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>

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

typedef struct node * Node;

#define NIL NULL


Node root;
 
Node treeMinimum (Node x ){
 
}
 
Node treeSearch (Node u, int k ){
    if (u == NIL || u->key == k ) return u;
    else
    if (u->key < k ){
        return treeSearch (u->right, k );
    }else{
        return treeSearch (u->left, k );
    } // end if 
}
 
Node treeSuccessor (Node x ){
 
}
 
void treeDelete (Node z ){
    Node y; // node to be deleted
    Node x; // child of y
}
 
void insert (int k ){
    Node y = NIL;
    Node x = root;
    Node z;
 
    z = malloc (sizeof (struct node ) );
    z->key = k;
    z->left = NIL;
    z->right = NIL;
 
    if (x == NIL ){
        root = z;
    }else{
        do{
            if (x->key < k ){
                y = x->right;
            }else{
                y = x->left;
            } // end if
 
            if (y != NIL ){
                y->parent = x;
            }else{
                if (x->key < k )
                    x->right = z;
                else
                    x->left = z;
            } // end if
            x = y;
        }while (x != NIL ); // end while
    } // end if
}
 
void inorder (Node u ){
    if (u == NIL ) return;
    inorder (u->left );
    printf (" %d", u->key );
    inorder (u->right );
}
 
void preorder (Node u ){
    if (u == NIL ) return;
    printf (" %d", u->key );
    preorder (u->left );
    preorder (u->right );
}
 
int main()
{
    int n, i, x;
    char com[20];
 
    root = NIL;
    scanf ("%d", &n );
    for (i = 0; i < n; i++ ){
        scanf ("%s", com );
        if (com[0] == 'i' ){    // case insert 
            scanf ("%d", &x );
            insert (x );
        }else
        if (com[0] == 'p' ){ // case print
            inorder (root );
            printf ("\n" );
            preorder (root );
            printf ("\n" );
        }else
        if (com[0] == 'f' ){    // case find
            scanf ("%d", &x );
            Node t = treeSearch (root, x );
            if ( t != NIL ) printf ("yes\n" );
            else printf ("no\n" );
        } // end if
    } // end for
 
    return 0;
}