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 Go (judge verdict: Accepted)

// AOJ ALDS1_8_A: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_8_A
// AOJ ALDS1_8_B: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_8_B
// AOJ ALDS1_8_C: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_8_C

package main

import (
	"fmt"
	"bufio"
	"os"
	"strconv"
)

type node struct {
	key                 int
	parent, left, right *node
}

var root *node
var sc = bufio.NewScanner(os.Stdin)

func insert(key int) {
	var y *node
	x := root

	z := &node{key, nil, nil, nil}

	for x != nil {
		y = x
		if z.key < x.key {
			x = x.left
		} else {
			x = x.right
		}
	}

	z.parent = y

	if y == nil {
		root = z
	} else {
		if z.key < y.key {
			y.left = z
		} else {
			y.right = z
		}
	}
}

func find(key int) *node {
	// start root node
	x := root
	for x != nil {
		// find key
		if x.key == key {
			return x
		}

		// move node
		if x.key > key {
			x = x.left
		} else {
			x = x.right
		}
	}
	return nil
}

func delete(n *node) {

	// 削除対象のnodeをyとする
	// nodeに子がない場合または子が1つの場合はnodeを削除対象にする
	// 子が2つある場合はnodeの次節点を削除対象にする
	var y *node
	if n.left == nil || n.right == nil {
		y = n
	} else {
		y = getSuccessor(n)
	}

	// yの子xを決める
	var x *node
	if y.left != nil {
		x = y.left
	} else {
		x = y.right
	}

	if x != nil {
		x.parent = y.parent // xの親を設定
	}

	if y.parent == nil {
		root = x // yがrootのとき、xをrootに設定する
	} else if y == y.parent.left {
		y.parent.left = x // yがyの親の左の子なら、xをyの親の左の子として設定する
	} else {
		y.parent.right = x // yがyの親の右の子なら、xをyの親の右の子として設定する
	}

	if y != n {			// nの次節点が削除された場合
		n.key = y.key	// yのkeyをnにコピーする
	}
}

func getSuccessor(n *node) *node {
	if n.right != nil {
		return getMinimum(n.right)
	}

	y := n.parent
	for y != nil && n == y.right {
		n = y
		y = n.parent
	}
	return y
}

func getMinimum(x *node) *node {
	for x.left != nil {
		x = x.left
	}
	return x
}

func inorder(u *node, list []int) []int {
	if u != nil {
		list = inorder(u.left, list)
		// fmt.Printf(" %v", u.key)
		list = append(list, u.key)
		list = inorder(u.right, list)
	}
	return list
}

func preorder(u *node, list []int) []int {
	if u != nil {
		// fmt.Printf(" %v", u.key)
		list = append(list, u.key)
		list = preorder(u.left, list)
		list = preorder(u.right, list)
	}
	return list
}

func printList(list []int) {
	buf := bufio.NewWriter(os.Stdout)
	for _, v := range list {
		buf.Write([]byte(fmt.Sprintf(" %d", v)))
	}
	buf.Write([]byte("\n"))
	buf.Flush()
}

func nextString() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	sc.Scan()
	v, _ := strconv.Atoi(sc.Text())
	return v
}

func main() {
	var command string
	var n, key int

	fmt.Scanf("%d", &n)

	sc.Split(bufio.ScanWords)
	for i := 0; i < n; i++ {
		command = nextString()
		switch command {
		case "insert":
			key = nextInt()
			insert(key)
		case "find":
			key = nextInt()
			if exist := find(key); exist != nil {
				fmt.Println("yes")
			} else {
				fmt.Println("no")
			}
		case "delete":
			key = nextInt()
			if node := find(key); node != nil {
				delete(node)
			}
		case "print":
			printList(inorder(root, []int{}))
			printList(preorder(root, []int{}))
		}
	}
}