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>

struct Node{
  int key;
  struct Node *right,*left,*parent;
};

struct Node *root,*NIL;

struct Node* find(struct Node *u,int k){
  while(u != NIL && k != u -> key){
    if(k < u -> key) u = u -> left;
    else u = u -> right;
  }
  return u;
}

void insert(int k){
  struct Node *y = NIL;
  struct Node *x = root;
  struct Node *z;

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

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

int main(){
  int n,i,x;
  char str[7];
  struct Node *t;
  
  scanf("%d",&n);

  for(i = 0;i < n;i++){
    scanf("%s",str);
    if(strcmp(str,"find") == 0){
      scanf("%d",&x);
      t = find(root,x);
      if(t != NIL) printf("yes\n");
      else printf("no\n");
    }
    else if(strcmp(str,"insert") == 0){
      scanf("%d",&x);
      insert(x);
    }
    else if(strcmp(str,"print") == 0){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
  }
  return 0;
}