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 JAVA (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int m = scanner.nextInt();
        Node root = null;
        for (int i = 0; i < m; i++) {
            String cmd = scanner.next();
            if ("insert".equals(cmd)) {
                Node node = new Node(scanner.nextInt());
                if (root == null) {
                    root = node;
                    continue;
                }
                insert(root, node);
            } else if ("find".equals(cmd)) {
                System.out.println(doesContain(root, scanner.nextInt())? "yes" : "no");
            } else {
                StringBuilder sb = new StringBuilder();
                root.inOrder(sb);
                sb.append("\n");
                System.out.print(sb.toString());
                sb = new StringBuilder();
                root.preOrder(sb);
                sb.append("\n");
                System.out.print(sb.toString());
            }
        }

    }

    private static boolean doesContain(Node node, int k) {
        while (node != null && node.key != k) {
            if (k < node.key) {
                node = node.left;
            } else {
                node = node.right;
            }
        }
        return node != null;
    }

    private static void insert(Node root, Node node) {
        Node parent = root;
        while (true) {
            if (node.key < parent.key) {
                if (parent.left == null) {
                    parent.left = node;
                    break;
                }
                parent = parent.left;
            } else {
                if (parent.right == null) {
                    parent.right = node;
                    break;
                }
                parent = parent.right;
            }
        }
    }

    private static class Node {
        int key;
        Node parent;
        Node left;
        Node right;

        private Node(int key) {
            this.key = key;
        }

        private void inOrder(StringBuilder sb) {
            if (left != null) {
                left.inOrder(sb);
            }
            sb.append(" " + String.valueOf(key));
            if (right != null) {
                right.inOrder(sb);
            }
        }

        private void preOrder(StringBuilder sb) {
            sb.append(" " + String.valueOf(key));
            if (left != null) {
                left.preOrder(sb);
            }
            if (right != null) {
                right.preOrder(sb);
            }
        }
    }
}