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>
#include <string.h>

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

struct node *tree = NULL;

void insert(struct node **root, struct node *node)
{
  struct node *parent = NULL;
  struct node *current = *root;

  while (current != NULL) {
    parent = current;
    if (node->key < current->key) {
      current = current->left;
    } else {
      current = current->right;
    }   
  }
    
  node->parent = parent;
    
  if (parent == NULL) {
    *root = node;
  } else if (node->key < parent->key) {
    parent->left = node;
  } else {
    parent->right = node;
  }
}

int find_tree(struct node* node, int key)
{
  if (node != NULL) {
    if (node->key > key) {
      return find_tree(node->left, key);
    } else if (node->key < key) {
      return find_tree(node->right, key);
    } else {
      return 1;
    }
  }
  return 0;
}

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

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

void tree_destroy(struct node* node)
{
  if (node != NULL) {
    tree_destroy(node->left);
    tree_destroy(node->right);
    free(node);
  }
}

int main (int argc, char** argv)
{
  int i, num;
  char str[32] = {0};
  fgets(str, 32, stdin);
  num = atoi(str);
  for (i = 0; i < num; i++) {
    fgets(str, 32, stdin);
    if (str[0] == 'i') {
      struct node *node = (struct node *)malloc(sizeof(struct node));
      node->key = atoi(&str[7]);
      node->left = NULL;
      node->right = NULL;
      insert(&tree, node);
    } else if (str[0] == 'f') {
      int key = atoi(&str[4]);
      printf("%s\n", find_tree(tree, key) ? "yes" : "no");
    } else if (str[0] == 'p') {
      inorder_traverse(tree);
      printf("\n");
      preorder_traverse(tree);
      printf("\n");
    }
  }
  tree_destroy(tree);
  return 0;
}