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: Accepted)

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

public class Main {

	public static class Node {
		int key;
		Node parent;
		Node right;
		Node left;

		public Node(int key) {
			this.key = key;
		}
	}

	public static Node root;

	public static Node treeSearch(Node u, int k) {
//		if (u == null) return null;
		Node x = u;
		while (x != null) {
			if (k < x.key) {
				x = x.left;
			} else if (x.key < k) {
				x = x.right;
			} else { // k == x.key
				return x;
			}
		}
		return null;
	}

	// x???root??¨??????tree????????§?????§???key?????????Node
	private static Node treeMaximum(Node x) {
		if (x == null) return null;
		while (x.right != null) {
			 x = x.right;
		}
		return x;
	}

	private static Node treeMinimum(Node x) {
		if (x == null) return null;
		while (x.left != null) {
			x = x.left;
		}
		return x;
	}

	// x?????????????????? x????????£?????´????????£???????????\???Node
	// ??£???????????\???Node???root??¨??????tree?????????????????£?????\??????
	private static Node treeSuccessor(Node x) {
		if (x.right == null && x.left == null) {
			return null;
		}
		if (x.right == null) {
			x.left.parent = x.parent;
			return x.left;
		}
		if (x.left == null) {
			x.right.parent = x.parent;
			return x.right;
		}

//		Node r = treeMaximum(x.left);
//		x.key = r.key;
//		treeDelete(r);
//		return x;

		Node l = treeMinimum(x.right);
		x.key = l.key;
		treeDelete(l);
		return x;
	}

	// z?????????????????? z?????£???????????\???Node??????????????£???
	// ??????Node??????pointer??????z?????????z??????poiter?????£???????????\??????
	public static void treeDelete(Node z) {
		if (z == null) return;

		Node p = z.parent;
		if (p == null) {
			treeSuccessor(root);
			return;
		}
		if (p.right == z) {
			p.right = treeSuccessor(z);
		} else { // p.left == z
			p.left = treeSuccessor(z);
		}
		return;

	}

	public static void insert(int k) {
		Node x = root;
		if (x == null) {
			root = new Node(k);
			return;
		}

		while (true) {
			if (k < x.key) {
				if (x.left == null) {
					x.left = new Node(k);
					x.left.parent = x;
					return;
				}
				x = x.left;
			} else { // x.key <= k
				if (x.right == null) {
					x.right = new Node(k);
					x.right.parent = x;
					return;
				}
				x = x.right;
			}
		}
	}

	public static void inorder(Node u) {
		if (u.left != null) inorder(u.left);

		System.out.print(" " + u.key);

		if (u.right != null) inorder(u.right);
	}

	public static void preorder(Node u) {
		System.out.print(" " + u.key);

		if (u.left != null) preorder(u.left);

		if (u.right != null) preorder(u.right);
	}

	public static void main(String[] args) throws Exception {
		// TODO ?????????????????????????????????????????????
		BufferedReader br =
				new BufferedReader( new InputStreamReader(System.in) );
		int n = Integer.parseInt(br.readLine());
		int x;
		for (int i=0; i< n; i++) {
			String[] com = br.readLine().split(" ");

			switch (com[0]) {
			case "find":
				x = Integer.parseInt(com[1]);
				Node t = treeSearch(root, x);
				if (t != null) System.out.println("yes");
				else System.out.println("no");
				break;

			case "insert":
				x = Integer.parseInt(com[1]);
				insert(x);
				break;

			case "print":
				inorder(root);
				System.out.println();
				preorder(root);
				System.out.println();
				break;

			case "delete":
				x = Integer.parseInt(com[1]);
				treeDelete( treeSearch(root, x) );
				break;
			}
		}
	}

}