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>

typedef struct d {
  struct d *parent;
  struct d *left;
  struct d *right;
  int key;
} node;
typedef node * Node;

 Node root;

void insert(int key){
  Node x = root;
  Node y = NULL;
  Node z;

  z = (Node)malloc(sizeof(node));
  z->key = key;
  z->left = NULL;
  z->right = NULL;

  while(x != NULL){
    y = x;
    if(z->key < x->key){
      x = x->left;
    }
    else{
      x = x->right;
    }
  }
  z->parent = y;

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

void find(int key){
  Node x = root;

  while(1){
    if(x == NULL){
      puts("no");
      return;
    }
    else if(x->key == key){
      puts("yes");
      return;
    }
    else if(key < x->key){
      x = x->left;
    }
    else if(x->key < key){
      x = x->right;
    }
  }
}

void inorderTreeWalk(Node x){
  if(x != NULL){
    inorderTreeWalk(x->left);
    printf(" %d",x->key);
    inorderTreeWalk(x->right);
  }
}

void preorderTreeWalk(Node x){
  if(x == NULL){
    return;
  }
  printf(" %d",x->key);
  preorderTreeWalk(x->left);
  preorderTreeWalk(x->right);
}

void printer(){
  inorderTreeWalk(root);
  printf("\n");
  preorderTreeWalk(root);
  printf("\n");
}

int main(){
  int i, n, key;
  char command[10];

  scanf("%d ",&n);
  for(i=0; i<n; i++){
    scanf("%s ",command);
    if(!strcmp(command, "insert")){
      scanf("%d ",&key);
      insert(key);
    }
    else if(!strcmp(command, "print")){
      printer();
    }
    else if(!strcmp(command, "find")){
      scanf("%d ",&key);
      find(key);
    }
  }

  return 0;
}