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>

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

Node *tmp, *NIL;

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

int main()
{
  int m, i, k;
  char c[1000];
  Node *judge;
  
  scanf("%d", &m);
  
  for( i = 0 ; i < m ; i++ ){
    scanf("%s", c);
    if( strcmp(c, "find") == 0 ){
      scanf("%d", &k);
      judge = find(tmp, k);
      if( judge != NIL ) printf("yes\n");
      else printf("no\n");
    }
    else if( strcmp(c, "insert") == 0 ){
      scanf("%d", &k);
      insert(k);
    }
    else if( strcmp(c, "print") == 0 ){
      inorder(tmp);
      printf("\n");
      preorder(tmp);
      printf("\n");
    }
  }
  
  return 0;
}

void insert(int k){
  Node *y = NIL;
  Node *x = tmp;
  Node *z;
  
  z = malloc(sizeof(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 ) tmp = z;
  else if( z->key < y->key ) {
    y->l = z;
  } else y->r = z;
  
}

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);
}

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