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>
struct node{
  int key;
  struct node *parent;
  struct node *right;
  struct node *left;
};
typedef struct node *Node;
Node T;
#define NIL NULL;
void Insert(int);
int Find(int);
void Preorder(Node);
void Inorder(Node);
int main()
{
  int n,i,key;
  char S[7];

  scanf("%d",&n);

  for(i=0;i<n;i++){
    scanf("%s",S);
    if(S[0]=='i'){
      scanf("%d",&key);
      Insert(key);
    }
    else if(S[0]=='f'){
      scanf("%d",&key);
      if(Find(key))printf("yes\n");
      else printf("no\n");
    }
    else{
      Inorder(T);
      printf("\n");
      Preorder(T);
      printf("\n");

    }
  }
  return 0;
}

void Insert(int key)
{
  Node y,x,z;
  y=NIL;
  x=T;
  z=malloc(sizeof(struct node));
  z->key=key;
  z->left=NIL;
  z->right=NIL;
  while(x!=NULL){
    y=x;
    if( z->key < x->key )x=x->left;
    else x=x->right;
  }
  z->parent=y;
  if(y==NULL){
    T=z;
  }
 else if(z->key<y->key){
      y->left=z;
  }
  else{
    y->right=z;
  }
}

int Find(int key)
{
  Node TT;
  TT=T;
  while(TT!=NULL && TT->key!=key){
    if(key<TT->key)TT=TT->left;
    else TT=TT->right;
  }
  if(TT==NULL)return 0;
  else return 1;
}
void Preorder(Node T)
{
  printf(" %d",T->key);
  if(T->left!=NULL){
    Preorder(T->left);
  }
  if(T->right!=NULL){
    Preorder(T->right);
  }

}

void Inorder(Node T)
{
  if(T->left!=NULL && T->right!=NULL){
    Inorder(T->left);
    printf(" %d",T->key);
    Inorder(T->right);

  }
  if(T->left!=NULL && T->right==NULL){
   Inorder(T->left);
     printf(" %d",T->key);
  }

  if(T->right!=NULL && T->left==NULL){
  printf(" %d",T->key);
 Inorder(T->right);

  }
  if(T->left==NULL && T->right==NULL)printf(" %d",T->key);

}