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>
#define MAX 500000

struct node
{
    int key;
    struct node* p;
    struct node *l, *r;
} typedef node;

void Insert(int);
int Find(int);
void Print(node*);
void Inorder(node*);
void Preorder(node*);

node *root = NULL;

int main()
{
    int i;
    int n, key;
    int flag;
    char order[7];

    scanf("%d", &n);
    for(i = 0; i < n; i++)
    {
        scanf("%s", order);
 
        if(strcmp(order, "insert") == 0)
        {
            scanf("%d", &key);
	        Insert(key);
	    }
	    if(strcmp(order, "find") == 0)
	    {
	        scanf("%d", &key);
	        flag = Find(key);
	        if(flag)
	        printf("yes\n");
	        else
	        printf("no\n");
	    }
        if(strcmp(order, "print") == 0)
        {
            Print(root);
        }
    }
    return 0;
}

void Insert(int key)
{
    node *x, *y, *z;

    x = root;
    y = NULL;
    z = (node*)malloc(sizeof(node));
    z->key = key;
	z->l = NULL;
	z->r = NULL;

    while(x != NULL)
    {
        y = x;
        if(z->key < x->key) x = x->l;
        else x = x->r;
    }
    z->p = y;

    if(y == NULL) 
    root = z;
    else if(z->key < y->key)
    y->l = z;
    else 
    y->r = z;
}

int Find(key)
{
    node *x;
    
    x = root;
    
    while(x != NULL)
    {
        if(key == x->key)
        return 1;
        
        if(key < x->key)
        x = x->l;
        else
        x = x->r;
    }
    return 0;
}
    
void Print(node *x)
{
    Inorder(x);
    printf("\n");
    Preorder(x);
    printf("\n");
}
 
void Inorder(node *x)
{
    if(x == NULL) return;

    Inorder(x->l);
    
    printf(" %d", x->key);
    
    Inorder(x->r);
}

void Preorder(node *x)
{
    if(x == NULL) return;
    
    printf(" %d", x->key);

    Preorder(x->l);
    Preorder(x->r);
}