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>
#define NIL NULL

struct node{
  int key;
  struct node *r;
  struct node *l;
  struct node *p;
};

typedef struct node * Node;

Node root;

void insert(int v){
  Node y=NIL;
  Node x=root;
  Node z;

  z=malloc(sizeof(struct node));
  z->key=v;
  z->l=NIL;
  z->r=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 u){
  if(u!=NIL){
    inorder(u->l);
    printf(" %d",u->key);
    inorder(u->r);
  }
}

void preorder(Node u){
  if(u!=NIL){
    printf(" %d",u->key);
    preorder(u->l);
    preorder(u->r);
  }
}

Node find(Node a,int k){
  if (a==NIL || k==a->key) return a;
  if(k < a->key) return find(a->l,k);
  else return find(a->r,k);
}

int main(){
  int n,i,x;
  char com[20];

  scanf("%d",&n);

  for(i=0;i<n;i++){
    scanf("%s",com);

  if(com[0]=='i'){
    scanf("%d",&x);
    insert(x);
  }
  else if(com[0]=='p'){
    inorder(root);
    printf("\n");
    preorder(root);
    printf("\n");
  }
  else if(com[0]=='f'){
    scanf("%d",&x);
    Node s=find(root,x);
    if(s!=NIL) printf("yes\n");
    else printf("no\n");
  }
  }
  return 0;
}