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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Text;

namespace ALDS1_8_B
{
    class Program
    {
        const int NIL = -1;
        const int ROOT = 0;
        static StringBuilder sbi;
        static StringBuilder sbp;
        class node
        {
            public int key; public int left; public int right;
            public node(int key)
            {
                this.key = key; left = NIL; right = NIL;
            }
        }
        static void Main(string[] args)
        {
            int m = int.Parse(Console.ReadLine());
            var T = new List<node>();
            int listnum = 0;
            for (int i = 0; i < m; i++)
            {
                var a = Console.ReadLine().Split(' ');
                if (a[0] == "insert")
                {
                    insert(T, int.Parse(a[1]), listnum++);
                }
                else if(a[0]=="print")
                {
                    sbi = new StringBuilder();
                    sbp = new StringBuilder();
                    inorder(T, 0);
                    Console.WriteLine(sbi);
                    preorder(T, 0);
                    Console.WriteLine(sbp);
                }
                else if (a[0]=="find")
                {
                    find(T, int.Parse(a[1]));
                }
            }

        }
        static void find(List<node> T,int k)
        {
            int x = ROOT;
            while(x!=NIL)
            {
                if (k < T[x].key) x = T[x].left;
                else if (k > T[x].key) x = T[x].right;
                else
                {
                    Console.WriteLine("yes");
                    return;
                }
            }
            Console.WriteLine("no");
        }    
        static void insert(List<node> T, int z, int listnum)
        {
            int y = NIL;
            T.Add(new node(z));
            if (listnum == 0) return;
            int x = ROOT;
            while (x != NIL)
            {
                y = x;
                if (z < T[x].key) x = T[x].left;
                else x = T[x].right;
            }
            if (z < T[y].key) T[y].left = listnum;
            else T[y].right = listnum;

        }

        static void preorder(List<node> T, int i)
        {
            sbp.Append(" " + T[i].key);
            if (T[i].left != NIL) preorder(T, T[i].left);
            if (T[i].right != NIL) preorder(T, T[i].right);
        }
        static void inorder(List<node> T, int i)
        {
            if (T[i].left != NIL) inorder(T, T[i].left);
            sbi.Append(" " + T[i].key);
            if (T[i].right != NIL) inorder(T, T[i].right);
        }
    }
}