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;

Node treeSearch(Node u, int k){
  while(u != NIL){
    if(u->key == k) break;

    if(u->key > k) u = u->left;

    else u = u->right;
  }

  return u;
}

/*
  Node treeSuccessor(Node x){
  }
 
  void treeDelete(Node z){
  }
*/

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

int main(void){
  int n, i, x;
  char com[20];
  scanf("%d", &n);
 
  for(i = 0; i < n; i++){
    scanf("%s", com);
    if (com[0] == 'f') {
      scanf("%d", &x);
      Node t = treeSearch(root, x);
      if (t != NIL) {
        printf("yes\n");
      } else {
        printf("no\n");
      }
    }

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

    else if(com[0] == 'p'){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }

    else if (com[0] == 'd'){
      /*
        scanf("%d", &x);
        treeDelete(treeSearch(root, x));
      */
    }
  }
 
  return 0;
}