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<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;
//NIL is NULL
#define NIL NULL
//Node structure
struct Node{
  int key;
  struct Node *parent;
  struct Node *leftc;
  struct Node *rightc;
};
//define Nodepointer
typedef struct Node * Nodepointer;

//root         
Nodepointer root;

//function insert
void insert(int k){
  Nodepointer x,y,z;
  y=NIL;
  x=root;
  //make memory
  z=new struct Node();

  z->key=k;
  z->leftc=NIL;
  z->rightc=NIL;

  while(x!=NIL){
    y=x;
    if(z->key < x->key) x=x->leftc;
    else x=x->rightc;
  }

  z->parent=y;

  if(y==NIL) root=z;

  else if(z->key<y->key) y->leftc=z;

  else y->rightc=z;


}

//function search
Nodepointer find(Nodepointer now,int data){
  if(now==NIL||data==now->key) return now;
  if(data<now->key) return find(now->leftc,data);
  else return find(now->rightc,data);
}

//function treeminimum
Nodepointer treeminimum(Nodepointer x){
  while(x->leftc!=NIL){
    x=x->leftc;
  }
  return x;
}
//function treesuccerssor
Nodepointer treesuccessor(Nodepointer x){
  Nodepointer y;
  if(x->rightc!=NIL) return treeminimum(x->rightc);
  y=x->parent;
  while(y!=NIL && x==x->rightc){
    x=y;
    y=y->parent;
  }
  return y;
}
//function treedelete
void treedelete(Nodepointer z){
  Nodepointer x,y;
  if(z->leftc==NIL ||z->rightc==NIL)y=z;
  else y=treesuccessor(z);

  if(y->leftc!=NIL)x=y->leftc;
  else x=y->rightc;
 
  if(x!=NIL)x->parent=y->parent;
  if(y->parent==NIL) root=x;
  else if(y==y->parent->leftc) y->parent->leftc=x;
  else y->parent->rightc=x;

  if(y!=z) z->key=y->key;
  //free memory
  delete z;
}

//print
void inorderprint(Nodepointer now){
  if(now!=NIL){
    inorderprint(now->leftc);
    printf(" %d",now->key);
    inorderprint(now->rightc);
  }
}

void preorderprint(Nodepointer now){
  if(now!=NIL){
    printf(" %d",now->key);
    preorderprint(now->leftc);
    preorderprint(now->rightc);
  }
}


int main(){

  int n,i,j,data;
  Nodepointer del;
  char str[10];
  //load n
  scanf("%d",&n);
  //load commnad and key
  for(i=0;i<n;i++){
    scanf("%s",str);
    //insert
    if(strcmp(str,"insert")==0) {
      scanf("%d",&data);
      insert(data);
    }
    //find
    else if(strcmp(str,"find")==0){
      scanf("%d",&data);
      if(find(root,data)!=NIL) printf("yes\n");
      else printf("no\n");
    }
    //delete
    else if(strcmp(str,"delete")==0){
      scanf("%d",&data);
      del=find(root,data);
      treedelete(del);
    }
    //print
    else if(strcmp(str,"print")==0){
      inorderprint(root);
      cout <<endl;
      preorderprint(root);
      cout <<endl;
    }
  }

  return 0;
}