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 <unistd.h>
#include <stdlib.h>
typedef struct node{
  struct node *r;
  struct node *l;
  struct node *parent;
  int key;
}node;
typedef struct node * Node;

int pre(Node);

int sch(int,Node);
int mid(Node);

Node nose(int);

int in(Node,int);

void freedom(Node);

int main(){
  int j,n,i,ndnm;
  char b[7];
  Node first,now;
  scanf("%d",&n);
  scanf("%s %d",b,&ndnm);
  first = nose(ndnm);
  for(i=0;i<n-1;i++){
    scanf("%s",b);
    if(b[0]=='i'){
      scanf("%d",&ndnm);
      in(first,ndnm);
    }else if(b[0]=='p'){
      mid(first);
      printf("\n");
      pre(first);
      printf("\n");
    }else{
      scanf("%d",&ndnm);
      if(sch(ndnm,first)==1){
	printf("yes\n");
      }else{
	printf("no\n");

      }
    }
  }
freedom(first);

}
int in(Node now,int ndnm){
  while(1){
//printf("now =%d ",now->key);
    if(ndnm >= now->key){
      if(now->r != NULL)
	now = now->r;
      else{
	now->r=nose(ndnm);
	break;
      }
    }else{
      if(now->l != NULL)
	now = now->l;
      else{
	now->l=nose(ndnm);
	break;
      }
    }
  }
return 0;
}
Node nose(int key){

Node set;
set =(Node)malloc(sizeof(node));
  set->key=key;
  set->r=NULL;
  set->l=NULL;
  return set;
}

int mid(Node a){
  if(a->l != NULL)
    mid(a->l);
  printf(" ");
  printf("%d",a->key);
  if(a->r !=NULL)
    mid(a->r);
  return 0;
}

int sch(int key,Node a){
  if(key == a->key)
    return 1;
  if(key<a->key){
    if(a->l != NULL)
      return sch(key,a->l);
    else
      return 0;
  }else{
    if(a->r !=NULL)
      return sch(key,a->r);
    else
      return 0;
  }
  return 0;
}

int pre(Node a){
  printf(" ");
  printf("%d",a->key);
  if(a->l != NULL)
    pre(a->l);
  if(a->r !=NULL)
    pre(a->r);
  return 0;
}

void freedom(Node a){
  if(a->l != NULL)
    freedom(a->l);
  if(a->r !=NULL)
    freedom(a->r);
free(a);
}