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 node{
  int key;
  struct node *p;       //親
  struct node *left;    //左の子
  struct node *right;   //右の子
} tree;
void insert(tree *);
void Inorder(tree *);
void Preorder(tree *);
void find(tree *,int);
tree *t = NULL;

int main(){
  int n,i,k;
  char function[10];
  tree *new;
  
  scanf("%d",&n);
   for(i=0;i<n;i++){
    scanf("%s",function);
     if(function[0] == 'f'){
      scanf("%d",&k);
      find(t,k);
      }
    if(function[0] == 'p'){
      Inorder(t);
      printf("\n");
      Preorder(t);
      printf("\n");
    }
    else if(function[0] == 'i'){
      scanf("%d",&k);
      new=malloc(sizeof(struct node));
      new->key=k;
      insert(new);
    }
    //  printf("%d\n",i);
  }
  return 0;
}

void Preorder(tree *x){
  if(x == NULL) return;
  else  printf(" %d",x->key);
  if(x->left != NULL) Preorder(x->left);
  if(x->right != NULL) Preorder(x->right);
}
void Inorder(tree *x){
  if(x == NULL) return;
  if(x->left != NULL) Inorder(x->left);
  if(x != NULL) printf(" %d",x->key);
  if(x->right != NULL) Inorder(x->right);
}

void insert(tree *new){
  tree *x;
  tree *y;
  
  y=NULL;
  x=t;
  
  while(x != NULL){
    y=x;
    if(x->key > new->key) x=x->left;
    else x=x->right;
  }
  new->p = y;
  
  if(y == NULL){
    t=new;
    new->left = NULL;
    new->right = NULL;
  }
  else if(y->key > new->key){
    y->left = new;
    new->left = NULL;
    new->right = NULL;
  }
  else{
    y->right = new;
    new->left = NULL;
    new->right = NULL;
  }
}

void find(tree *t,int key){
  if(t == NULL){
    printf("no\n");
    return;
  }
  if(t->key == key){
    printf("yes\n");
    return;
  }
  if(t->key > key){
    find(t->left,key);
    return;
  }
  else{
    find(t->right,key);
    return;
  }
}