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)

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


struct Node{
  int key;
  struct Node *right,*parent,*left;
};

void insert(int);
struct Node inorder(struct Node *);
struct Node preorder(struct Node *);
struct Node * find(struct Node *,int);
void delete(struct Node *);
struct Node * getPoint(struct Node *);
struct Node * getmin(struct Node *);

struct Node *root, *NIL;


int main(){
  int n=0;
  int i=0;
  int number=0;
  char word[6];
  char space;
  int print_flag=0;
  struct Node *f;
  scanf("%d", &n);
  for(i=0;i<n;i++){
    scanf("%s",word);

    if(word[0]=='i')
      {
	scanf("%d%c",&number,&space);
	insert(number);
      }

    else if(word[0]=='p')
      {
	print_flag=1;
      }

    else if(word[0]=='f')
      {
	scanf("%d",&number);
	f=find(root,number);
	if(f != NIL) printf("yes\n");
	else if(f==NIL) printf("no\n");
	f=NIL;
      }

    else if(word[0]=='d')
      {
	scanf("%d",&number);
	delete(find(root,number));
      }

    if(print_flag==1){
      inorder(root);
      printf("\n");
      preorder(root);
      printf("\n");
      print_flag=0;
    }

    print_flag=0;
  }

  return 0;
}

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

  z=(struct Node *)malloc(sizeof(struct Node));
  z->key=number;
  z->left=NIL;
  z->right=NIL;

  while(x!=NIL){
    y=x;
    if( z->key < x->key ) x=x->left;
    else x=x->right;
  }
  z->parent=y;
  if(y==NIL){
    root=z;
  }
  else{
    if( z->key < y->key){
      y->left=z;
    }
    else{
      y->right=z;
    }
  }
}

struct Node inorder(struct Node *a){
  if(a==NIL)return;
  inorder(a->left);
  printf(" %d",a->key);
  inorder(a->right);
}

struct Node preorder(struct Node *a){
  if(a==NIL)return;
  printf(" %d",a->key);
  preorder(a->left);
  preorder(a->right);
}

struct Node * find(struct Node *a, int number){
  while( a != NIL && number != a->key)
    {
      if(number < a->key) a=a->left;
      else a=a->right;
    }
  return a;
}

void delete(struct Node *a){
  struct Node *b;
  struct Node *c;
  if(a->left==NIL || a->right==NIL) b=a;

  else b=getPoint(a);

  if(b->left!=NIL) c=b->left;
  else c=b->right;

  if(c!=NIL) c->parent=b->parent;

  if(b->parent==NIL) root=c->parent;

  else if(b==b->parent->left) b->parent->left=c;
  else b->parent->right=c;

  if(b!=a) a->key=b->key;
}

struct Node * getPoint(struct Node *a){
  struct Node *b;
  if(a->right != NIL) return getmin(a->right);

  b=a->parent;
  while(b!=NIL && a==b->right){
    a=b;
    b=b->parent;
  }
  return b;
}

struct Node * getmin(struct Node *a){
  while(a->left != NIL) a=a->left;
  return a;
}