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

#define NIL NULL

struct node {
  int key;
  struct node *left;
  struct node *right;
  struct node *point;
};
struct node *root;

void inorder(struct node *);
void preorder(struct node *);
void insert(int);
struct node *find(int);

int main()
{
  int i, x, n, key;
  char s[10];

  scanf("%d", &n);
  for(i=0; i<n; i++) {
    scanf("%s", s);
    if(strcmp("insert", s) == 0) {
      scanf("%d", &x);
      insert(x);
    }
    else if(strcmp("print", s) == 0) {
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    else if(strcmp("find", s) == 0) {
      scanf("%d", &key);
      if(find(key) != NIL)
	printf("yes\n");
      else
	printf("no\n");
    }
  }
  return 0;
}

void inorder(struct node *T)
{
  if(T != NIL) {
    if(T->left != NIL)
      inorder(T->left);
    printf(" %d", T->key);
    if(T->right != NIL)
      inorder(T->right);
  }
}

void preorder(struct node *T)
{
  printf(" %d", T->key);
  if(T != NIL) {
    if(T->left != NIL)
      preorder(T->left);
    if(T->right != NIL)
      preorder(T->right);
  }
}

void insert(int key)
{
  struct node *y = NIL;
  struct node *x = root;
  struct node *z;

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

  while(x != NIL) {
    y = x;
    if(z->key < x->key)
      x = x->left;
    else
      x = x->right;
  }
  z->point = y;
  if(y == NIL)
    root = z;
  else if(z->key < y->key)
    y->left = z;
  else
    y->right = z;
}

struct node *find(int key)
{
  struct node *x = root;
  while(x != NIL && key != x->key) {
    if(key < x->key)
      x = x->left;
    else
      x = x->right;
  }
  return x;
}