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;

Node root = NULL;

void insert(int k)
{
  Node x = root;
  Node y = NULL;
  Node z;

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

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

  z->parent = y;

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

  return;
}

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

void preorder(Node x)
{
  if(x == NULL)return;

  printf(" %d", x->key);
  preorder(x->left);
  preorder(x->right);

  return;
}

Node treeSearch(Node x, int k)
{
  if(x == NULL || x->key == k)return x;
  // else if(x == NULL)return NULL;

  if(k < x->key)return treeSearch(x->left, k);
  else return treeSearch(x->right, k);
}

int main()
{
  int i;
  int m, k;
  char com[10];
  Node p;

  scanf("%d", &m);

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