数据结构入门-二叉树的层序遍历

如何判断一棵二叉树的深度？

层序遍历

过程演示

使用队列完成层序遍历：

1.定义变量深度depth=0，树根入队即第一层入队

2.树根出队，depth+1

3.树根的左右子树也就是第二层入队

4.B节点出队，B节点的左右子树入队

5.C节点出队，depth+1，C节点的左右子树入队

以此循环，求出二叉树总深度depth。

代码实现

cpp 复制代码

//获取二叉树深度
int maxDepth(TreeNode* root)
{
	if (root == NULL)
	{
		return 0;
	}

	int depth = 0;//深度
	Queue* q = initQueue();//初始化队列
	equeue(q, root);//树根入队

	while (!isEmpty(q))
	{
		int count = queueSize(q);
		while (count > 0)
		{
			TreeNode* curr;
			dequeue(q, &curr);
			if (curr->lchild != NULL)
			{
				equeue(q, curr->lchild);
			}
			if (curr->rchild != NULL)
			{
				equeue(q, curr->rchild);
			}
			count--;
		}
		depth++;
	}
	return depth;
}

主程序

这个程序中求二叉树深度的实现依靠队列等知识点

cpp 复制代码

#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
using namespace std;
const int MAXSIZE =100;
typedef char TreeType;

//树的结构
typedef struct TreeNode
{
	TreeType data;
	struct TreeNode* lchild;
	struct TreeNode* rchild;
}TreeNode;

typedef TreeNode* ElemType;

//队列结构
typedef struct
{
	ElemType* data;
	int front;
	int rear;
}Queue;

typedef TreeNode* BiTree;

char str[] = "ABDH#K###E##CFI###G#J##";
int index = 0;

void createTree(BiTree *T)
{
	TreeType ch;
	ch = str[index++];
	if (ch == '#')
	{
		*T=NULL;
	}
	else
	{
		*T = new TreeNode;
		(*T)->data = ch;
		createTree(&(*T)->lchild);
		createTree(&(*T)->rchild);
	}
}
//初始化
Queue* initQueue()
{
	Queue* q = new Queue;
	q->data = new ElemType[MAXSIZE];
	q->front = 0;
	q->rear = 0;
	return q;

}

//判断队列是否为空
int isEmpty(Queue* Q)
{
	if (Q->front == Q->rear)
	{
		cout << "空的" << endl;
		return 1;
	}
	else
	{
		return 0;
	}
}

//入队
int equeue(Queue* Q, ElemType e)
{
	if ((Q->rear + 1) % MAXSIZE == Q->front)
	{
		cout << "满了" << endl;
		return 0;
	}
	Q->data[Q->rear] = e;
	Q->rear = (Q->rear + 1) % MAXSIZE;
	return 1;


}

//出队
int dequeue(Queue* Q, ElemType* e)
{
	if (Q->front == Q->rear)
	{
		cout << "空的" << endl;
		return 0;
	}
	*e = Q->data[Q->front];
	Q->front = (Q->front + 1) % MAXSIZE;
	return 1;
}
//获取队头元素
int getHead(Queue* Q, ElemType* e)
{
	if (Q->front == Q->rear)
	{
		cout << "空的" << endl;
	}
	*e = Q->data[Q->front];
	return 1;
}

//获取队列元素数量
int queueSize(Queue* Q)
{
	if (!isEmpty(Q))
	{
		return (Q->rear - Q->front+MAXSIZE)%MAXSIZE;
	}
	else
	{
		return 0;
	}
}

//获取二叉树深度
int maxDepth(TreeNode* root)
{
	if (root == NULL)
	{
		return 0;
	}

	int depth = 0;//深度
	Queue* q = initQueue();//初始化队列
	equeue(q, root);//树根入队

	while (!isEmpty(q))
	{
		int count = queueSize(q);
		while (count > 0)
		{
			TreeNode* curr;
			dequeue(q, &curr);
			if (curr->lchild != NULL)
			{
				equeue(q, curr->lchild);
			}
			if (curr->rchild != NULL)
			{
				equeue(q, curr->rchild);
			}
			count--;
		}
		depth++;
	}
	return depth;
}


int main()
{
	BiTree T;
	createTree(&T);
	cout << maxDepth(T) << endl;

	return 0;
}

运行程序可获得该二叉树深度为5。