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>

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

typedef struct node * Node;

Node root;

void Insert(int);
int treeSearch(Node, int);
void Preorder(Node);
void Inorder(Node);

int main(){
  int i, m, k, find;
  char in[20];

  scanf("%d",&m);
  for(i = 0; i < m; i++){
    scanf("%s",in);
    if(in[0] == 'i'){
      scanf("%d",&k);
      Insert(k);
    }
    if(in[0] == 'f'){
      scanf("%d",&k);
      find = treeSearch(root, k);
      if(find == 1) printf("yes\n");
      else printf("no\n");
    }
    if(in[0] == 'p'){
      Inorder(root);
      printf("\n");
      Preorder(root);
      printf("\n");
    }
  }

  return 0;
}

void Insert(int k){
  Node y = NULL;
  Node x = root;
  Node v;

  v = malloc(sizeof(struct node));
  v->key = k;
  v->parent = NULL; 
  v->left = NULL;
  v->right = NULL;

  while(x != NULL){
    y = x;
    if(v->key < x->key) x = x->left;
    else x = x->right;
  }

  v->parent = y;

  if(y == NULL) root = v;
  else if(v->key < y->key) y->left = v;
  else y->right = v;

}

int treeSearch(Node u, int k){
  int f = 0;
  Node x = u;
  
  while(x != NULL){
    if(k < x->key) x = x->left;
    else if(k > x->key) x = u->right;
    else{
      f = 1;
      break;
    }
  }

  return f;
  
}

void Preorder(Node u){
  printf(" %d", u->key);

  if(u->left != NULL) Preorder(u->left);
  
  if(u->right != NULL) Preorder(u->right);

}

void Inorder(Node u){

  if(u->left != NULL) Inorder(u->left);
  printf(" %d",u->key);

  if(u->right != NULL) Inorder(u->right);
}