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>
#define N 500000

struct BiT_Node{
  int key;
  struct BiT_Node *p;
  struct BiT_Node *left;
  struct BiT_Node *right;
};

typedef struct BiT_Node *Node;

Node root;

void insert (int v){
  Node y = NULL;
  Node x = root;
  Node z;
  z = malloc(sizeof(struct BiT_Node));
  z->key = v;
  z->left = NULL;
  z->right = NULL;
  y = NULL;
  while(x != NULL){
    y = x;
    if(z->key < x->key) x = x->left;
    else x = x->right;
  }
  
  z->p = y;

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

void in_walk(Node u){
  if(u != NULL){
    in_walk(u->left);
    printf(" %d",u->key);
    in_walk(u->right);
  }
}

void pre_walk(Node u){
  if(u == NULL) return;
  printf(" %d",u->key);
  if(u->left != NULL) pre_walk(u->left);
  if(u->right != NULL) pre_walk(u->right);
}

int find(int key){
  Node u;
  u = root;
  while(u != NULL){
    if(u->key == key) return 1;
    else if(key > u->key) u = u->right;
    else u = u->left;
  }
  return 0;
}

int main()
{
  int n,i,tmp;
  char buf[20];
  scanf("%d",&n);
  for(i = 0 ; i < n; i++){
    scanf("%s",buf);
    if(buf[0] == 'i'){
      scanf("%d",&tmp);
      insert(tmp);
    }
    else if(buf[0] == 'f') {
      scanf("%d",&tmp);
      if(find(tmp) == 1) printf("yes\n");
      else printf("no\n");
    }
    else if(buf[0] == 'p') {
      in_walk(root);
      printf("\n");
      pre_walk(root);
      printf("\n");
    }
  }
  return 0;
}