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>
#define N 10000
#define NIL NULL
struct node{
  struct node *left;
  struct node *right;
  struct node *parent;
  int key;
};

typedef struct node * Node;
Node root;

void insert(int k){
  Node y = NIL;
  Node x = root;
  Node z;
  z = malloc(sizeof(struct node));
  z->key = k;
  z->left = NIL;
  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;
    }
}
void inorder(Node u){
  if(u != NIL){
    inorder(u->left);
    printf(" ");
    printf("%d",u->key);
    inorder(u->right);
  }
 
}
void preorder(Node u){ 
    if (u != NIL) {
      printf(" ");
      printf("%d",u->key); 
      preorder(u->left);
      preorder(u->right);
    
    }
}
Node IterativeTreeSearch(Node x,int k){
  if(x == NIL || k == x -> key) return x;
  if(k < x -> key) return IterativeTreeSearch(x -> left, k);
  else return IterativeTreeSearch(x -> right, k);

 
}

int main(){
  int i,n,m,x;
  char str[10];
  scanf("%d",&m);
  for(i=0;i<m;i++){
    scanf("%s",str);
    if(str[0]=='f'){
      scanf("%d", &x);
      Node t = IterativeTreeSearch(root, x);
      if ( t != NIL ){ 
	printf("yes\n");
      }
      else {
	printf("no\n");
      }
    }
    else if(str[0]=='i'){  
      scanf("%d",&n);
      insert(n);
    }
    
    else if(str[0]=='p'){
      
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
  }
return 0;
}