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: Runtime Error)

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

public class Main{

	public static Node root = null;
	private static class Node {
		Node() {
			this.value = -1;
			this.leftNode = null;
			this.rightNode = null;
		}
		public int value;
		public Node leftNode;
		public Node rightNode;
	}

	public static void main(String[] args) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
//		Scanner s = new Scanner(System.in);
		int cnt = new Integer(br.readLine()).intValue();
		for(int i=0 ; i<cnt ; i++) {
			String[] tmp = br.readLine().split(" ");
			if("insert".equals(tmp[0])) {
				Node n = new Node();
				n.value = new Integer(tmp[1]).intValue();
				insert(n);
			}else if("find".equals(tmp[0])) {
				Node n = new Node();
				n.value = Integer.parseInt(tmp[1]);
				boolean result = find(n);
				if(result)
					System.out.println("yes");
				else
					System.out.println("no");
			}else if("delete".equals(tmp[0])) {
				Node n = new Node();
				n.value = Integer.parseInt(tmp[1]);
				delete(n);
			}
			else {
				inorder(root);
				System.out.println();
				preorder(root);
				System.out.println();
			}
		}
		if(br!=null) {
			br.close();
			br = null;
		}
	}

	public static void insert(Node node) {
		if(root==null){
			root = node;
			return;
		}
		Node targetNode = root;
		Node parent = null;
		while(targetNode != null) {
			parent = targetNode;
			if(targetNode.value > node.value)
				targetNode = targetNode.leftNode;
			else
				targetNode = targetNode.rightNode;
		}
		if(parent.value > node.value)
			parent.leftNode = node;
		else
			parent.rightNode = node;
	}

	public static boolean find(Node node) {
		if(root==null)
			return false;
		Node target = root;
		while(target!=null) {
			if(target.value==node.value)
				return true;
			else{
				if(target.value>node.value) {
					target = target.leftNode;
				}else{
					target = target.rightNode;
				}
			}
		}
		return false;
	}

	public static void delete(Node node) {
		if(root==null)
			return;
		Node parent = null;
		Node targetNode = root;
		Node leftNode = null;
		boolean isLeft = true;
		while(targetNode!=null) {
			if(targetNode.value == node.value) {
				break;
			}else {
				if(targetNode.value>node.value) {
					parent = targetNode;
					targetNode = targetNode.leftNode;
					isLeft = true;
				}else{
					parent = targetNode;
					targetNode = targetNode.rightNode;
					isLeft = false;
				}
			}
		}
		if(targetNode.leftNode!=null && targetNode.rightNode!=null) { //??????????±??????????????????????????????´???
			//??????????±?????????????????????¨?????¨????????§??????????????????
			int value = maxNode(leftNode);
			Node n = new Node();
			n.value = value;
			delete(n);
			targetNode.value = value;
		}else if((targetNode.leftNode!=null && targetNode.rightNode==null) || (targetNode.leftNode==null && targetNode.rightNode!=null)) {
			if(targetNode.leftNode==null) {
				if(isLeft){
					parent.leftNode = targetNode.rightNode;
				}else{
					parent.rightNode = targetNode.rightNode;
				}
				targetNode = null;
			}else {
				if(isLeft) {
					parent.leftNode = targetNode.leftNode;
				}else {
					parent.rightNode = targetNode.leftNode;
				}
				targetNode = null;
			}
		}else {
			if(isLeft){
				parent.leftNode = null;
			}else {
				parent.rightNode = null;
			}
		}
	}

	public static int maxNode(Node leftNode) {
		int leftV = Integer.MIN_VALUE;
		int rightV = Integer.MIN_VALUE;
		int selfV = leftNode.value;
		if(leftNode.leftNode!=null)
			leftV = maxNode(leftNode.leftNode);
		if(leftNode.rightNode!=null)
			rightV = maxNode(leftNode.rightNode);
		return Math.max(Math.max(leftV, rightV), selfV);

	}

	public static void preorder(Node root) {
		System.out.print(" " + root.value);
		if(root.leftNode != null)
			preorder(root.leftNode);
		if(root.rightNode != null)
			preorder(root.rightNode);
	}

	public static void inorder(Node root) {
		if(root.leftNode != null)
			inorder(root.leftNode);
		System.out.print(" " + root.value);
		if(root.rightNode != null)
			inorder(root.rightNode);
	}
}