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 {
  long key;
  struct Node *p, *l, *r;
} N;

N *root, *NIL;

void insert(long k) {
  N *y = NIL;
  N *x = root;
  N *z;
    
  z = (N *)malloc(sizeof(N));
  z->key = k;
  z->l = z->r = NIL;
    
  while (x != NIL) {
    y = x;
    if (z->key < x->key) x = x->l;
    else x = x->r;
  }
  z->p = y;
    
  if (y == NIL) root = z;
  else if (z->key < y->key) y->l = z;
  else y->r = z;
}

N* find(N *x, long k) {
  while (x != NIL && k != x->key) {
    if (k < x->key) x = x->l;
    else x = x->r;
  }
  return x;
}

void inorder(N *u) {
  if (u == NIL) return;
  inorder(u->l);
  printf(" %ld", u->key);
  inorder(u->r);
}

void preorder(N *u) {
  if (u == NIL) return;
  printf(" %ld", u->key);
  preorder(u->l);
  preorder(u->r);
}

void print() {
  inorder(root);
  printf("\n");
  preorder(root);
  printf("\n");
}

int main() {
  long n, i, x;
  char st[20];
  scanf("%ld", &n);
  for (i = 0; i < n; i++) {
    scanf("%s", st);
    scanf("%ld", &x);
    if (st[0] == 'f') {
      if (find(root, x) != NIL) printf("yes\n");
      else printf("no\n");
    }
    else if (st[0] == 'i') insert(x);
    else if (st[0] == 'p') print();
  }
  return 0;
}