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 NULL

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

typedef struct node * Node;
Node root;

Node find(Node u, int k){
  if(u == NIL || k == u->key) return u;     
  if(k < u->key) return find(u->left,k);
  else return find(u->right,k);      
}


void insert(int k){
  Node y=NIL;
  Node x=root;
  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 u){
  if(u==NIL)return;
  inorder(u->left);
  printf(" %d",u->key);
  inorder(u->right);
}
void preorder(Node u){
  if(u==NIL)return;
  printf(" %d",u->key);
  preorder(u->left);
  preorder(u->right);
}

int main(){
  int n, i, x, key;
    char com[20];
    scanf("%d", &n);
    for (i=0;i<n;i++)
      {
	scanf("%s", &com);
	if (com[0]=='i')
	  {
	    scanf("%d", &x);
	    insert(x);
	  }
	else if (com[0]=='p')
	  {
	    inorder(root);
	    printf("\n");
	    preorder(root);
	    printf("\n");
	  }
	else{
	  scanf("%d",&key);
	  if(find(root,key)==NIL) printf("no\n");
	  else printf("yes\n");       
	}
      }
	return 0;
      }