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>

typedef struct Node{
  int key;
  struct Node *right;
  struct Node *left;
  struct Node *parent;
} node;

node *root,*nil;

node *find(node *u,int k){
  while(u!=nil && k!=u->key){
    if(k<u->key)u=u->left;
    else u=u->right;
  }
  return u;
}

void insert(int k){
  node *a=root;
  node *b=nil;
  node *c;
  c=(node *)malloc(sizeof(node));
  c->key=k;
  c->left=nil;
  c->right=nil;
  while(a!=nil){
    b=a;
    if(c->key<a->key){
      a=a->left;
    }else{
      a=a->right;
    }
  }
  c->parent=b;
  if(b==nil){
    root=c;
  }else{
    if(c->key<b->key){
      b->left=c;
    }else{
      b->right=c;
    }
  }
}

void inorder(node *u){
  if(u==nil)return;
  inorder(u->left);
  printf(" %d",u->key);
  inorder(u->right);
}

void preorder(node *u){
  if(u==nil)return;
  printf(" %d",u->key );
  preorder(u->left);
  preorder(u->right);
}

int main(){
  int n,i,x;
  char c[100];
  scanf("%d",&n);
  for(i= 0;i<n;i++){
    scanf("%s",c);
    if('f'==c[0]){
      scanf("%d",&x);
      struct Node *t = find(root,x);
      if(t != nil)printf("yes\n" );
      else printf("no\n");
    }else if(strcmp(c,"insert")==0){
      scanf("%d",&x);
      insert(x);
    }else if(strcmp(c,"print")==0){
      inorder(root);
      printf("\n" );
      preorder(root);
      printf("\n");
    }
  }
  return 0;
}