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>

const int NILL = -1;

typedef long int lint;

typedef struct node
{
  lint key;
  struct node* parent;
  struct node* left;
  struct node* right;
  
}TREE;

TREE* root = NULL;

void insert(TREE* t)
{
  TREE* x;
  TREE* y;

  y = NULL;
  x = root;

  while(x != NULL)
  {
    y = x;
    if(t->key < x->key){
      x = x->left;
    }
    else{
      x = x->right;
    }
  }
  
  if(y == NULL) root = t;
  else if(t->key < y->key){
    y->left = t;
  }
  else{
    y->right = t;
  }
}

int find(TREE* p, lint key)
{
  while(p != NULL && p->key != key){
    if(p->key > key){
      p = p->left;
      //print();
    }
    else{
      p = p->right;
      //print();
    }
  }
  if(p != NULL) return 1;
  else return 0;
}

void PreOrder(TREE* n)
{
  if(n == NULL) return;
  printf(" %ld",n->key);
  PreOrder(n->left);
  PreOrder(n->right);
}

void InOrder(TREE* n)
{
  if(n == NULL) return;
  InOrder(n->left);
  printf(" %ld",n->key);
  InOrder(n->right);
}

void print()
{
  InOrder(root);
  printf("\n");
  PreOrder(root);
  printf("\n");
}

int main()
{
  int m;
  int i;
  char order[20];
  lint key;
  
  scanf("%d",&m);

  for(i = 0; i < m;i++){
    scanf("%s",order);
    
    if(order[0] == 'i'){
      scanf("%ld", &key);

      //if(i == 0) root = tree;
      TREE* t = (TREE *)malloc(sizeof(TREE));
      t->right = t->left = NULL;

      t->key = key;
      insert(t);
    }
    else if(order[0] == 'f'){
      scanf("%ld",&key);
      
      if(find(root, key)) printf("yes\n");
      else printf("no\n");
    }
    else if(strcmp(order,"print") == 0){
      print();
    }
  }
  return 0;
}