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 {
  struct node *ri;
  int key;
  struct node *le;
};
typedef struct node * NodePointer;
 
NodePointer head, tail;
void init(void);
NodePointer makenode(int);
void insert(int,NodePointer);
void preorder(NodePointer);
void inorder(NodePointer);
int find(int,NodePointer);

void init(void){
  head=makenode(-1);
  tail=makenode(-1);
  head->ri=tail;
  head->le=tail;
}
 
NodePointer makenode(int k){
  NodePointer x;
 
  x=malloc(sizeof(struct node));
  x->key = k;
  x->le = x->ri = tail;
 
  return x;
}
 
void insert(int k, NodePointer p){
  if(k < p->key){
    if(p->le == tail){
      p->le = makenode(k);
    }else{
      insert(k , p->le);
    }
  }else{
    if(p->ri == tail){
      p->ri = makenode(k);
    }else{
      insert(k , p->ri);
    }
  }
}
 
void preorder(NodePointer node){
  if(node != tail){
    printf(" %d", node->key);
    preorder(node->le);
    preorder(node->ri);
  }
}
 
void inorder(NodePointer node){
  if(node != tail){
    inorder(node->le);
    printf(" %d", node->key);
    inorder(node->ri);
  }
}
  
int find(int k,NodePointer node){
  if(node == tail){
    return 0;
  }
 
  if(node->key == k){
    return 1;
  }else if(node->key < k){
    return find(k , node->ri);
  }else{
    return find(k , node->le);
  }
}
int main(){
  char str[10];
  int n,k;
 
  init();
  scanf("%d" ,&n);
  while(n--){
    scanf("%s" ,str);
 
    if(str[0] == 'i'){
      scanf("%d" ,&k);
      insert(k, head);
    }else if(str[0] == 'p'){
      inorder(head->ri);
      printf("\n");
      preorder(head->ri);
      printf("\n");
    }else{
      scanf("%d" ,&k);
      if(find(k,head->ri)){
    printf("yes\n");
      }else{
    printf("no\n");
      }
    }
  }
 
  return 0;
}