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: Accepted)

class Node
  def initialize(val)
    @val = val
    @left = nil
    @right = nil
  end
  def insert(val)
    if val < @val
      if @left
        @left.insert(val)
      else
        @left = Node.new(val)
      end
    else
      if @right
        @right.insert(val)
      else
        @right = Node.new(val)
      end
    end
  end
  def print
    puts " #{inorder([]).join(" ")}"
    puts " #{preorder([]).join(" ")}"
  end
  def preorder(list)
    #root
    list << @val
    #left
    list = @left.preorder(list) if @left
    #right
    list = @right.preorder(list) if @right
    return list
  end
  def inorder(list)
    #left
    list = @left.inorder(list) if @left
    #root
    list << @val
    #right
    list = @right.inorder(list) if @right
    return list
  end
  def find(num)
    if @val == num then
      return "yes"
    elsif @val > num
      if @left
        return @left.find(num)
      else
        return "no"
      end
    else
      if @right
        return @right.find(num)
      else
        return "no"
      end
    end
  end
  def del(num)
    if @val == num then
      # delete
      if @left && @right then
        @val = @right.next_val
        @right = @right.del(@val)
        return self
      elsif @left != nil && @right == nil then
        return @left
      elsif @left == nil && @right != nil then
        return @right
      else
        return nil
      end
    elsif @val > num
      @left = @left.del(num) if @left
      return self
    else
      @right = @right.del(num) if @right
      return self
    end
  end
  def next_val
    if @left
      return @left.next_val
    else
      return @val
    end
  end
end

n = gets.to_i
tree = nil

n.times{
  command, num = gets.split
  case command;
  when "insert";
    if tree
      tree.insert(num.to_i)
    else
      tree = Node.new(num.to_i)
    end
  when "find";
    puts tree.find(num.to_i)
  when "delete";
    tree = tree.del(num.to_i)
  when "print";
    tree.print
  end
}