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: Time Limit Exceeded)

#include <stdio.h>

typedef struct pair* ppair;

typedef struct pair {
  int first, second;
} pair;


int size;
pair v[1000000];
int psize;
pair preorder[1000000];

void swap(ppair a, ppair b) {
  pair t = *a;
  *a = *b;
  *b = t;
}

int getp(int begin, int end) {
  int i;
  int p = begin;
  for(i = begin+1; i < end; ++i) {
    if(v[i].first < v[p].first) {
      p = i;
    }
  }
  swap(&v[end-1], &v[p]);
  return end-1;
}

void qsort(int begin, int end) {
  int i, j;
  if(begin >= end) return;
  getp(begin,end);
  preorder[psize++] = v[end-1];
  if(begin+1 == end) return;
  for(i = begin, j = begin; i < end; ++i) {
    if(v[i].second < v[end-1].second) {
      swap(&v[i], &v[j++]);
    }
  }
  swap(&v[j],&v[end-1]);
  qsort(begin, j);
  qsort(j+1, end);
}

int binary_search(int k) {
  int l, r;
  l = 0;
  r = size;
  while(l < r) {
    int m = (l+r)/2;
    if(v[m].second == k) {
      return m;
    } else if(v[m].second < k) {
      l = m+1;
    } else {
      r = m;
    }
  }
  return -1;
}

int main() {
  int i, j;
  int n, k;
  char s[100];
  size = 0;
  scanf("%d", &n);
  for(i = 0; i < n; ++i) {
    scanf("%s", s);
    if(s[0] == 'i') {
      scanf("%d", &k);
      v[size] = (pair){size,k};
      ++size;
    } else if(s[0] == 'p') {
      psize = 0;
      qsort(0, size);
      for(j = 0; j < size; ++j) {
        printf(" %d", v[j].second);
      }
      printf("\n");
      for(j = 0; j < size; ++j) {
        printf(" %d", preorder[j].second);
      }
      printf("\n");
    } else {
      scanf("%d", &k);
      psize = 0;
      qsort(0, size);
      printf(binary_search(k)!=-1?"yes\n":"no\n");
    }
  }
  return 0;
}