[置顶] 二叉树层次遍历的应用--判断一颗二叉树是否为规则二叉树

一 问题

二 解题方法

采用二叉树的层次遍历，需要队列作为辅助，

如图所示，队列保存着层次遍历时二叉树结点的地址，Thislevel记录了当前层的结点数，Nextlevel记录了下一层结点数。当队列中每出一个结点，Thislevel必须减1，当前结点的左或右孩子入队，Nextlevel必须加1。当Thislevel为0时，说明二叉树的一层遍历结束，开始新的一层。

三 测试

四 代码

/*
 * to judge whether a binary tree is a binary tree
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define ElemType int
#define END -1
#define MAX 100
typedef struct BinNode {
		ElemType data;
		struct BinNode *left;
		struct BinNode *right;
}BinNode;
int leaves[MAX];
typedef struct QueueNode {
		struct BinNode *data;
		struct QueueNode *next;
}QueueNode;
QueueNode *front, *rear;
void InQueue(struct BinNode *e) {
		QueueNode *p = (QueueNode *)malloc(sizeof(QueueNode));
		if(!p) {
				perror("memory error!
");
				exit(EXIT_FAILURE);
		}
		p->data = e;
		p->next = 0;
        if(rear) rear->next = p;
		rear = p;
		if(!front) front = rear;
}
struct BinNode *DeQueue() {
		if(!front) {
				perror("the queue is empty!
");
				exit(EXIT_FAILURE);
		}
		struct BinNOde *p = front->data;
		QueueNode *r = front;
		front = front->next;
		free(r);
		if(!front) rear = NULL;
		return p;
}
int QueueEmpty() {
		return  front == NULL?1:0;
}
void CreateBinTree(BinNode **t) {
		ElemType e;
		if(scanf("%d", &e) != 1) {
				perror("input error!
");
				exit(EXIT_FAILURE);
		}
		if(e == END) return;
		if(*t == NULL) {
				*t = (BinNode *)malloc(sizeof(BinNode *));
				(*t)->left = NULL;
				(*t)->right = NULL;
				(*t)->data = e;
		}
		CreateBinTree(&((*t)->left));
		CreateBinTree(&((*t)->right));
		
}
void PreTranverse(BinNode *t) {
		if(t) {
				printf("%d
", t->data);
				PreTranverse(t->left);
				PreTranverse(t->right);
		}
}
int JudgeRuleBinTree(BinNode *t) {
		if(!t) return 1;
		int level = 1;   // the level of bintree
		int thislevel;   // the number of nodes in this level
		int nextlevel;   // the number of nodes in next level
		int k = 0;       // the number of leaves in bintree 
		int i, j;
		BinNode *p;
        InQueue(t);
		thislevel = 1;  // when the root node is added into the queue
		nextlevel = 0;
        while(!QueueEmpty()) {
				p = DeQueue();
				/*
				 * if a leaf occurs
				*/
				if(!p->left && !p->right) leaves[k++] = level;
				thislevel--;  // when a node is out from the queue
				if(p->left) {
						InQueue(p->left);
						nextlevel++;  // the children of current node
				}
				if(p->right) {
						InQueue(p->right);
						nextlevel++;
				}
				if(!thislevel) {
						thislevel = nextlevel;
						nextlevel = 0;
						level++;
				}
		}
		printf("the level of all the leaves in binary tree is:
");
        for(i = 0;i < k;i++) printf("%d	", leaves[i]);
        for(i = 0;i < k - 1;i++) {
				for(j = i + 1;j < k;j++) {
						if(fabs(leaves[i] - leaves[j]) != 0 && fabs(leaves[i] - leaves[j]) != 1) {
								return 0;
						}
				}
		}
		return 1;
}
int main() {
		BinNode *root = NULL;
		CreateBinTree(&root);
		PreTranverse(root);
        if(JudgeRuleBinTree(root)) printf("
rule binary tree!
");
		else printf("
NOT rule binary tree!
");
		return 0;
}

五 编程体会

本题实际上是利用二叉树的层次遍历，关键是找到每个叶子节点的深度。为此，本人使用了thislevel和nextlevel这两个变量来记录层次变化情况。