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>
#include <string.h>

struct Point{
  int next;
  struct Point *P,*L,*R;
};

struct Point *squrt,*setsu;
void inorder(struct Point *st);
void preorder (struct Point *st);
void insert (int a);
struct Point *find (struct Point *st,int b);
int main()
{
  int i,n,p;
  char hi[10];

  scanf("%d",&n);

  for(i=0;i<n;i++){
    scanf("%s",hi);
    if( hi[0] == 'f'){
     scanf("%d",&p);
     struct Point *q =find(squrt,p);
     if(q!=setsu)
       printf("yes\n");
     else printf("no\n");
    }
    else  if(hi[0]=='i'){        //*insert*//
      scanf("%d",&p);
      insert(p);
    }else if(hi[0]=='p'){   //*print*//
      inorder(squrt);
      printf("\n");
      preorder(squrt);
      printf("\n");
    }
  }
  return 0;
}

void inorder(struct Point *st){
  if(st==setsu)
    return;
  inorder(st->L);
  printf(" %d",st->next);
  inorder(st->R);
  
}

void preorder(struct Point *st){
  if(st==setsu)
    return;
  printf(" %d",st->next);
  preorder(st->L);
  preorder(st->R);

}

void insert (int a){
  struct Point *x=squrt;
  struct Point *y=setsu;
  struct Point *z;

  z=(struct Point *)malloc(sizeof(struct Point));
  z->next=a;
  z->L=setsu;
  z->R=setsu;

  while(x!=setsu){
    y=x;
    if(x->next > z->next){
      x=x->L;
    }else
      x=x->R;
    
  }

  z->P=y;
  if(y==setsu){
    squrt=z;
  }else{
    if(y->next > z->next){
      y->L=z;
    }else
      y->R=z;
    
  }
}
    
    
struct Point *find (struct Point *st,int b){
  while(st !=setsu && b !=st->next){
    if(b < st->next)
      st=st->L;
    else st=st->R;
  }
  return st;
}