數據結構——17 二叉樹（遞歸）

二叉樹——遞歸法

二叉樹——使用遞歸方法，創建樹、前中後序遍歷樹
建立樹時，按照左子樹小於樹根，右子樹大於樹根，這樣中序遍歷就是有序表

#include<iostream>
using namespace std;
class node            //樹節點定義
{
public:
	int data;         //元素值
	node *parent;     //父節點
	node *left;       //左子節點
	node *right;      //右子節點
public:
//	node():data(-1),parent(NULL),left(NULL),right(NULL){};
	node(int num):data(num),parent(NULL),left(NULL),right(NULL){};        //構造函數，初始化類成員變量


};

class tree            //樹定義
{
public:
	tree(int num[],int len);           //構造函數


	void insertNode(int data);         //安左低右高插入樹的節點
	void preOrderTree();               //前序
	void inOrderTree();                //中序             
	void postOrderTree();              //後序


private:
	void insertNode(node *root,int data);	    //插入遞歸
	void preOrderTree(node *current);           //前序遞歸
	void inOrderTree(node *current);            //中序遞歸
	void postOrderTree(node *current);          //後序遞歸


	node *root;                       //樹的根節點

};

tree::tree(int num[],int len)         //構造函數
{
	root=new node(num[0]);
	for(int i=1;i<len;i++)
		insertNode(num[i]);           //調用插入函數
}

void tree::insertNode(int data)
{
	if(root!=NULL)
		insertNode(root,data); 
}

void tree::insertNode(node *current,int data)      //遞歸插入函數樹節點函數
{
	if(data<= current->data)
	{
		if(current->left==NULL)
		{
			current->left =new node(data);
			current->left->parent=current;
		}
		else 
			insertNode(current->left,data);
	}


	else if(data> current->data)
	{
		if(current->right==NULL)
		{
			current->right =new node(data);
			current->right->parent=current;
		}
		else 
			insertNode(current->right,data);
	}


	return;
}

void tree::preOrderTree()      //前序遍歷
{
	if(root==NULL)
		return;
	preOrderTree(root);
}
void tree::preOrderTree(node *current)
{
	if(current!=NULL)
	{
		cout<<current->data<<"  ";
		preOrderTree(current->left);
		preOrderTree(current->right);
	}
}

void tree::inOrderTree()       //中序遍歷
{
	if(root==NULL)
		return;
	inOrderTree(root);
}
void tree::inOrderTree(node *current)
{
	if(current!=NULL)
	{
		inOrderTree(current->left);
		cout<<current->data<<"  ";
		inOrderTree(current->right);
	}
}




void tree::postOrderTree()     //後序遍歷
{
	if(root==NULL)
		return;
	postOrderTree(root);
}
void tree::postOrderTree(node *current)
{
	if(current!=NULL)
	{
	
		postOrderTree(current->left);
		postOrderTree(current->right);
		cout<<current->data<<"  ";
	}
}


int main()
{
	int num[8]={5,3,7,2,4,6,8,1};
	tree t(num,8);


	cout<<"前序遍歷:  ";
	t.preOrderTree();
	cout<<endl<<endl;


	cout<<"中序遍歷:  ";
	t.inOrderTree();
	cout<<endl<<endl;


	cout<<"後序遍歷:  ";
	t.postOrderTree();
	cout<<endl;


	return 0;
}

前面爲了安全，程序寫的比較麻煩，遞歸方法都放在private裏，然後通過public裏的接口調用，現在可以直接寫成public的，容易理解。

#include<iostream>
using namespace std;
class node            //樹節點定義
{
public:
	int data;         //元素值
	node *left;       //左子節點
	node *right;      //右子節點
public:
//	node():data(-1),parent(NULL),left(NULL),right(NULL){};
	node(int num):data(num),left(NULL),right(NULL){};        //構造函數，初始化類成員變量

};

class tree            //樹定義
{
public:
	node *root;                       //樹的根節點
	tree(int num[],int len);           //構造函數

	void insertNode(node *root,int data);	    //插入遞歸 按左低右高插入樹的節點   
	void preOrderTree(node *current);           //前序遞歸
	void inOrderTree(node *current);            //中序遞歸
	void postOrderTree(node *current);          //後序遞歸
};

tree::tree(int num[],int len)         //構造函數
{
	root=new node(num[0]);
	for(int i=1;i<len;i++)
		insertNode(root,num[i]);      //調用插入函數
}

void tree::insertNode(node *current,int data)      //遞歸插入函數樹節點函數
{
	if(data<= current->data)
	{
		if(current->left==NULL)
			current->left =new node(data);
		else 
			insertNode(current->left,data);
	}


	else
	{
		if(current->right==NULL)
			current->right =new node(data);
		else 
			insertNode(current->right,data);
	}
	
}


void tree::preOrderTree(node *current)    //前序遍歷
{
	if(current!=NULL)
	{
		cout<<current->data<<"  ";
		preOrderTree(current->left);
		preOrderTree(current->right);
	}
}


void tree::inOrderTree(node *current)    //中序遍歷
{
	if(current!=NULL)
	{
		inOrderTree(current->left);
		cout<<current->data<<"  ";
		inOrderTree(current->right);
	}
}


void tree::postOrderTree(node *current)   //後序遍歷
{
	if(current!=NULL)
	{
	
		postOrderTree(current->left);
		postOrderTree(current->right);
		cout<<current->data<<"  ";
	}
}


int main()
{
	int num[8]={5,3,7,2,4,6,8,1};
	tree t(num,8);


	cout<<"前序遍歷:  ";
	t.preOrderTree(t.root);
	cout<<endl<<endl;


	cout<<"中序遍歷:  ";
	t.inOrderTree(t.root);
	cout<<endl<<endl;


	cout<<"後序遍歷:  ";
	t.postOrderTree(t.root);
	cout<<endl;


	return 0;
}