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>

#define NIL NULL

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

typedef struct node * Node;

Node root;

Node treeMinimum(Node x)
{
  while(x->left != NIL)
    {
      x = x->left;
    }
  
  return x;
}

Node treeMaximum(Node x)
{
  while(x->right != NIL)
    {
      x = x->right;
    }
  
  return x;
}

Node treeSearch(Node u, int k)
{
  if(u == NIL || k == u->key) return u;
  if(k < u->key) return treeSearch(u->left,k);
  else return treeSearch(u->right,k);

}

Node treeSuccessor(Node x)
{
  Node y;
  
  if(x->right != NIL)
    {
      return treeMinimum(x->right);
    }
  y = x->parent;

  while(y != NIL && x == y->right)
    {
      x = y;
      y = y->parent;
    }
  
  return y;
}

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;
    }

  return;
}

void inorder(Node u)
{
  if(u == NIL) return;

  inorder(u->left);
  printf(" %d",u->key);
  inorder(u->right);

  return;
}
void preorder(Node u)
{
  if(u == NIL) return;

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

  return;
}


int main()
{
  int n, i, x;
  char com[20];
  scanf("%d", &n);

  for ( i = 0; i < n; i++ )
    {
      scanf("%s", com);
      if ( com[0] == 'f' )
	{
	  scanf("%d", &x);
	  Node t = treeSearch(root, x);
	  if ( t != NIL ) printf("yes\n");
	  else printf("no\n");
	}
      else if ( com[0] == 'i' )
	{
	  scanf("%d", &x);
	  insert(x);
	}
      else if ( com[0] == 'p' )
	{
	  inorder(root);
	  printf("\n");
	  preorder(root);
	  printf("\n");
	}
    }

  return 0;
}