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 Ruby (judge verdict: Wrong Answer)

#AOJ ALDS1_8_C
#binary_search_tree 3

class FindMixin
  def find(n)
    # printf("find %d:[%d][%d]\n",n,self.key,(n == self.key)?1:0)
    if n == self.key
      return self
    end
    ret = nil
    if self.left != nil && self.key > n 
      return self.left.find(n)
    end
    if self.right != nil && self.key < n 
      return self.right.find(n)
    end
  end
end

module DeleteMixin
  def delete(node)
    if node.left == nil && node.right == nil
      par = node.parent
      if par == nil
        self.root = nil
      elsif par.left == node
        par.left = nil
      else
        par.right = nil
      end
    elsif node.left == nil && node.right != nil
      par = node.parent
      if par == nil
        self.root = node.right
        node.parent = nil
      elsif par.left == node
        par.left = node.right
        node.right.parent = par
      else
        par.right= node.right
        node.right.parent = par
      end
    elsif node.left != nil && node.right == nil
      par = node.parent
      if par == nil
        self.root = node.left
        node.parent = nil
      elsif par.left == node
        par.left = node.left
        node.left.parent = par
      else
        par.right= node.leftt
        node.leftt.parent = par
      end
    else
      x = node.left
      while x.right != nil
        x = x.right
      end
      node.key = x.key
      x.parent.right = nil
    end
  end
end

class Node < FindMixin

  attr_accessor :key,:parent,:left,:right

  def initialize(n)
    @key    = n
    @parent = nil
    @left   = nil
    @right  = nil
  end

  def add_left(child)
      self.left    = child
      child.parent = self
  end

  def add_right(child)
      self.right    = child
      child.parent = self
  end

  def preorder
    printf(" %d",self.key)
    if(left != nil)
      left.preorder
    end
    if(right!= nil)
      right.preorder
    end
  end

  def inorder
    if(left != nil)
      left.inorder
    end
    printf(" %d",self.key)
    if(right!= nil)
      right.inorder
    end
  end

  def postorder
    if(left != nil)
      left.postorder
    end
    if(right!= nil)
      right.postorder
    end
    printf(" %d",self.key)
  end

end

class Bin_search_tree
  include DeleteMixin
  attr_accessor :root

  def initialize
    @root = nil
  end

  def inorder
    self.root.inorder
  end

  def preorder
    self.root.preorder
  end

  def insert(node)
    y = nil
    x = self.root
    while x != nil
      y = x
      if node.key < x.key
        x = x.left
      else
        x = x.right
      end
    end
    
    node.parent = y

    if y == nil
      self.root = node
    elsif node.key < y.key
      y.left = node
    else
      y.right= node
    end
  end

  def find(n)
    self.root.find(n)
  end
end

$n = STDIN.gets.split[0].to_i
$b_s_tree = Bin_search_tree.new

0.upto($n-1){|i|
  s = STDIN.gets.split
  if s[0].to_s == "insert"
    node = Node.new(s[1].to_i)
    $b_s_tree.insert(node)
  elsif s[0].to_s == "print"
    $b_s_tree.inorder
    printf("\n")
    $b_s_tree.preorder
    printf("\n")
  elsif s[0].to_s == "find"
    ky = s[1].to_i
    if nil != $b_s_tree.find(ky)
      puts "yes"
    else
      puts "no"
    end
  elsif s[0].to_s == "delete"
    ky = s[1].to_i
    node = $b_s_tree.find(ky)
    if node != nil
      $b_s_tree.delete(node)
    end
  end
}