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 JAVA (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

class Node{
	int id;
	Node left,right;
	
	public void display(){
		System.out.print(" "+id);
	}
}

class Tree{
	private Node root;
	
	public boolean delete(int key){
		Node current = root;
		Node parent = root;
		while(current.id!=key){
			parent = current;
			if(current.id>key){
				current = current.left;
			}else if(current.id<key){
				current = current.right;
			}
			if(current==null)
				return false;
		}
		
		//Node????????????
		if(current.left==null && current.right==null){
			if(current == root)
				root = null;
			else if(parent.left == current)
				parent.left = null;
			else if(parent.right == current)
				parent.right = null;
		}else if(current.left==null){
			if(current == root){
				root = current.right;
			}else if(parent.left==current){
				parent.left = current.right;
			}else if(parent.right==current){
				parent.right = current.right;
			}
		}else if(current.right == null){
			if(current == root)
				root = current.left;
			else if(parent.left == current)
				parent.left = current.left;
			else if(parent.right== current)
				parent.right = current.right;
			//????????????
		}else{
			Node successor = getSuccessor(current);
			if(current == root)
				root = successor;
			else if(parent.left ==current)
				parent.left = successor;
			else if(parent.right ==current)
				parent.right = successor;
			
			successor.left = current.left;
		}
		return true;
	}
	
	private Node getSuccessor(Node delNode){
		Node successorParent = delNode;
		Node successor = delNode;
		Node current = delNode.right;
		while(current!=null){
			successorParent = successor;
			successor = current;
			current = current.left;
		}
		if(successor != delNode.right){
			successorParent.left = successor.right;
			successor.right = delNode.right;
		}
		return successor;
	}
	
	
	public boolean find(int key){
		Node current = root;
		while(current!=null){
			if(current.id>key)
				current = current.left;
			else if(current.id<key)
				current = current.right;
			else if(current.id==key){
				System.out.println("yes");
				return true;
			}
		}
		System.out.println("no");
		return false;
	}
	public void insert(int id){
		Node newNode = new Node();
		newNode.id = id;
		if(root==null) 
			root = newNode;
		else{
			Node current = root;
			Node parent;
			while(true){
				parent = current;
				if(current.id>id){
					current = current.left;
					if(current == null){
						parent.left = newNode;
						return;
					}
				}else{
					current = current.right;
					if(current==null){
						parent.right = newNode;
					 	return;
					}
				}
			}
		}
	}
	
	public void inOrder(Node localRoot){
		if(localRoot!=null){
			inOrder(localRoot.left);
			localRoot.display();
			inOrder(localRoot.right);
		}
	}
	public void preOrder(Node localRoot){
		if(localRoot!=null){
			localRoot.display();
			preOrder(localRoot.left);
			preOrder(localRoot.right);
		}
	}
	public void print(){
		inOrder(root);
		System.out.println("");
		preOrder(root);
	}
}

public class Main{
	public static void main(String[] args) throws IOException{
		Tree tree = new Tree();
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		String in;
		String[] input;
		for(int i=0;i<n;i++){
			in = br.readLine();
			if(in.charAt(0)=='i'){
				input = in.split(" ");
				tree.insert(Integer.parseInt(input[1]));
			}
			else if(in.charAt(0)=='p'){
				tree.print();
				System.out.println("");
			}else if(in.charAt(0)=='f'){
				input = in.split(" ");
				tree.find(Integer.parseInt(input[1]));
			}else if(in.charAt(0)=='d'){
				input = in.split(" ");
				tree.delete(Integer.parseInt(input[1]));
			}
		}
	}
}