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{
  int key;
  struct node *p;
  struct node *l;
  struct node *r;
};

typedef struct node *NodePointer;

NodePointer r,NIL;

NodePointer find(NodePointer x,int k)
{
  while(x != NIL && k != x->key)
    {
      if(k < x->key)
	{
      
	  x = x->l;
	}
      else
	{
	  x = x->r;
	}
    }
  return x;
}

void insert(int k)
{
  NodePointer y = NIL;
  NodePointer x = r;

  NodePointer z = (NodePointer)malloc(sizeof(struct node));
  z->key = k;
  z->l = NIL;
  z->r = NIL;

  while(x != NIL)
    {
      y = x;
      if(z->key < x->key)
	{
	  x = x->l;
	}
      else
	{
	  x = x->r;
	}
    }
  z->p = y;

  if(y == NIL)
    {
      r = z;
    }else if(z->key < y->key)
    {
      y->l = z;
    }
  else
    {
      y->r = z;
    }
}

void inorder(NodePointer u)
{
  if(u == NIL)
    {
      return;
    }
  inorder(u->l);
  printf(" %d",u->key);
  inorder(u->r);
}

void preorder(NodePointer u)
{
  if(u == NIL)
    {
      return;
    }
  printf(" %d",u->key);
  preorder(u->l);
  preorder(u->r);
}

void print()
{
  inorder(r);
  puts("");
  preorder(r);
  puts("");
}

int main()
{
  int n,i,j,z,x;
  char s[10];

  scanf("%d",&n);
  for(i=0;i<n;i++)
    {
      scanf("%s",s);
      if(s[0] == 'f')
	{
	  scanf("%d",&x);
	  NodePointer t = find(r,x);
	  if(t == NIL)printf("no\n");
	  else printf("yes\n");

	}
      else if(s[0] == 'i')
	{
      
	  scanf("%d",&z);
	  insert(z);
	}
      else
	{
	  print();
	}
    }

  return 0;
}