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 {
  struct Node *parent;
  struct Node *left;
  struct Node *right;
  int key;
} node;
void preOrder(node *);
void inOrder(node *);
void insert(int);
node *find(int, node *);
node *root;
int n;
int main() {
  int i, j, key;
  char command[7];

  scanf("%d", &n);
  for (i = 0; i < n; i++) {    
    scanf("%s", command);
    switch (command[0]) {
    case 'i':
      scanf("%d", &key);
      insert(key);
      break;
    case 'f':
      scanf("%d", &key);
      node *tmp = find(key, root);
      if (tmp != NULL) {
	printf("yes\n");
      } else {
	printf("no\n");
      }
      break;
    default:
      inOrder(root);
      printf("\n");
      preOrder(root);
      printf("\n"); 
      break;
    }
  }
  return 0;
}
void inOrder(node *u) {
  if (u == NULL) {
    return ;
  }
  if (u->left != NULL) inOrder(u->left);
  printf(" %d",u->key);
  if (u->right != NULL) inOrder(u->right);
  return ;
}
void preOrder(node *u) {
  if (u == NULL) {
    return ;
  }
  printf(" %d",u->key);
  if (u->left != NULL) preOrder(u->left);
  if (u->right != NULL) preOrder(u->right);
  return ;
}
void insert(int key) {
  node *y = NULL;
  node *x = root;
  node *z;

  z = (node*) malloc(sizeof(node));
  z->left = NULL;
  z->right = NULL;
  z->key = key;

  while (x != NULL) {
    y = x;
    if (key < x->key) {
      x = x->left;
    } else {
      x = x->right;
    }
  }
 
  z->parent = y;
  if ( y==NULL ) {
    root = z;
  } else if (z->key < y->key) {
    y->left = z;
  } else {
    y->right = z;
  }
  return ;
}
node *find(int key, node *u) {
  node *x;
  x = u;
  while (x != NULL && x->key != key) {
    if (x->key < key) x = x->right;
    else  x = x->left;
  }
  return x;
}