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>
#define NIL NULL
  
struct node 
{
  
  int key;
  struct node *left;
  struct node *right;
  struct node *parent;
};
  
typedef struct node* Node;
Node root;
  
Node treeSearch(Node x,int k) 
{
  if(x == NIL || k == x-> key)
    return x;
  if(k < x->key)
    return treeSearch(x->left,k);
  else return treeSearch(x->right,k );
}
  
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;
     
 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;
 
}

void inorder(Node u) 
{
  
  if(u->left != NIL)
    inorder(u->left);
  printf(" %d",u->key);
  if(u->right != NIL)
    inorder(u->right);
}
  
void preorder(Node u) 
{
  printf(" %d",u->key);
  if(u->left != NIL)
    preorder(u->left);
  if(u->right != NIL)
    preorder(u->right);
}
  
int main(void) 
{
    
  int i,n,x;
  char c[5];
    
  scanf("%d",&n);
    
  for(i=0;i<n;i++) 
    {
      scanf("%s",c);
      if(c[0] == 'f') 
	{
	  scanf("%d",&x);
	  if(treeSearch(root,x) != NIL)
	    printf("yes\n");
	  else printf("no\n");
	}
      else if(c[0] == 'i') 
	{
	  scanf("%d",&x);
	  insert(x);
	}
      else if(c[0] == 'p') 
	{
	  if(root != NIL) 
	    inorder(root);
	  printf("\n");
	  if(root != NIL)
	    preorder(root);
	  printf("\n");
	  
	}
    }
  return 0;
}