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

typedef struct node * Node;

Node root;

void insert(int);
void inorder(Node);
void preorder(Node);
Node find(Node,int);

int main(){
  int a,b,i;
  char com[20];
 
  scanf("%d",&a);
 
  for(i=0;i<a;i++){
    scanf("%s",com);
 
    if(com[0]=='i'){
        scanf("%d",&b);
        insert(b);
    }

    else if(com[0]=='p'){
        inorder(root);
        printf("\n");
        preorder(root);
        printf("\n");
    }

    else if(com[0]=='f'){
        scanf("%d",&b);
        Node s=find(root,b);
        if(s!=NULL) printf("yes\n");
        else printf("no\n");
    }
  }
  return 0;
}

void insert(int v){
  Node y=NULL;
  Node x=root;
  Node c;
  c=malloc(sizeof(struct node));
  c->key=v;
  c->l=NULL;
  c->r=NULL;
  while(x!=NULL){
    y=x;
    if(c->key < x->key) x=x->l;
    else x=x->r;
  }
    c->p=y;
    if(y==NULL) root=c;
    else if(c->key < y->key) y->l=c;
    else y->r=c;
}

void inorder(Node w){
  if(w!=NULL){
    inorder(w->l);
    printf(" %d",w->key);
    inorder(w->r);
  }
}
 
void preorder(Node w){
  if(w!=NULL){
    printf(" %d",w->key);
    preorder(w->l);
    preorder(w->r);
  }
}
 
Node find(Node a,int b){
  if (a==NULL || b==a->key) return a;
  if(b < a->key) return find(a->l,b);
  else return find(a->r,b);
}