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: Wrong Answer)

import java.io._
import scala.io.StdIn.{readInt, readLine}

object Main {
  val out:BufferedWriter =
    new BufferedWriter(new OutputStreamWriter(new FileOutputStream(FileDescriptor.out), "ASCII"), 512)
  var count = 0
  def printstr(str:String) = {
    out.write(str)
    if(count<500) count += 1
    else { out.flush; count = 0 }
  }

  class Node(var key:Int, var left:Node = null, var right:Node = null, var parent:Node = null) { }

        def getNodeToInsert(node:Node,keyNode:Node):Node = if(node.key > keyNode.key) {
                        if(node.left == null) node
                        else getNodeToInsert(node.left,keyNode)
                } else {
                        if(node.right == null) node
                        else getNodeToInsert(node.right,keyNode)
                }

  def insert(tree:Node, keyNode:Node) = {
    val target = getNodeToInsert(tree,keyNode)
    if(keyNode.key < target.key) target.left = keyNode
    else target.right = keyNode
    keyNode.parent = target
  }

  def inOrder(tree:Node):Unit =
    if(tree == null || tree.key == -1) return
    else {
      inOrder(tree.left)
      printstr(" ")
      printstr(tree.key.toString)
      inOrder(tree.right)
    }

  def preOrder(tree:Node):Unit =
    if(tree == null || tree.key == -1) return
    else {
      printstr(" ")
      printstr(tree.key.toString)
      preOrder(tree.left)
      preOrder(tree.right)
    }

  def find(tree:Node, key:Int):Node = {
          def loop(node:Node):Node = {
      if(node == null || node.key == -1) {
        null
      } else if(node.key > key) {
        loop(node.left)
      } else if(node.key < key) {
        loop(node.right)
      } else {
        node
      }
    }

    loop(tree)
  }

  def delete(tree:Node, key:Int):Unit = {
    val node = find(tree, key)
    if(node!=null) {
      val parent = node.parent
      if(node.left == null && node.right == null) {
        if(parent == null) { tree.key = -1; tree.right = null; tree.left = null }
        else if(parent.left == node) parent.left = null
        else if(node.parent.right == node) parent.right = null
      } else if(node.left != null && node.right == null) {
        if(parent == null) { tree.key = node.key; tree.right = null; tree.left = node.left;node.left.parent = null }
        else if(parent.left == node) { parent.left = node.left; node.left.parent = parent }
        else if(node.parent.right == node) { parent.right = node.left; node.left.parent = parent }
      } else if(node.right != null && node.left == null) {
        if(parent == null) { tree.key = node.key; tree.left = null; tree.right = node.right; node.right.parent = null }
        else if(parent.left == node) { parent.left = node.right; node.right.parent = parent }
        else if(parent.right == node) { parent.right = node.right; node.right.parent = parent }
      } else {
        node.key = node.left.key
        delete(node.left, node.left.key)
      }
    }
  }

  def main(args:Array[String]) = {
    val n = readInt
    val tree = new Node(-1)

    for(i<-0 until n) {
      val s = readLine.split(" ")
      s(0) match {
        case "insert" =>
          if(tree.key == -1) tree.key = s(1).toInt
          else insert(tree, new Node(s(1).toInt))
        case "find" => {
          val node = find(tree, s(1).toInt)
          if(node!=null) printstr("yes\n") else printstr("no\n")
        }
        case "delete" => {
          delete(tree, s(1).toInt)
        }
        case _ => {
          inOrder(tree)
          printstr("\n")
          preOrder(tree)
          printstr("\n")
        }
      }
    }
    out.flush
    out.close
  }
}