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: Time Limit Exceeded)

#include<stdio.h>
#include<stdlib.h>
#define NIL NULL

typedef struct node *Node;
struct node{
  int key;
  Node Right;
  Node Left;
  Node Parent;
};

Node root;
Node Find[500001];
int i,j=0;

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;
}

Node find(Node r,int k){
  while(r != NIL){
    if(k == r->key)
      return r;
    else if(k > r->key)
      r = r->Right;
    else
      r = r->Left;
  }
  return NIL;
}

void inorder(Node r){
  if(r == NIL) return;
  inorder(r->Left);
  printf(" %d",r->key);
  inorder(r->Right);
}

void preorder(Node r){
  if(r == NIL) return;
  printf(" %d",r->key);
  preorder(r->Left);
  preorder(r->Right);
}
void print()
{
  for(i=0; i<j; i++){
    if(Find[i] != NIL)
      printf("yes\n");
    else
      printf("no\n");
  } 
  inorder(root);
  printf("\n");
  preorder(root);
  printf("\n");
}

int main()
{
  int m,k;
  char s[6];
  scanf("%d",&m);

  for(i=0; i<m; i++){
    scanf("%s%d",s,&k);
    if(s[0] == 'i')
      insert(k);
    else if(s[0] == 'f')
      Find[j++] = find(root,k);
    else
      print();
  }
  return 0;
}