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 Node {
  int k;
  struct Node *r,*l,*p;
};
typedef struct Node* node;
node root;
node NIL;

void insert(int);
void inorder(node);
void preorder(node);
node find(node,int);

int main(){
  int n,i,x;
  char com[20];
  scanf("%d",&n);
  root = NIL;
  
  for(i=0;i<n;i++){
    scanf("%s",com);
    if(com[0]=='i'){
      scanf("%d",&x);
      insert(x);
    }
    else if(com[0]=='p'){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    if(com[0]=='f'){
      scanf("%d",&x);
      node t=find(root,x);
      if(t!=NIL)printf("yes\n");
      else printf("no\n");
    }
  }
  return 0;
}
void insert(int k){
  node y=NIL;//xの親
  node x=root;
  node z;
  
  z=(node)malloc(sizeof(struct Node));

  z->k = k;
  z->l = NIL;
  z->r = NIL;
 
  while(x != NIL){
    y=x;//親を設定
    if( z->k < x->k )
      x = x->l;//左の子へ
    else x = x->r;//右の子へ
  }
  z->p = y;
  
  if(y==NIL)
    root = z;
  else {
    if( z->k < y->k ){
      y->l = z;
    }
    else
      y->r = z;
  }
}
void inorder(node u){
  if(u==NIL)return;
  inorder(u->l);
  printf(" %d",u->k);
  inorder(u->r);
}
void preorder(node u){
  if(u==NIL)return;
  printf(" %d",u->k);
  preorder(u->l);
  preorder(u->r);
}
node find(node u,int k){
  while(u!=NIL && k!=u->k){
    if( k < u->k ) u=u->l;
    else u=u->r;
  }
  return u;
}