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>

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

Tree *root;

void insert(int k){
  Tree *a = NULL;
  Tree *b = root;
  Tree *t;

  t = malloc(sizeof(Tree));

  t->key = k;
  t->l = NULL;
  t->r = NULL;

  while(b != NULL){
    a = b;
    if(t->key < b->key){
      b = b->l;
    }else{
      b = b->r;
    }
  }

  t->p = a;

  if(a == NULL){
    root = t;
  }else{
    if(t->key < a->key){
      a->l = t;
    }else{
      a->r = t;
    }
  }
}

Tree *find(Tree *t, int k){
  while(t != NULL && k != t->key){
    if(k < t->key){
      t = t->l;
    }else{
      t = t->r;
    }
  }
  return t;
}

void ino(Tree *t){
  if(t == NULL) return;
  ino(t->l);
  printf(" %d",t->key);
  ino(t->r);
}

void pre(Tree *t){
  if(t == NULL) return;
  printf(" %d",t->key);
  pre(t->l);
  pre(t->r);
}

int main(){
  int n,x,y,i;
  Tree *found;
  char order[10];

  scanf("%d",&n);

  for(i = 0; i < n; i++){

    scanf("%s",order);

    if(order[0] == 'i'){
      scanf("%d",&x);
      insert(x);

    }else if(order[0] == 'p'){
      ino(root);
      printf("\n");
      pre(root);
      printf("\n");

    }else if(order[0] == 'f'){
      scanf("%d",&y);
      found = find(root,y);

      if(found != NULL){
	printf("yes\n");
      }else{
	printf("no\n");
      }

    }
  }
  return 0;
}