二叉树的简单接口
直接上代码：
#pragma once
#include<queue>
#include<stack>
#include<iostream>
using namespace std;
//树中节点结构
template<class T>
struct BinaryTreeNode
{
T _data;
BinaryTreeNode<T>* _left;
BinaryTreeNode<T>* _right;
//节点需要初始化(赋值)
BinaryTreeNode(const T& x)
:_data(x)
,_left(NULL)
,_right(NULL)
{}
};
//树的结构
template<class T>
class BinaryTree
{
public:
//无参构造
BinaryTree()
:_root(NULL)
{}
//传来一个数组 构造一棵树
BinaryTree(const T* a,size_t size)
{
size_t index = 0;//数组中的下标；
_root = _CreateTree(a,size,index);
}
//拷贝构造
BinaryTree(const BinaryTreeNode<T>& x)
{
_root = _Copy(x);
}
BinaryTree<T>* _Copy(BinaryTreeNode<T>* root)
{
if (root == NULL)
{
return NULL;
}
BinaryTreeNode<T>* newRoot = new BinaryTreeNode<T>(root->_data);
newRoot->_left = _Copy(root->_left);
newRoot->_right = _Copy(root->_right);
return newRoot;
}
//赋值运算符的重载
BinaryTree<T>& operator=(const BinaryTreeNode<T>& x)
{
if(this != &x)
{
swap(_root,x._root);
}
return *this;
}
//深度
int Depth(BinaryTreeNode<T>* root)
{
if(root == NULL)
{
return 0;
}
else
{
int LeftDepth = Depth(root->_left);
int RightDepth = Depth(root->_right);
return LeftDepth > RightDepth ? LeftDepth+1:RightDepth+1;
}
}
//查找节点
BinaryTreeNode<T>* Find(BinaryTreeNode<T>* root,const T& x)
{
if(root == NULL)
{
return NULL;
}
else if(root->_data == x)
{
return root;
}
else
{
BinaryTreeNode<T>* tem =Find(root->_left,x);
if(tem)
{
return tem;
}
else
{
return Find(root->_right,x);
}
}
}
//大小
//int Size(BinaryTreeNode<T>* root,int& size)
//{
// if(root == NULL)
// {
// return 0;
// }
// else
// {
// ++size;
// }
// Size(root->_left,size);
// Size(root->_right,size);
// return size;
//}
//大小
int GetNodeNum(BinaryTreeNode<T>* root)
{
if(root == NULL) //递归出口
{
return 0;
}
return GetNodeNum(root->_left) + GetNodeNum(root->_right) + 1;
}
//中序遍历
void InOrder(BinaryTreeNode<T>* root)
{
if(root != NULL)
{
InOrder(root->_left);
cout<<root->_data<<"-";
InOrder(root->_right);
}
}
//后序遍历
void PostOrder(BinaryTreeNode<T>* root)
{
if(root != NULL)
{
PostOrder(root->_left);
PostOrder(root->_right);
cout<<root->_data<<"-";
}
}
//层序遍历
void LevelOrder(BinaryTreeNode<T>* root)
{
queue<BinaryTreeNode<T>*> q;
if(root == NULL)
{
return;
}
BinaryTreeNode<T>* node = NULL;
q.push(root);
while(!q.empty())
{
node = q.front();
q.pop();
cout<<node->_data<<"-";
if(node->_left != NULL)
{
q.push(node->_left);
}
if(node->_right != NULL)
{
q.push(node->_right);
}
}
}
//前序遍历
void PrveOrder(BinaryTreeNode<T>* root)
{
if(root != NULL)
{
cout<<root->_data<<"-";
PrveOrder(root->_left);
PrveOrder(root->_right);
}
}
//求二叉树第K层的节点个数
//递归解法：
//（1）如果二叉树为空或者k<1返回0
//（2）如果二叉树不为空并且k==1，返回1
//（3）如果二叉树不为空且k>1，返回左子树中k-1层的节点个数与右子树k-1层节点个数之和
int GetNodeNumKthLevel(BinaryTreeNode<T>* root, int k)
{
if(root == NULL || k < 1)
{
return 0;
}
if(k == 1) //能下来说明 ROOT不是空
{
return 1; //递归结束条件
