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;
 
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 x){
  if(x!=NIL){
    inorder(x->left);
    printf(" %d",x->key);
    inorder(x->right);
  }
}
 
void preorder(Node x){
  if(x!=NIL){
    printf(" %d",x->key);
    preorder(x->left);
    preorder(x->right);
  }
   
}

int Find(Node x, int k){
  while( x != NIL && k != x->key){
    if(k < x->key)
      x = x->left;
    else
      x = x->right;
  }
  if(x == NIL)return 0;
  else return 1;
}

 
int main(){
  int n, i, x;
  char com[20];

  scanf("%d", &n);
 
  for ( i = 0; i < n; i++ ){
    scanf("%s", com);
    if ( com[0] == 'i' ){
      scanf("%d", &x);
      insert(x);
    } else if ( com[0] == 'p' ){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    } else if ( com[0] == 'f' ){
      scanf("%d",&x);
      if(Find(root,x)==0)printf("no\n");
      else printf("yes\n");
    }
    
  }

 
  return 0;
}