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 Scala (judge verdict: Accepted)

object Main extends App {
  val n: Int = io.StdIn.readInt()
  val bt: BTree = Empty

  (0 until n).foldLeft[BTree](bt){(t, _) =>
    val op: Array[String] = io.StdIn.readLine().split(" ")
    op(0) match {
      case "print" => t.show; t
      case "insert" => t.insert(op(1).toInt)
      case "find" => {
        val key: Int = op(1).toInt
        println(if (t.find(key)) "yes" else "no")
        t
      }
      case "delete" => {
        val key: Int = op(1).toInt
        t.delete(key)
      }
      case _ => throw new Error("Unknown operation")
    }
  }

  sealed trait BTree {
    def insert(x: Int): BTree
    def preorder: List[Int]
    def inorder: List[Int]
    def show: Unit = {
      println(" " + this.inorder.mkString(" "))
      println(" " + this.preorder.mkString(" "))
    }
    def find(x: Int): Boolean
    def delete(x: Int): BTree
    def leftmost: Int
  }
  case object Empty extends BTree {
    def insert(x: Int): BTree = Node(x, Empty, Empty)
    def preorder: List[Int] = Nil
    def inorder: List[Int] = Nil
    def find(x: Int): Boolean = false
    def delete(x: Int): BTree = this
    def leftmost: Int = throw new NoSuchElementException("error")
  }
  case class Node(v: Int, l: BTree, r: BTree) extends BTree {
    def insert(x: Int): BTree =
      if (x < v) Node(v, l.insert(x), r)
      else Node(v, l, r.insert(x))
    def preorder: List[Int] = v :: (l.preorder ::: r.preorder)
    def inorder: List[Int]  = l.inorder ::: (v :: r.inorder)
    def find(x: Int): Boolean =
      if (x == v) true
      else if (x < v) l.find(x)
      else r.find(x)
    def delete(x: Int): BTree = {
      if (x == v) {
        this match {
          case Node(_, Empty, Empty) => Empty
          case Node(_, _, Empty) => l
          case Node(_, Empty, _) => r
          case _ => {
            val n: Int = r.leftmost
            Node(n, l, r.delete(n))
          }
        }
      }
      else if (x < v) Node(v, l.delete(x), r)
      else Node(v, l, r.delete(x))
    }
    def leftmost: Int = l match {
      case Empty => v
      case _ => l.leftmost
    }
  }
}