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

typedef struct node * Node;
Node root;
Node find(Node u, int k);
void insert(int k);
void inorderTreeWalk(Node x);
void preorderTreeWalk(Node x);
  
int main()
{
  char str[7];
  int m,i,x,key;
  scanf("%d",&m);
  for( i=0 ; i<m ; i++ ){
    scanf("%s",str);
    if(str[0]=='i'){
      scanf("%d",&x);
      insert(x);
    }
    else if(str[0]=='p'){
      inorderTreeWalk(root);
      printf("\n");
      preorderTreeWalk(root);
      printf("\n");
    }
    else{
      scanf("%d",&key);
      if( find(root,key)==NIL ){
	printf("no\n");
      }else{
	printf("yes\n");
      }   
    }
  }
  return 0;
   
}
Node find(Node u, int k){
      if( u == NIL || k == u->key ){
          return u;
      }  
      if( k < u->key ){
        return find(u->l,k);
      }else{
        return find(u->r,k);
      }
}

void insert(int k)
{
  Node x;
  Node y;
  Node z;
  y = NIL;
  x = root;
  z = (Node)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) root = z;
  else if(z->key<y->key) y->l = z;
  else y->r = z;
}
 
void inorderTreeWalk(Node x)
{
  if(x==NIL) return;
  inorderTreeWalk(x->l);
  printf(" %d",x->key);
  inorderTreeWalk(x->r);
}
 
void preorderTreeWalk(Node x)
{
  if(x==NIL) return;
    printf(" %d",x->key);
    preorderTreeWalk(x->l);
    preorderTreeWalk(x->r);
   
}