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)

use std::boxed::Box;
use std::io::Read;
use std::string::String;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    print!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();

    let mut tree: BinarySearchTree = BinarySearchTree::new();

    let mut result = String::new();
    for _ in 0..n {
        let command = iterator.next().unwrap();
        if command == "insert" {
            let k: i64 = iterator.next().unwrap().parse().unwrap();
            tree.insert(k);
        } else if command == "find" {
            let k: i64 = iterator.next().unwrap().parse().unwrap();
            if tree.find(k) {
                result.push_str("yes\n");
            } else {
                result.push_str("no\n");
            }
        } else {
            tree.print_in_order(&mut result);
            result.push('\n');
            tree.print_pre_order(&mut result);
            result.push('\n');
        }
    }

    return result;
}

enum BinarySearchTree {
    Node {
        value: i64,
        left: Box<BinarySearchTree>,
        right: Box<BinarySearchTree>,
    },
    Nil,
}

impl BinarySearchTree {
    fn new() -> Self {
        BinarySearchTree::Nil
    }

    fn insert(&mut self, new_value: i64) {
        match *self {
            BinarySearchTree::Nil => {
                *self = BinarySearchTree::Node {
                    value: new_value,
                    left: Box::new(BinarySearchTree::Nil),
                    right: Box::new(BinarySearchTree::Nil),
                }
            },
            BinarySearchTree::Node {
                ref mut value,
                ref mut left,
                ref mut right
            } => {
                if new_value < *value {
                    left.insert(new_value)
                } else {
                    right.insert(new_value)
                }
            },
        }
    }

    fn find(&self, search_value: i64) -> bool {
        match *self {
            BinarySearchTree::Nil => {
                false
            },
            BinarySearchTree::Node {
                ref value,
                ref left,
                ref right
            } => {
                if search_value == *value {
                    true
                } else if search_value < *value {
                    left.find(search_value)
                } else {
                    right.find(search_value)
                }
            }
        }
    }

    fn print_in_order(&self, buf: &mut String) {
        match *self {
            BinarySearchTree::Nil => {},
            BinarySearchTree::Node {
                ref value,
                ref left,
                ref right
            } => {
                left.print_in_order(buf);
                buf.push_str(&format!(" {}", value));
                right.print_in_order(buf);
            }
        }
    }

    fn print_pre_order(&self, buf: &mut String) {
        match *self {
            BinarySearchTree::Nil => {},
            BinarySearchTree::Node {
                ref value,
                ref left,
                ref right
            } => {
                buf.push_str(&format!(" {}", value));
                left.print_pre_order(buf);
                right.print_pre_order(buf);
            }
        }
    }
}