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>
#define N 500000

typedef struct{
  int key, left, right;
}Node;

Node tree[N+1];
int size;

void insert(int x){
  int p = 0;
  while(1){
    if(x < tree[p].key){
      if(tree[p].left == -1){
        tree[p].left = size;
        tree[size++].key = x;
        break;
      }else p = tree[p].left;
    }else{
      if(tree[p].right == -1){
        tree[p].right = size;
        tree[size++].key = x;
        break;
      }else p = tree[p].right;
    }
  }
}

void inorder(int p){
  if(tree[p].left != -1) inorder(tree[p].left);
  printf(" %d", tree[p].key);
  if(tree[p].right != -1) inorder(tree[p].right);
}

void preorder(int p){
  printf(" %d", tree[p].key);
  if(tree[p].left != -1) preorder(tree[p].left);
  if(tree[p].right != -1) preorder(tree[p].right);
}

int find(int p, int x){
  if(tree[p].key == x) return 1;
  if(x < tree[p].key && tree[p].left != -1) if(find(tree[p].left, x)) return 1;
  if(tree[p].key < x && tree[p].right != -1) if(find(tree[p].right, x)) return 1;
  return 0;
}

int main(){
  int n, i, first;
  first = 1;
  scanf("%d", &n);

  for(i=0;i<=n;i++){
    if(i<=n)break;
  }
  
  for(i=0;i<=n;i++) tree[i].key = tree[i].left = tree[i].right = -1;
  size = 0;
  while(n--){
    char str[100];
    scanf("%s", str);
    if(!strcmp(str, "insert")){
      int in;
      scanf("%d", &in);
      if(first){
        tree[size++].key = in;
        first = 0;
      }
      else insert(in);
    }else if(!strcmp(str, "find")){
      int in;
      scanf("%d", &in);
      printf("%s\n", (find(0, in) ? "yes" : "no"));
    }else{
      inorder(0);
      printf("\n");
      preorder(0);
      printf("\n");
    }
  }
  return 0;
}