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>
#define NIL NULL

typedef struct node{
  struct node *parent, *left, *right;
  int key;
}*N;

N root = NIL;

void insert(int);
N find(N, int);
void inorder(N);
void preorder(N);

int main(){
  int m, i, k;
  char str[256];

  scanf("%d", &m);

  for(i = 0; i < m; i++){
    scanf("%s", str);
    if(strcmp(str, "insert") == 0){
      scanf("%d", &k);
      insert(k);
    }else if(strcmp(str, "print") == 0){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }else if(strcmp(str, "find") == 0){
      scanf("%d", &k);
      if(find(root, k) != NIL)   printf("yes\n");
      else                                printf("no\n");
    }  
  }
    
  return 0;
}

void insert(int v){
  N y = NIL, x = root, z;
  
  z = malloc(sizeof(struct node));
  z->key = v;
  z->left = z-> right = NIL;
  
  while(x != NIL){
    y = x;
    if(z->key < x->key)   x = x->left;
    else                           x = x->right;
  }

  z->parent = y;

  if(y == NIL)  root = z;
  else if(z->key < y->key)   y->left = z;
  else                                   y->right = z;
}

N find(N u, int k){
  while(u != NIL && k != u->key){
    if(k< u->key)   u = u->left;
    else                  u = u->right;
  }
    return u;
}

void inorder(N u){
  if(u == NIL)   return;
  inorder(u->left);
  printf(" %d",  u->key);
  inorder(u->right);
}

void preorder(N u){
  if(u == NIL)   return;
  printf(" %d", u->key);
  preorder(u->left);
  preorder(u->right);
}