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{
  struct node *par;
  struct node *left;
  struct node *right;
  int key;
};
typedef struct node* NodePointer;
 
void init(void);
NodePointer makenode(int);
void insert(int,NodePointer);
void preorder(NodePointer);
void inorder(NodePointer);
NodePointer find(int,NodePointer);
void delete_node(NodePointer); 
NodePointer tree_successor(NodePointer);
NodePointer tree_minimum(NodePointer);

NodePointer head, tail;
 
int main(){
  char str[7];
  int n,k;
  NodePointer x;
 
  init();
  scanf("%d" ,&n);
  while(n--){
    scanf("%s" ,str);
 
    if(str[0] == 'i'){
      scanf("%d" ,&k);
      insert(k, head);
    }else if(str[0] == 'p'){
      inorder(head->right);
      puts("");
      preorder(head->right);
      puts("");
    }else if(str[0] == 'f'){
      scanf("%d" ,&k);
      if(find(k,head->right) != NULL){
        printf("yes\n");
      }else{
        printf("no\n");
      }
    }else{
      scanf("%d" ,&k);
      x = find(k,head->right);
      delete_node(x);
    }
  }
 
  return 0;
}
 
void init(){
  head = makenode(-1);
  tail = makenode(-1);
  head->par = head;;
  head->right = tail;
  head->left = tail;
}
 
NodePointer makenode(int k){
  NodePointer x;
 
  x = malloc(sizeof(struct node));
  x->key = k;
  x->left = x->right = tail;
 
  return x;
}
 
void insert(int k, NodePointer p){
  if(k < p->key){
    if(p->left == tail){
      p->left = makenode(k);
      p->left->par = p;
    }else{
      insert(k,p->left);
    }
  }else{
    if(p->right == tail){
      p->right = makenode(k);
      p->right->par = p;
    }else{
      insert(k,p->right);
    }
  }
}
 
void preorder(NodePointer node){
  if(node != tail){
    printf(" %d", node->key);
    preorder(node->left);
    preorder(node->right);
  }
}
 
void inorder(NodePointer node){
  if(node != tail){
    inorder(node->left);
    printf(" %d", node->key);
    inorder(node->right);
  }
}
 
NodePointer find(int k,NodePointer node){
  if(node == tail){
    return NULL;
  }
 
  if(node->key == k){
    return node;
  }else if(node->key < k){
    return find(k,node->right);
  }else{
    return find(k,node->left);
  }
}

void delete_node(NodePointer node){
  NodePointer x,y;
  if(node->left == tail || node->right == tail){
    y = node;
  }else{
    y = tree_successor(node);
  }

  if(node->left != tail){
    x = y->left;
  }else{
    x = y->right;
  }

  if(x != tail){
    x->par = y->par;
  }
  if(y->par == tail){
    node->par = x;
  }else if(y == y->par->left){
    y->par->left = x;
  }else{
    y->par->right = x;
  }

  if(y != node){
    node->key = y->key;
  }
}

NodePointer tree_successor(NodePointer x){
  NodePointer y;

  if(x->right != tail){
    return tree_minimum(x->right);
  }

  y = x->par;
  while(y != tail && x == y->right){
    x = y;
    y = y->par;
  }

  return y;
}

NodePointer tree_minimum(NodePointer x){
  while(x->left != tail){
    x = x->left;
  }
  return x;
}