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 *pa,*le,*ri;
};

struct Node *ro,*NIL;

void insert(int);
void pre(struct Node *);
void ino(struct Node *);
struct Node * find(struct Node *,int);

int main(){
  int num,buf;
  int i;
  char word[10];
  struct Node * buff;
  scanf("%d",&num);
  
  for(i=0;i<num;i++){
    scanf("%s",word);
    scanf("%d",&buf);
    if(word[0]=='i'){
      insert(buf);
    }else if(word[0]=='p'){
      ino(ro);
      printf("\n");
      pre(ro);
      printf("\n");
    }else if(word[0]=='f'){
      if((buff=find(ro,buf))!=NIL) printf("yes\n");
      else printf("no\n");
    }
  }
  return 0;
}

void insert(int buf){
  struct Node *x,*y,*z;
  y=NIL;
  x=ro;

  z=(struct Node *)malloc(sizeof(struct Node));
  z->key=buf;
  z->le=NIL;
  z->ri=NIL;
  
  while(x!=NIL){
    y=x;
    if(z->key < x->key) x=x->le;
    else x=x->ri;
  }
  z->pa=y;
  if(y==NIL) ro=z;
  else if(z->key < y->key)y->le=z;
  else y->ri=z;
}

void pre(struct Node *ro){
  if(ro==NIL) return;
  printf(" %d",ro->key);
  pre(ro->le);
  pre(ro->ri);
}

void ino(struct Node *ro){
  if(ro==NIL) return;
  ino(ro->le);
  printf(" %d",ro->key);
  ino(ro->ri);
}

struct Node * find(struct Node *x,int buf){
  while(x!=NIL&&buf!=x->key){
    if(buf < x->key) x=x->le;
    else x=x->ri;
  }
  return x;
}