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
	attr_reader :key
	attr_accessor :left, :right
	def initialize key
		@key = key
		@left = nil
		@right = nil
	end

	def insert k
		if @key > k
			if !@left
				@left = Tree.new k
			else
				@left.insert(k)
			end

		else
			if !@right
				@right = Tree.new k
			else
				@right.insert k
			end
		end
	end

	def inorder list
		if @left
			list = @left.inorder list
		end
		list << @key
		if @right
			list = @right.inorder list
		end
		list
	end

	def preorder list
		list << @key
		if @left
			list = @left.preorder list
		end
		if @right
			list = @right.preorder list
		end
		list
	end

	def find key
		if @key == key
			key
		else
			bool = nil
			if @left && @key > key
				bool = @left.find key
			end

			if @right && @key < key
				bool = @right.find key
			end
			bool
		end
	end

	def delete k
		parent = traverse(k)
		child = parent.left.key == k ? parent.left : parent.right if parent

		if child
			if child.left && child.right 
				if parent.left.key == k
					parent.left = child.left
				else
					parent.right = child.left
				end
				child.left.right = child.right

			elsif child.left
				if parent.left.key == k
					parent.left = child.left
				else
					parent.right = child.left
				end

			elsif child.right
				if parent.left.key == k
					parent.left = child.right
				else
					parent.right = child.right
				end

			else
				if parent.left.key == k
					parent.left = nil
				else
					parent.right = nil
				end
			end
		end
	end

	def traverse k
		if (@left && @left.key == k) || (@right && @right.key == k)
			self
		else
			tree = nil
			tree = @left.traverse k if @left
			tree = @right.traverse k if @right
			tree
		end
	end
end
n = gets.to_i
head = nil

n.times do
	num = gets.to_s.chomp!
	if num == "print"
		puts " #{head.inorder([]).join(" ")}"
		puts " #{head.preorder([]).join(" ")}"
	else
		num = num.split
		if num[0].to_s == "insert"
			if head
				head.insert(num[1].to_i)
			else
				head = Tree.new(num[1].to_i)
			end
		elsif num[0].to_s == "delete"
			head.delete num[1].to_i 
		else
			puts head.find(num[1].to_i) ?  "yes" : "no"
		end

	end

end