Problem:
Binary Search Tree II

Write a program which performs the following operations to a binary search tree $T$ by adding the find operation to A: Binary Search Tree I.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$ 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

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print

Sample Output 1

yes
no
1 12 17 20 25 30 88
30 12 1 20 17 25 88

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Ruby (judge verdict: Time Limit Exceeded)


class Tree
	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,bool)
		if @key == key
			bool = "yes"
		else
			if @left
				bool = @left.find(key,bool)
			end

			if @right
				bool = @right.find(key,bool)
			end
		end
		bool
	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
		else
			puts head.find(num[1].to_i,"no")
		end

	end

end