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>
 
#define NIL NULL
 
struct node{
  struct node *l;
  struct node *r;
  struct node *p;
  int key;
};
 
typedef struct node * Node;
 
Node root;

void Preorder(Node );
void Inorder(Node );
void insert(int );
Node Search(Node ,int );
Node Minimum(Node );
Node Successor(Node );
void Delete(Node );


main(){
  int n, i, x;
  char str[20];
   
  scanf("%d",&n);
 
  for ( i = 0; i < n; i++ ){
    scanf("%s",str);
 
    if(str[0]=='i'){
      scanf("%d",&x);
      insert(x);
    } 
    else if(str[0]=='p'){
      Inorder(root);
      printf("\n");
       
      Preorder(root);
      printf("\n");
    }
    else if(str[0]=='f'){
      scanf("%d",&x);
      Node s=Search(root,x);
      if (s!= NIL ) printf("yes\n");
      else printf("no\n");
    }
    else if(str[0]=='d'){
      scanf("%d",&x);
      Delete(Search(root, x));
    }
  }
  return 0;
}

Node Successor(Node t){
  if(t->r!=NIL)return Minimum(t->r);
  Node y=t->p;
  while(y!=NIL && t==y->r){
    t=y;
    y=y->p;
  }
  return y;
}
 
void Delete(Node z){
  Node y;
  Node x;
 
  if(z->l==NIL || z->r==NIL) y=z;
  else y=Successor(z);
 
  if(y->l!=NIL) x=y->l;
  else x=y->r;
 
  if(x!=NIL) x->p=y->p;
 
  if(y->p==NIL)root=x;
  else if(y==y->p->l) y->p->l=x;
  else  y->p->r=x;
 
  if(y!=z)z->key=y->key;
}

void insert(int k){
  Node y=NIL;
  Node x=root;
  Node z;
 
  z = malloc(sizeof(struct node));
  z->key=k;
  z->l=NIL;
  z->r=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;
}
 
Node Search(Node t,int k){
  if(t==NIL || k==t->key) return t;
  if(k<t->key) return Search(t->l,k);
  else return Search(t->r,k);
}
 
Node Minimum(Node t){
  while(t->l!=NIL){
    t=t->l;
  }
  return t;
}

void Preorder(Node t){
  printf(" %d",t->key);
  if(t!=NIL){
    if(t->l!=NIL)Preorder(t->l);
    if(t->r!=NIL)Preorder(t->r);
  }
}
 
void Inorder(Node t){
   
  if(t!=NIL){
    if(t->l!=NIL){
      Inorder(t->l);
      }
    printf(" %d",t->key);
     
    if(t->r!=NIL){
      Inorder(t->r);
      }
  }
}