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 NIL NULL

struct node{
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;
};

typedef struct node * Node;
Node root;
void insert(Node);
void inorder(Node);
void preorder(Node);
Node search(Node,int);

int main()
{
  int n,i,x;
  char m[10];
  Node A,t;
  
  scanf("%d",&n);
  
  for(i=0;i<n;i++){
    scanf("%s%d",m,&x);
    if(m[0]=='i'){
      A = (Node)malloc(sizeof(struct node));
      A->right = NIL;
      A->left = NIL;
      A->parent = NIL;
      A->key = x;
      insert(A);
    }
    else if(m[0]=='p'){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    else if(m[0]=='f'){
      t = search(root,x);
      if(t!=NIL) printf("yes\n");
      else printf("no\n");
    }
  }

  return 0;
}

void insert(Node A)
{
  Node y,x;

  y = NIL;
  x = root;
  
  while(x!=NIL){
    y = x;
    if(A->key < x->key) x = x->left;
    else x = x->right;
  }
  A->parent = y;

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

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

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

Node search(Node r,int x)
{
  int f;
  
  while(r!=NIL && x!=r->key){
    if(x<r->key) r = r->left;
    else r = r->right;
  }
  return r;
}