Problem:
Binary Search Tree III

Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

delete $k$: Delete a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

The operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:

If $z$ has no children, we modify its parent $z.p$ to replace $z$ with NIL as its child (delete $z$).

If $z$ has only a single child, we "splice out" $z$ by making a new link between its child and its parent.

If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$, delete $k$ 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

18
insert 8
insert 2
insert 3
insert 7
insert 22
insert 1
find 1
find 2
find 3
find 4
find 5
find 6
find 7
find 8
print
delete 3
delete 7
print

Sample Output 1

yes
yes
yes
no
no
no
yes
yes
1 2 3 7 8 22
8 2 1 3 7 22
1 2 8 22
8 2 1 22

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)

//Binary search tree 3

#include<stdio.h>
#include<string.h>
#include<stdlib.h>

struct Node
{
  int key;
 struct Node *p, *l, *r;
};

struct Node *root,*NIL;

struct Node *min(struct Node *x)
{
  while(x->l != NIL) x = x->l;
  return x;
}

struct Node *ser(struct Node *x)
{
  struct Node *y = x->p;
  if(x->r != NIL) return min(x->r);

  while(y != NIL && x == y->r)
    {
      x = y;
      y = y->p;
    }
  return y;
}

void insert(int key)
{
 struct Node *y = NIL;
 struct Node *x = root;
 struct Node *z;

  z = (struct Node *)malloc(sizeof(struct Node));
  z->key = key;
  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;
  }
}

struct Node *find(struct Node *x, int key)
{
  while(x != NIL && key != x->key)
    {
      if(key < x->key) x = x->l;
      else x = x->r;
    }
  return x;
}

void delete(struct Node *x)
{
  struct Node *y;
  struct Node *z;

  if(x->l == NIL || x->r == NIL) y = x;
  else y = ser(x);

  if(y->l != NIL) z = y->l;
  else z = y->r;

  if(z != NIL) z->p = y->p;

  if(y->p == NIL) root = z;
  else if(y == y->p->l) y->p->l = z;
  else y->p->r = z;

  if(y != z) x->key = y->key;

  free(y);
      
}

void pre(struct Node *x)
{
  if(x == NIL) return;
  printf(" %d",x->key);
  pre(x->l);
  pre(x->r);
}

void in(struct Node *x)
{
  if(x == NIL) return;
  in(x->l);
  printf(" %d",x->key);
  in(x->r);
}


int main()
{
  int i,n,num;
  char alp[20];
  //Node *imp;
  
  scanf("%d",&n);

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

      if(alp[0] == 'i')
	{
	  scanf("%d",&num);
	  insert(num);

	}
      else if(alp[0] == 'f')
	{
	  scanf("%d",&num);

	  if(find(root,num)) printf("yes\n");
	  else printf("no\n");
	}

      else if(alp[0] == 'd')
	{
	  scanf("%d",&num);

	  delete(find(root,num));
	}

      else if(alp[0] == 'p')
	{
	  in(root);
	  printf("\n");
	  pre(root);
	  printf("\n");
	}
    }
  
return 0;

}