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{
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;
 
Node root;
Node find(Node root,int key){
  if(root==NIL||root->key==key)
    return root;
  if(root->key > key)
    return find(root->left,key);
  else
    return find(root->right,key);
}
void insert(int key){
   Node y = NIL;
   Node x = root;
   Node z;
    
   z =malloc(sizeof(struct node));
   z->key = key;
   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 root){
  if(root->left!=NIL)
    inorder(root->left);
  printf(" %d",root->key);
  if(root->right!=NIL)
    inorder(root->right);
}
 
void preorder(Node root){
  if(root!=NIL)
    printf(" %d",root->key);
  if(root->left!=NIL)
    preorder(root->left);
  if(root->right!=NIL)
    preorder(root->right);
}
 
int main(){
  int n, i, x;
  char com[10];
  scanf("%d", &n);
  for ( i = 0; i < n; i++ ){
    scanf("%s", com);
    if ( com[0] == 'f' ){
      scanf("%d", &x);
     Node t = find(root, x);
      if ( t != NIL ) printf("yes\n");
      else printf("no\n");
    }
    if ( com[0] == 'i' ){
      scanf("%d", &x);
      insert(x);
    } else if ( com[0] == 'p' ){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
  }
  return 0;
}