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++14 (judge verdict: Accepted)

#include <iostream>
using namespace std;

struct Node
{
    int key;
    Node *parent;
    Node *left;
    Node *right;
};

Node *root;
Node *nil;

void InsertNode(int key)
{
    Node *x = root;
    Node *y = nil;
    Node *z = (Node *)malloc(sizeof(Node));
    z->key = key;
    z->parent = nil;
    z->left = nil;
    z->right = nil;

    while (x != nil)
    {
        y = x;
        if (z->key < x->key)
        {
            x = x->left;
        }
        else
        {
            x = x->right;
        }
    }
    z->parent = y;

    if (y == nil)
    {
        root = z;
    }
    else if (z->key < y->key)
    {
        y->left = z;
    }
    else
    {
        y->right = z;
    }

    return;
}

void FindNode(int key, Node *x)
{
    if (x == nil)
    {
        cout << "no" << endl;
        return;
    }

    if (key == x->key)
    {
        cout << "yes" << endl;
        return;
    }
    else if (key < x->key)
    {
        FindNode(key, x->left);
    }
    else
    {
        FindNode(key, x->right);
    }

    return;
}

void PrintInOrder(Node *x)
{
    if (x == nil)
    {
        return;
    }

    PrintInOrder(x->left);
    cout << " " << x->key;
    PrintInOrder(x->right);

    return;
}

void PrintPreOrder(Node *x)
{
    if (x == nil)
    {
        return;
    }

    cout << " " << x->key;
    PrintPreOrder(x->left);
    PrintPreOrder(x->right);

    return;
}

int main()
{
    int n;
    cin >> n;

    for (int i = 0; i < n; i++)
    {
        string s;
        cin >> s;

        if (s == "insert")
        {
            int key;
            cin >> key;
            InsertNode(key);
        }
        else if (s == "find")
        {
            int key;
            cin >> key;
            FindNode(key, root);
        }
        else
        {
            PrintInOrder(root);
            cout << endl;
            PrintPreOrder(root);
            cout << endl;
        }
    }

    return 0;
}