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>

#define NIL NULL

struct node{
  int d;
  struct node *p;
  struct node *r;
  struct node *l;
};
typedef struct node *NP;

NP root;

void my_insert(NP);
void my_inorder_print(NP);
void my_preorder_print(NP);
int my_find(NP,int);
NP make_node(int);

int main(){
  int i,n,input;
  char in[7];
  NP z;
  scanf("%d",&n);
  for(i=0; i<n; i++){
    scanf("%s",in);
    if(strcmp(in,"insert")==0){
      scanf("%d",&input);
      //INSERT
      z=make_node(input);
      my_insert(z);
    }
    if(strcmp(in,"print")==0){
      //PRINT
      my_inorder_print(root);
      printf("\n");
      my_preorder_print(root);
      printf("\n");
    }
    if(strcmp(in,"find")==0){
      scanf("%d",&input);
      //FIND
      if(my_find(root,input)==1) printf("yes\n");
      else printf("no\n");
    }
  }
  return 0;
}

void my_insert(NP z){
  NP x,y;
  y=NIL;
  x=root;
  while(x!=NIL){
    y=x;
    if(z->d<x->d) x=x->l;
    else x=x->r;
  }
  z->p=y;

  if(y==NIL){
    root=z;
  }else if(z->d<y->d){
    y->l=z;
  }else{
    y->r=z;
  }
}

void my_inorder_print(NP p){
  if(p!=NIL){
    my_inorder_print(p->l);
    printf(" %d",p->d);
    my_inorder_print(p->r);
  }
}

void my_preorder_print(NP p){
  if(p!=NIL){
    printf(" %d",p->d);
    my_preorder_print(p->l);
    my_preorder_print(p->r);
  }
}

NP make_node(int key){
  NP p;
  p=(NP)malloc(sizeof(struct node));
  p->d=key;
  p->p=NIL;
  p->r=NIL;
  p->l=NIL;
  return p;
}

int my_find(NP x,int k){
  if(x==NIL) return 0;
  if(x->d==k) return 1;
  if(k<x->d) return my_find(x->l,k);
  else return my_find(x->r,k);
}