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)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

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


struct node *treeInsert(struct node *T, struct node *z)
{
    struct node *r, *x, *y;
    r = T;
    y = NULL;
    x = r;
    while (x != NULL)
    {
        y = x;
        if (z->key < x->key)
        {
            x = x->left;
        }
        else
        {
            x = x->right;
        }
    }
    z->parent = y;
    if (y == NULL)
    {
        r = z;
    }
    else
    {
        if (z->key < y->key)
        {
            y->left = z;
        }
        else
        {
            y->right = z;
        }
    }
    return r;
}

void inorder_tree_work(struct node *T)
{
    if (T != NULL)
    {
        inorder_tree_work(T->left);
        printf(" %d", T->key);
        inorder_tree_work(T->right);
    }
}

void preorder_tree_work(struct node *T)
{
    if (T != NULL)
    {
        printf(" %d", T->key);
        preorder_tree_work(T->left);
        preorder_tree_work(T->right);
    }
}

struct node *treeSearch(struct node *T, int a)
{
    struct node *x = T;

    while (x != NULL && x->key != a)
    {
        if (a < x->key)
        {
            x = x->left;
        }
        else
        {
            x = x->right;
        }
    }
    return x;
}

int main(void)
{
    struct node *Tree = NULL;
    struct node *y, *z;
    int n;
    int key;
    char command[10];

    scanf("%d", &n);
    for (int i = 0; i < n; i++)
    {
        scanf("%s", command);
        if (command[0] == 'i')
        {
            scanf("%d", &key);
            z = (struct node *)malloc(sizeof(struct node));
            z->key = key;
            z->left = NULL;
            z->right = NULL;
            Tree = treeInsert(Tree, z);
        }
        else if (command[0] == 'p')
        {
            inorder_tree_work(Tree);
            printf("\n");
            preorder_tree_work(Tree);
            printf("\n");
        }
        else if (command[0] == 'f')
        {
            scanf("%d", &key);
            z = (struct node *)malloc(sizeof(struct node));
            z->key = key;
            z->left = NULL;
            z->right = NULL;
            y = treeSearch(Tree, z->key);
            if (y != NULL)
            {
                printf("yes\n");
            }
            else
            {
                printf("no\n");
            }
        }
    }
    return 0;
}