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 Rust (judge verdict: Accepted)

// ALDS1_8_B: Binary Search Tree 2

use std::cell::RefCell;
use std::rc::Rc;
use std::str::FromStr;

fn scan<T: FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().parse().ok().unwrap()
}

enum BST {
    Node { key: i64, left: Rc<RefCell<BST>>, right: Rc<RefCell<BST>> },
    Nil
}

impl BST {
    fn new() -> BST {
        BST::Nil
    }
    fn insert(&mut self, k: i64) {
        match *self {
            BST::Nil => {
                *self = BST::Node {
                    key:k,
                    left: Rc::new(RefCell::new(BST::Nil)),
                    right: Rc::new(RefCell::new(BST::Nil)),
                }
            },
            BST::Node { ref mut key, ref mut left, ref mut right } => {
                if k < *key {
                    left.borrow_mut().insert(k);
                } else {
                    right.borrow_mut().insert(k);
                }
            }
        }
    }
    fn find(&self, k: i64) -> bool {
        match *self {
            BST::Nil => { 
                false
            },
            BST::Node { ref key, ref left, ref right} => {
                if k < *key {
                    left.borrow().find(k)
                } else if k > *key {
                    right.borrow().find(k)
                } else {
                    true
                }
            }
        }
    }
    fn preorder(&self) {
        match *self {
            BST::Nil => {},
            BST::Node { ref key, ref left, ref right } => {
                print!(" {}", *key);
                left.borrow().preorder();
                right.borrow().preorder();
            }
        }
    }
    fn inorder(&self) {
        match *self {
            BST::Nil => {},
            BST::Node { ref key, ref left, ref right } => {
                left.borrow().inorder();
                print!(" {}", *key);
                right.borrow().inorder();
            }
        }
    }
}

fn main() {
    let n = scan::<usize>();
    let mut t = BST::new();
    for _ in 0..n {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        let mut it = s.split_whitespace();
        let com = it.next().unwrap();
        if com == "find" {
            let x = it.next().unwrap().parse::<i64>().ok().unwrap();
            if t.find(x) {
                println!("yes");
            } else {
                println!("no");
            }
        } else if com == "insert" {
            let x = it.next().unwrap().parse::<i64>().ok().unwrap();
            t.insert(x);
        } else if com == "print" {
            t.inorder();
            println!();
            t.preorder();
            println!();
        }
    }
}