}
int leftNum = GetNodeNumKthLevel(root->_left,k-1);
int rightNum = GetNodeNumKthLevel(root->_right,k-1);
return (leftNum+rightNum);
}
//求二叉树中叶子节点的个数
int GetLeafNodeNum(BinaryTreeNode<T>* root)
{
if(root == NULL)
{
return 0;
}
if(root->_left == NULL && root->_right == NULL)
{
return 1;
}
int leftNum = GetLeafNodeNum(root->_left);
int rightNum = GetLeafNodeNum(root->_right);
return leftNum+rightNum;
}
//非递归 前序遍历
void PrevOrder_NonR()
{
stack<BinaryTreeNode<T>*> s; //栈里边全是指针
if (_root != NULL)
{
s.push(_root) //头不空 头入栈
}
while (!s.empty())
{
BinaryTreeNode<T>* top = s.top();//取栈顶
s.pop(); //出栈
cout << top->_data << " ";
if (_root->_left) //左右访问
{
s.push(_root->_left);
}
if (_root->_right)
{
s.push(_root->_right);
}
}
cout << endl;
}
//非递归 中序遍历
void InOrder_NonR()
{
stack<BinaryTreeNode<T>*> s;
BinaryTreeNode<T>* cur = _root; //cur始终指向头
while (cur || !s.empty())
{
//就是说，将cur指向的所有左路都入栈
while (cur)
{
s.push(cur); //第一次是头入栈；
cur = cur->_left; //所有左边依次入栈
}
//中序遍历 现在访问左 在到右边
while (!s.empty())
{
BinaryTreeNode<T>* top = s.top();
s.pop();
cout << top->_data << " ";
cur = top->_right; //走右边
}
}
}
//非递归，后序遍历
void PostOrder_NonR()
{
stack<BinaryTreeNode<T>*> s;
BinaryTreeNode<T>* cur = _root;
BinaryTreeNode<T>* prevVisted = NULL;
while (cur || !s.empty())
{
while (cur)
{
s.push(cur);
cur = cur->_left;
}
BinaryTreeNode<T>* top = s.top();
if (top->_right == NULL || top->_right = prevVisted)
{
cout << top->_data << " ";
prevVisted = top;
s.pop();
}
else
{
cur = top->_right;
}
}
cout << endl;
}
//清除
void _Destroy(BinaryTreeNode<T>*& root)
{
if (root == NULL)
{
return;
}
if (root->_left == NULL || root->_right == NULL)
{
delete root;
root = NULL;
return;
}
_Destroy(root->_left);
_Destroy(root->_right);
delete root;
}
protected:
BinaryTreeNode<T>* _CreateTree(const T* a,size_t size,size_t& index)
{
if(a[index] != '#' && index < size)
{
BinaryTreeNode<T>* root = new BinaryTreeNode<T>(a[index]);
root->_left = _CreateTree(a,size,++index);//v 为神魔啊 有问题呢 加加不可以放后边
root->_right = _CreateTree(a,size,++index);
return root;
}
else
{
return NULL;
}
}
public:
BinaryTreeNode<T>* _root;
};
#include"BinaryTree.h"
void Test()
{
BinaryTreeNode<int>* _root = NULL;
int a[7] = {1,2,'#','#',3,'#','#'};
BinaryTree<int> s1(a,10);
cout<<"先序遍历"<<endl;
s1.PrveOrder(s1._root);
cout<<endl;
cout<<"中序遍历"<<endl;
s1.InOrder(s1._root);
cout<<endl;
cout<<"后序遍历"<<endl;
s1.PostOrder(s1._root);
cout<<endl;
cout<<"层序遍历"<<endl;
s1.LevelOrder(s1._root);
cout<<endl;
int size = 0;
//cout<<"Size:"<<s1.Size(s1._root,size)<<endl;
cout<<"Depth:"<<s1.Depth(s1._root)<<endl;
cout<<"Find:"<<s1.Find(s1._root,1)<<endl;
cout<<"大小："<<s1.GetNodeNum(s1._root)<<endl;
cout<<"第K层的节点数："<<s1.GetNodeNumKthLevel(s1._root,2)<<endl;
cout<<"叶子节点数："<<s1.GetLeafNodeNum(s1._root)<<endl;
}
int main()
{
Test();
return 0;
}
