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>
#define NIL -1

typedef struct node{

  int key;  
  struct node *p;
  struct node *r;
  struct node *l;
}Node; 

void insert(int);
void nodegene(Node *, int);
void print();
void in_p(Node *);
void pre_p(Node *);
void find(Node *,int ); 
Node *root = NULL;

int main(){

  char str[10];
  int i,n,m,l;
  Node *node;

  scanf("%d", &n);

  //scanf("%d", &l);
  //nodegene( root,l);

  for( i = 0; i < n; i++){

    scanf("%s", str);

    switch(str[0]){
    case 'i':
      scanf("%d",&m);
      insert(m);
      break;

    case 'p':
      print();
      break;

    case 'f':
      scanf("%d",&l);
      find( root, l);
      break;
    }
  }
return 0;
}

void nodegene(Node *n,int num){
  n -> key = num;
  n -> p = NULL;
  n -> r = NULL;  
  n -> l = NULL;
}


void insert(int n){
 
  Node *p = malloc(sizeof(Node));
  Node *search;

  nodegene( p, n);

  if(root == NULL){
    root = p;
    return;
  }

  search = root;

  while (1) {
    if (p -> key < search -> key) {
      if (search -> l == NULL) {
	search -> l = p;
	break;
      } 
      else {
	search = search -> l;
      }
    } 
    else {
      if (search -> r == NULL) {
	search -> r = p;
	break;
      } 
      else {
	search = search -> r;
      }
    }
  }
  search = p;
 
}


void in_p(Node *n){
  
  if(n != NULL){
    in_p(n -> l);
    printf(" %d", n -> key);
    in_p(n -> r);
  }
}

void pre_p(Node *n){
  
  if(n != NULL){  
    printf(" %d", n -> key);
    pre_p(n -> l);
    pre_p(n -> r);
  }
}

void print(){

  in_p( root);
  printf("\n");  
  pre_p( root);
  printf("\n");
}

void find(Node *node,int n){

  if(node == NULL){
    printf("no\n");
    return;
  }
  
  if(node -> key == n){
    printf("yes\n");
    return;
  }
  
    if(n < node -> key) find( node -> l, n);

    if(n > node -> key) find( node -> r, n);
}