Problem:
Binary Search Tree III

Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

delete $k$: Delete a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

The operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:

If $z$ has no children, we modify its parent $z.p$ to replace $z$ with NIL as its child (delete $z$).

If $z$ has only a single child, we "splice out" $z$ by making a new link between its child and its parent.

If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$, delete $k$ or print are given.

Output

For each find $k$ operation, print "yes" if $T$ has a node containing $k$, "no" if not.

In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key

Constraints

The number of operations $\leq 500,000$

The number of print operations $\leq 10$.

$-2,000,000,000 \leq key \leq 2,000,000,000$

The height of the binary tree does not exceed 100 if you employ the above pseudo code.

The keys in the binary search tree are all different.

Sample Input 1

18
insert 8
insert 2
insert 3
insert 7
insert 22
insert 1
find 1
find 2
find 3
find 4
find 5
find 6
find 7
find 8
print
delete 3
delete 7
print

Sample Output 1

yes
yes
yes
no
no
no
yes
yes
1 2 3 7 8 22
8 2 1 3 7 22
1 2 8 22
8 2 1 22

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in C++ (judge verdict: Accepted)

#include<iostream>

using namespace std;

struct Node{
	Node * Lson;
	Node * Rson;
	Node * parent;
	int key;
}; 

void print();
void insert(int k);
void In(Node * p);
void Pro(Node * p);
int find(int k);
void Delete(int k);
Node * getDelete(Node * p);

Node * root;

int main(void)
{
	int m;
	
	cin>>m;
	while(m--)
	{
		char order[10];
		
		cin>>order;
		if(order[0]=='i')
		{
			int k;
			
			cin>>k;
			insert(k);
		}
		else if(order[0]=='p') 
		{
			print();
		}
		else if(order[0]=='f')
		{
			int k;
			
			cin>>k;
			if(find(k))
			{
				cout<<"yes"<<endl;
			}
			else
			{
				cout<<"no"<<endl;
			}
		}
		else
		{
			int k;
			
			cin>>k;
			Delete(k);
		}
	}
	
	return 0;
}

int find(int k)
{
	Node * temp=root;
	
	while(temp!=NULL&&temp->key!=k)
	{
		if(k<temp->key)
		{
			temp=temp->Lson; 
		}
		else temp=temp->Rson;
	}
	if(temp==NULL)
		return 0;
	else return 1;
}

void insert(int k)
{
	Node *father,*temp;
	
	father=NULL;
	temp=root;
	
	Node *New=new Node;
	New->key=k;
	New->parent=NULL;
	New->Lson=NULL;
	New->Rson=NULL;
	
	while(temp!=NULL)
	{
		father=temp;
		if(k<temp->key)
			temp=temp->Lson;
		else temp=temp->Rson;
	}
	
	New->parent=father;
	if(father==NULL)
		root=New;
	else if(k<father->key)
		father->Lson=New;
	else father->Rson=New;
}

void print()
{
	In(root);
	cout<<endl;
	Pro(root);
	cout<<endl;
}

void In(Node * p)
{
	if(p==NULL)
		return;
	In(p->Lson);
	cout<<" "<<p->key;
	In(p->Rson);
}

void Pro(Node * p)
{
	if(p==NULL)
		return ;
	cout<<" "<<p->key;
	Pro(p->Lson);
	Pro(p->Rson);
}

void Delete(int k)
{
	Node * temp=root,*wait_delete,*wait_temp;//temp k??????  wait_delete´????????? wait_temp ´????????????£??×?????  
	if(find(k))
	{
		while(temp!=NULL&&temp->key!=k)
		{
			if(k<temp->key)
			{
				temp=temp->Lson; 
			}
			else temp=temp->Rson;
		}
		if(temp->Lson==NULL||temp->Rson==NULL)
		{
			wait_delete=temp;
		} 
		else wait_delete=getDelete(temp);
		if(wait_delete->Lson!=NULL)
			wait_temp=wait_delete->Lson;
		else wait_temp=wait_delete->Rson;
		
		if(wait_temp!=NULL)
			wait_temp->parent=wait_delete->parent;
		
		if(wait_delete->parent==NULL)	
			root=wait_temp;
		else if(wait_delete==wait_delete->parent->Lson)
			wait_delete->parent->Lson=wait_temp;
		else wait_delete->parent->Rson=wait_temp;
		
		if(wait_delete!=temp)
			temp->key=wait_delete->key;
	}
	delete wait_delete;
} 

Node * getDelete(Node * p)
{
	if(p->Rson!=NULL)
	{
		p=p->Rson; 
		while(p->Lson!=NULL)
			p=p->Lson;
		return p;
	}
	Node * father=p->parent;
	while(father!=NULL&&p==father->Rson)
	{
		p=father;
		father=father->parent;
	}
	return father;
}