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 *r,*l,*p;
};

typedef struct node Node;

Node *root,*nil;

void insert(int t){
  Node *x=root,*y=nil,*z;

  z=malloc(sizeof(Node));
  z->key = t;
  z->r=nil;
  z->l=nil;

  while(x!=nil){
    y=x;

    if(z->key < x->key){
      x = x->l;
    }
    else {
      x = x->r;
    }
  }

  z->p = y;
  if(y==nil)root = z;
  else {
    if(z->key < y->key){
      y->l = z;
    }
    else {
      y->r = z;
    }
  }
}

void inorder(Node *q){
  if(q==nil)return;

  inorder(q->l);
  printf(" %d",q->key);
  inorder(q->r);
}
void preorder(Node *q){
  if(q==nil)return;

  printf(" %d",q->key);
  preorder(q->l);
  preorder(q->r);
}

void find(int t){
  Node *aaa=root;

  while(1){
    if(aaa==nil){
      printf("no\n");
      break;
    }
    else if(aaa->key == t){
      printf("yes\n");
      break;
    }
    else if(aaa->key < t){
      aaa = aaa -> r;
    }
    else {
      aaa = aaa-> l;
    }
  }
}

int main(){
  int n,i,j,t;
  char s[10];

  root = nil;
  
  scanf("%d",&n);

  for(i=0;i<n;i++){
    scanf("%s",s);
    if(s[0]=='i'){
      scanf("%d",&t);
      insert(t);
    }
    else if(s[0]=='p'){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
    }
    else if(s[0]=='f'){
      scanf("%d",&t);
      find(t);
    }
  }
  return 0;
}