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)

CMD=0
VAL=1
 
class Node
  attr_accessor :value,:left,:right
  def initialize (value)
    @value = value
    @left = nil
    @right = nil
  end
 
  def insert (value)
    if value < @value
      if @left.nil?
        @left = Node.new(value)
      else
        @left.insert(value)
      end
    else
      if @right.nil?
        @right = Node.new(value)
      else
        @right.insert(value)
      end
    end
  end
 
  def find(value)
    if value==@value
      print "yes\n"
    elsif value < @value
      if @left.nil?
        print "no\n"
      else
        @left.find(value)
      end
    else
      if @right.nil?
        print "no\n"
      else
        @right.find(value)
      end
    end
  end
 
 # delete node and return new node 
  def delete(value)
    if value == @value
      if @left.nil? and @right.nil?
        # no child
        return nil
      elsif @left.nil?
        # right child only
        return @right
      elsif @right.nil?
        # left child only
        return @left
      else
        # more than 2 child
        # swap value
        @value = @right.get_new_value
        # delete swapped node
        @right = @right.delete(@value)
        return self
      end
    elsif value < @value
      @left = @left.delete(value)
      return self
    else
      @right = @right.delete(value)
      return self
    end
  end
 
 # find minimum key of subtree
  def get_new_value
    unless @left.nil?
      return @left.get_new_value
    else
      return @value
    end
  end
       
  def print_inorder
    @left.print_inorder unless @left.nil?
    print " #{value}"
    @right.print_inorder unless @right.nil?
  end
   
  def print_preorder
    print " #{value}"
    @left.print_preorder unless @left.nil?
    @right.print_preorder unless @right.nil?
  end
end
 
num_of_cmd = STDIN.gets()
inputs = STDIN.read().split("\n").map{ |input| input.split(' ') }
 
root=nil
inputs.each do |input|
  if input[CMD] == 'insert'
    if root.nil?
      root = Node.new(input[VAL].to_i)
    else
      root.insert(input[VAL].to_i)
    end
  elsif input[CMD] == 'find'
    root.find(input[VAL].to_i)
  elsif input[CMD] == 'delete'
    root.delete(input[VAL].to_i)
  else
    root.print_inorder unless root.nil?
    print "\n"
    root.print_preorder unless root.nil?
    print "\n"
  end
end