数据结构-二叉树的遍历及相关应用

1、定义二叉树结点结构

2、编写主程序

3、三种方法遍历二叉树，并实现求树的深度，叶子数，某一层的结点数

4、实现代码（带交互界面）

#include
using namespace std;
typedef struct BiTNode
{
	char data;
	struct BiTNode* lchild, * rchild;
}BiTNode, * BitTree;

BitTree creatTree()
{
	BitTree T = NULL;
	char ch;
	cin >> ch;
	if (ch == '#')
	{
		T = NULL;
		return T;
	}
	else
	{
		T = new BiTNode;
		if (T == NULL)
			return NULL;
		T->data = ch;
		T->lchild = NULL;
		T->rchild = NULL;
		T->lchild = creatTree();
		T->rchild = creatTree();
		return T;
	}
}
void Zhongxu(BitTree T)
{
	if (T)
	{
		Zhongxu(T->lchild);
		cout << T->data;
		Zhongxu(T->rchild);
	}
}
void Xianxu(BitTree T)
{
	if (T)
	{
		cout << T->data;
		Xianxu(T->lchild);
		Xianxu(T->rchild);
	}
}
void Houxu(BitTree T)
{
	if (T)
	{
		Houxu(T->lchild);
		Houxu(T->rchild);
		cout << T->data;
	}
}
void printmenu()
{
	cout << "欢迎使用二叉树遍历及相关应用工具\n";
	cout << "请输入功能选项（1-3）:\n";
	cout << "\t1.创建二叉树\n";
	cout << "\t2.遍历二叉树\n";
	cout << "\t3.打印二叉树深度\n";
	cout << "\t4.打印二叉树叶子个数\n";
	cout << "\t5.打印二叉树第n层结点个数\n";
	cout << "\t0.退出\n";
}
int TreeDepth(BitTree T)
{
	if (T == NULL)
		return 0;
	else
		return (TreeDepth(T->lchild) > TreeDepth(T->rchild) ? TreeDepth(T->lchild) : TreeDepth(T->rchild)) + 1;   //选择左孩子和右孩子中较大的深度，然后加上一个根结点
}
int LeafCount(BitTree T)
{
	if (T == NULL)
		return 0;
	else
	{
		if (T->lchild == NULL && T->rchild == NULL)   //如果递归到叶子，计数+1
			return 1;
		else
			return LeafCount(T->lchild) + LeafCount(T->rchild);   //递归到叶子
	}
}
int NodeCount(BitTree T,int n)
{
	if (T == NULL)
		return 0;
	if (n == 1)  //如果到第n层，返回1
		return 1;
	return NodeCount(T->lchild, n - 1) + NodeCount(T->rchild, n - 1); //递归到第n层

}

int main()
{
	BitTree T = NULL;
	int choose;
	int method;
	choose = -1;
	while (choose != 0) {
		
		printmenu();
		cin >> choose;
		switch (choose) {
		case 1:
			cout << "创建你的二叉树吧，用#表示空指针:\n";
			T = creatTree();
			cout << "二叉树创建成功\n";
			break;
		case 2: {
			method = -1;
			while (method != 0)
			{
				cout << "\t1.先序遍历\n";
				cout << "\t2.中序遍历\n";
				cout << "\t3.后序遍历\n";
				cout << "\t0.返回上一级\n";
				cout << "请输入功能选项（0-3）";
				cin >> method;
				switch (method)
				{
				case 1:Xianxu(T); break;
				case 2:Zhongxu(T); break;
				case 3:Houxu(T); break;
				case 0:method = 0; break;
				}
			}
			printmenu();
			break;
		}
		case 3:
			cout << "该二叉树的深度是:" << TreeDepth(T)<<"\n"; break;
		case 4:
			cout << "该二叉树的叶子数是:" << LeafCount(T)<<"\n"; break;
		case 5:
			int n;
			cout << "请输入你要查询的层数:";
			cin >> n;
			cout << "该层共有" << NodeCount(T, n) << "个结点\n";
			break;
		case 0:
			cout << "感谢使用，欢迎多提宝贵意见！\n" << endl;
			return 0;
		}
	}

}