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 M 500000
#define P 10
#define NIL NULL

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

Node root;

void insert(int);
void inorder(Node);
void preorder(Node);
int find(int,Node);


int main() {

  int m,k,i,f;
  char s[10];

  scanf("%d",&m);

  for (i=0 ; i<m ; i++){
    scanf("%s",s);

    if(s[0]=='i'){
      scanf("%d",&k);
      insert(k);
    }
    if(s[0]=='f'){
      scanf("%d",&k);
      f=find(k,root);
      if(f==0) printf("no\n");
      else printf("yes\n");
    }

    else if(s[0]=='p'){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
  }

  return 0;
}

void insert(int k){
  Node x = root;
  Node y = NIL;
  Node z;

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

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

  z->parent=y;

  if(y==NIL) root=z;
  else if(z->key < y->key) y->left=z;
  else y->right=z;

}

void inorder(Node r){
  if(r->left!=NIL) inorder(r->left);
  printf(" %d",r->key);
  if(r->right!=NIL)inorder(r->right);
}


void preorder(Node r){
    printf(" %d",r->key);
    if(r->left!=NIL) preorder(r->left);
    if(r->right!=NIL)preorder(r->right);
}


int find(int k,Node r){

  int a=0;
  Node x=r;

  while(x!=NIL){
    if(k < x->key) x = x->left;
    else if (k > x->key) x = x->right;
    else {
      a=1;
      break;
    }
  }

  return a;
}