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<string.h>
#include<stdlib.h>
#define MAX 10000

struct node{
  struct node *r,*l,*p;
  int key;
};

typedef struct node * Node;

#define NIL NULL

int t[MAX];
Node root;

void insert(int k){
  Node y=NIL;
  Node x=root;
  Node z;
  z=malloc(sizeof(struct node));
  z->key=k;
  z->l=NIL;
  z->r=NIL;

  while(x!=NIL){
    y=x;
    if(z->key < x->key){
      x=x->l;
    }else{
      x=x->r;
    }
  }
  z->p=y;
  if(y==NIL){
    root=z;
  }else{
    if(z->key < y->key){
      y->l=z;
    }else{
      y->r=z;
    }
  }
}

Node treeSearch(int x,Node u){
  while(u!=NIL && x!=u->key){
    if(x<u->key){
      u=u->l;
    }else{
      u=u->r;
    }
  }
  return u;
}
  

void inorder(Node u){
  if(u==NIL) return;
  inorder(u->l);
  printf(" %d",u->key);
  inorder(u->r);
}

void preorder(Node u){
  if(u==NIL) return;
  printf(" %d",u->key);
  preorder(u->l);
  preorder(u->r);
}
  
int main(){
  int n,i,x;
  char s[10];
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%s",s);
    if(strcmp(s,"insert")==0){
      scanf("%d",&x);
      insert(x);
    }else if(strcmp(s,"print")==0){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }else{
      scanf("%d",&x);
      if(treeSearch(x,root)==NIL){
	printf("no\n");
      }else{
	printf("yes\n");
      }
    }	
  }
  return 0;
}