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)

class Tree
  class Node
    attr_accessor :value, :parent, :left, :right

    def initialize(value, parent=nil)
      @value = value
      @parent = parent
      @left = nil
      @right = nil
    end

    def ==(other)
      @value == other.value
    end

    def insert(value)
      if value < @value
        if @left
          @left.insert(value)
        else
          @left = Node.new(value, self)
        end
      else
        if @right
          @right.insert(value)
        else
          @right = Node.new(value, self)
        end
      end
    end

    def find(value)
      return self if value == @value

      if value < @value
        return @left && @left.find(value)
      else
        return @right && @right.find(value)
      end
    end

    def visit_inorder(&block)
      @left.visit_inorder(&block) if @left
      block.call(self) if block
      @right.visit_inorder(&block) if @right
    end

    def visit_preorder(&block)
      block.call(self) if block
      @left.visit_preorder(&block) if @left
      @right.visit_preorder(&block) if @right
    end
  end

  def initialize
    @root = nil
  end

  def insert(value)
    if @root
      @root.insert(value)
    else
      @root = Node.new(value)
    end
  end

  def include?(value)
    return false unless @root

    !!@root.find(value)
  end

  def delete(value)
    return false unless @root

    target = @root.find(value)
    return false unless target

    if target.left && target.right
      min_node = target.right
      while min_node.left
        min_node = min_node.left
      end

      parent = min_node.parent
      child = min_node.right
      parent.left = child
      child.parent = parent if child
      min_node.parent = min_node.right = nil

      target.value = min_node.value
    else
      parent = target.parent
      child = target.left || target.right

      if parent
        child.parent = parent if child

        if parent.left == target
          parent.left = child
        else
          parent.right = child
        end
      else
        @root = child
      end

      target.parent = target.left = target.right = nil
    end

    true
  end

  def visit_inorder(&block)
    @root.visit_inorder(&block) if @root
  end

  def visit_preorder(&block)
    @root.visit_preorder(&block) if @root
  end
end

if $PROGRAM_NAME == __FILE__
  n = gets.to_i

  tree = Tree.new

  n.times do
    command, value = gets.chomp.split

    value = value.to_i if value

    case command
    when 'insert'
      tree.insert(value)
    when 'find'
      puts tree.include?(value) ? 'yes' : 'no'
    when 'delete'
      tree.delete(value)
    when 'print'
      tree.visit_inorder do |node|
        print " #{node.value}"
      end
      puts

      tree.visit_preorder do |node|
        print " #{node.value}"
      end
      puts
    else
      raise "unknown command: #{command}"
    end
  end
end