNode;  

void CreateBitTree2(BitTree *T,char str[]);//非递归创建二叉树
void DestroyBitTree(BitTree *T);//销毁二叉树
int LeafNum(BitTree T);//统计二叉树中的叶子结点的数目
int NotLeafCount(BitTree T);//统计二叉树中的非叶子结点的数目
int BitTreeDepth(BitTree T);//计算二叉树的深度  

#include "LinkBiTree.h"  

void CreateBitTree2(BitTree *T,char str[])//非递归创建二叉树
{
    char ch;
    BitTree stack[MAXSIZE];
    int top = -1;
    int flag,k;
    BitNode *p;
    *T = NULL,k = 0;
    ch = str[k];
    while(ch != '\0')
    {
        switch(ch)
        {
        case '(':
            stack[++top] = p;
            flag = 1;
            break;
        case ')':
            top--;
            break;
        case ',':
            flag = 2;
            break;
        default:
            p = (BitTree)malloc(sizeof(BitNode));
            p->data = ch;
            p->lchild = NULL;
            p->rchild = NULL;
            if(*T == NULL)
            {
                *T = p;
            }
            else
            {
                switch(flag)
                {
                case 1:
                    stack[top]->lchild = p;
                    break;
                case 2:
                    stack[top]->rchild = p;
                    break;
                }
            }
        }
        ch = str[++k];
    }
}
void DestroyBitTree(BitTree *T)//销毁二叉树
{
    if(*T)
    {
        if((*T)->lchild)
        {
            DestroyBitTree(&((*T)->lchild));
        }
        if((*T)->rchild)
        {
            DestroyBitTree(&((*T)->rchild));
        }
        free(*T);
        *T = NULL;
    }
}
int LeafNum(BitTree T)//统计二叉树中的叶子结点的数目
{
    if(!T)
    {
        return 0;
    }
    else if(!T->lchild && !T->rchild)
    {
            return 1;
    }
    else
    {
        return LeafNum(T->lchild)+LeafNum(T->rchild);
    }
}
int NotLeafCount(BitTree T)//统计二叉树中的非叶子结点的数目
{
    if(!T)
    {
        return 0;
    }
    else if(!T->lchild && !T->rchild)
    {
        return 0;
    }
    else
    {
        return NotLeafCount(T->lchild)+NotLeafCount(T->rchild)+1;
    }
}
int BitTreeDepth(BitTree T)//计算二叉树的深度
{
    if(T == NULL)
    {
        return 0;
    }
    else
    {
        return BitTreeDepth(T->lchild) > BitTreeDepth(T->rchild)
            ? 1+BitTreeDepth(T->lchild) : 1+BitTreeDepth(T->rchild);
    }
}  

#include "LinkBiTree.h"  

int main(void)
{
    BitTree T,root;
    int num,depth;
    printf("根据括号嵌套建立二叉树：(a(b(c,d),e(f(,g),h(i))))\n");
    CreateBitTree2(&T,"(a(b(c,d),e(f(,g),h(i))))");
    num = LeafNum(T);
    printf("叶子结点的个数 = %2d\n",num);
    num = NotLeafCount(T);
    printf("非叶子结点的个数 = %2d\n",num);
    depth = BitTreeDepth(T);
    printf("二叉树的深度 = %2d\n",depth);
    printf("根据括号嵌套建立二叉树：(A(B(D(,H(J)),E(,I(K,L))),C(F,G)))\n");
    CreateBitTree2(&root,"(A(B(D(,H(J)),E(,I(K,L))),C(F,G)))");
    num = LeafNum(root);
    printf("叶子结点的个数 = %2d\n",num);
    num = NotLeafCount(root);
    printf("非叶子结点的个数 = %2d\n",num);
    depth = BitTreeDepth(root);
    printf("二叉树的深度 = %2d\n",depth);
    DestroyBitTree(&T);
    DestroyBitTree(&root);
    return 0;
}  

运行结果如下：

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