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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

struct node{
  int key;
  struct node *parent;
  struct node *left;
  struct node *right;
} ;

int flag = 0;

typedef struct node Node;

Node *root, *NIL;

void Insert(int);
void Inorder(Node *);
void Preorder(Node *);
void Find(Node *, int);

int main()
{
  int n,i,a;
  char in[7],insert[7] = "insert",find[5] = "find",print[6] = "print";
  scanf("%d",&n);
  for(i = 0; i < n; i++){
    scanf("%s",in);
    (void)getchar();
    if(strcmp(in, insert) == 0) {
      scanf(" %d",&a);
      Insert(a);
    }
    else if(strcmp(find, in) == 0) {
      scanf("%d",&a);
      Find(root,a);
      if(flag == 1) printf("yes\n");
      else printf("no\n");
      flag = 0;
    }
    else  {
      Inorder(root);
      printf("\n");
      Preorder(root);
      printf("\n");
    }
  }
  return 0;
}

void Insert(int a) {
  Node *b = NIL;
  Node *c = root;
  Node *d;

  d = malloc(sizeof(Node));
  d -> key = a;
  d -> left = NIL;
  d -> right = NIL;
  while(c != NIL) {
    b = c;
    if(d -> key < c -> key) c = c -> left;
    else  c = c -> right;
  }

  d -> parent = b;
  if(b == NIL)  root = d;
  else {
    if(d -> key < b -> key)  b -> left = d;
    else    b -> right = d;
  }
}

void Inorder(Node *u) {
  if(u == NIL) return;
  else {
    Inorder(u -> left);
    printf(" %d", u->key);
    Inorder(u -> right);
  }
}

void Preorder(Node *u) {
  if(u == NIL) return;
  else {
    printf(" %d", u->key);
    Preorder(u -> left);
    Preorder(u -> right);
  }
}

void Find(Node *u, int k) {
    if(u == NIL) return;
  else {
    if(u -> key == k) {
      flag = 1;
      return;
    }
    Find(u -> left, k);
    Find(u -> right, k);
  }
}