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 l;
  struct Node *ri;
  struct Node *le;
  struct Node *pa;
};

struct Node *root, *NIL;

void Insert(int);
void Inorder(struct Node *);
void Preorder(struct Node *);
struct Node * Find(struct Node *,int);


int main(){
  int i,h,valu,findnum;
  char C1[10];

  scanf("%d",&h);

  for(i=0;i<h;i++){

    scanf("%s",C1);

    if(strcmp(C1,"insert")==0){
      scanf("%d",&valu);
      Insert(valu);
    }
    else if(strcmp(C1,"print")==0){
      Inorder(root);
      printf("\n");
      Preorder(root);
      printf("\n");
    }
    else if(strcmp(C1,"find")==0){
      scanf("%d",&findnum);
      struct Node *F = Find(root,findnum);
      if(F !=NIL)printf("yes\n");
      else printf("no\n");
    }
  }
  
  return 0;
}

void Insert(int h){
  struct Node *x = root;
  struct Node *y= NIL;
  struct Node *z;

  z = (struct Node *)malloc(sizeof(struct Node));
  z -> l = h;
  z -> le = NIL;
  z -> ri = NIL;

  while(x != NIL){
    y = x;
    if(z->l < x->l){
      x = x-> le;
    }
    else{
      x = x-> ri;
    }
  }

  z -> pa=y;
  if( y == NIL){
    root = z;
  }
  else{
    if(z->l < y->l){
      y -> le = z;
    }
    else{
      y -> ri = z;
    }
  }
}


void Inorder(struct Node *x){
  if(x == NIL)return;
  Inorder(x -> le);
  printf(" %d",x -> l);
  Inorder(x -> ri);
}

void Preorder(struct Node *y){
  if(y==NIL)return;
  printf(" %d",y -> l);
  Preorder(y->le);
  Preorder(y->ri);
}

  struct Node * Find(struct Node *x, int h){
    while(x != NIL && h!= x -> l){
      if(h < x -> l ) x = x -> le;
      else x = x -> ri;
    }
    return x;
  }