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>
 
typedef struct node{
  int key;
  struct node *p;
  struct node *l;
  struct node *r;
} Node;
 
typedef Node *NodePointer;
NodePointer root = NULL;
 
NodePointer createNode(){
  NodePointer z = malloc(sizeof(Node));
  z->l = NULL;
  z->r = NULL;
  z->p = NULL;
  z->key = 0;
  return z;
}
 
void insert(int key){
   
  NodePointer z = createNode();
  NodePointer y = NULL;
  NodePointer x = root;
  z->key = key;
   
  while(x != NULL){
    y = x;
    if(z->key < x->key) x = x->l;
    else x = x->r;
  }
  z->p = y;
  if(y == NULL) root = z;
  else if(z->key < y->key) y->l = z;
  else y->r = z;
}
   
void inorder(NodePointer p){
     
  if(p != NULL){
    inorder(p->l);
    printf(" %d",p->key);
    inorder(p->r);
  }
}
 
void preorder(NodePointer p){
  if(p != NULL){
    printf(" %d",p->key);
    preorder(p->l);
    preorder(p->r);
  }
}

int find(NodePointer p, int key){

  if(p == NULL) return 0;
  else if(p->key == key) return 1;

  if(key < p->key)  return find(p->l,key);
  else  return find(p->r,key);

}
 
int main(void){
 
  int i,key,n,x;
  char str[20];
 
  scanf("%d",&n);
 
  for(i=0;i<n;i++){
    scanf("%s",str);
 
    if(str[0] == 'i'){
      scanf("%d",&key);
      insert(key);
    }
    else if(str[0] == 'p'){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    else{
      scanf("%d",&key);
	x = find(root,key);
	if(x == 1) printf("yes\n");
	else printf("no\n");
    }
  }
  return 0;
}