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>
#define NIL -1
#define MAX 500000

void insert(int);
int find(int);
void print();
void pO(int);
void iO(int);

int Root = NIL;
int l[MAX],r[MAX],key[MAX],p[MAX];

int main(){
  
  int i,j,k=0;
  int N;
  char in[15];
  
  scanf("%d",&N);
  for(i=0;i<MAX;i++) key[i]=l[i]=r[i]=p[i]=NIL;
  for(i=0;i<N;i++){
    scanf("%s",in);
    if(in[0]=='i'){
      scanf("%d",&j);
      key[k]=j;
      insert(k++);
    }
    else if(in[0]=='p')print();
    else if(in[0]=='f'){
       scanf("%d",&j);
       if(find(j)==1)printf("yes\n");
       else printf("no\n");
    }
  }
  
  return 0;
}

void insert(int a){
  int x=NIL;
  int y=Root;
  while(y!=NIL){
    x=y;
    if(key[a]<key[y]) y=l[x];
    else y=r[y];
  }
  p[a]=y;
  if(x==NIL) Root=a;
  else if(key[a]<key[x]) l[x]=a;
  else r[x]=a;  
}

int find(int b){
  int i=0;
  int x=NIL,y=Root;
   while(y!=NIL){
     if(key[y]==b)return 1;
    x = y;
    if(b<key[y]) y=l[y];
    else y=r[y];
  }
   return 0;
}

void print(){
  iO(Root);
  printf("\n");
  pO(Root);
  printf("\n");
}

void pO(int c){
  if(c==NIL)return;
  printf(" %d",key[c]);
  pO(l[c]);
  pO(r[c]);
}

void iO(int d){
  if(d==NIL)return;
  iO(l[d]);
  printf(" %d",key[d]);
  iO(r[d]);
}