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>
#define true 1
#define false 0
struct node{
  int key;
  struct node *prev;
  struct node *left;
  struct node *right;
};
typedef struct node *NodePointer;
void insert(NodePointer);
NodePointer makenode(int);
void InorderPrint(NodePointer);
void PreorderPrint(NodePointer);
int Search(NodePointer, int);
NodePointer Node; 
int m;
NodePointer root = NULL;

int main()
{
  int i, key;
  char order[7];
  NodePointer NewNode;
  
  scanf("%d",&m);

  for(i = 0 ; i < m ; i++){
    scanf("%s",order);
    
    if(strcmp(order,"insert") == 0){
      scanf("%d",&key);
      NewNode = makenode(key);
      insert(NewNode); }
    if(strcmp(order,"print") == 0){
      InorderPrint(root);
      printf("\n");
      PreorderPrint(root);
      printf("\n"); }
    if(strcmp(order,"find") == 0){
      scanf("%d",&key);
      if(Search(root,key) == true) printf("yes\n");
      if(Search(root,key) == false) printf("no\n"); }
  }
  
  return 0;
}

void insert(NodePointer z)
{
  NodePointer y, x;
    
  y = NULL; /* xの親 */
  x = root;

  while(x != NULL){   
    y = x; /* 親を設定 */
    if(z->key < x->key) x = x->left;
    else x = x->right; }

  z->prev = y;

  if(y == NULL) root = z;
  else if (z->key < y->key) y->left = z;
  else y->right = z;
    
}

NodePointer makenode(int key)
{
  NodePointer NewNode;

  NewNode = (NodePointer)malloc(sizeof(struct node));

  NewNode->key = key;
  NewNode->left = NULL;
  NewNode->right = NULL;
  
  return NewNode;
}

void InorderPrint(NodePointer u)
{
  if(u == NULL) return; 

  InorderPrint(u->left);
  printf(" %d",u->key);
  InorderPrint(u->right);
}

void PreorderPrint(NodePointer u)
{
  if(u == NULL) return;
  
  printf(" %d",u->key);

  PreorderPrint(u->left);
  PreorderPrint(u->right);
}

int Search(NodePointer x, int k)
{
  if(x == NULL || k == x->key){
    if(x == NULL) return false;
    else return true; }
  if(k < x->key) return Search(x->left,k);
  else return Search(x->right,k);
}