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 *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;
#define NIL NULL
 
Node root;

Node treeMinimum(Node x){
  while(x->left != NIL)
    {
      x = x->left;
    }
  return x;
}
 
Node treeSearch(Node u, int k){
  if(u == NIL || k == u->key)
    {
      return u;
    }
 
  if(k < u->key)
    {
      return treeSearch(u->left, k);
    }
  else
    {
      return treeSearch(u->right, k);
    }
}
 
Node treeSuccessor(Node x){
  Node y;
 
  if(x->right != NIL)
    {
      return treeMinimum(x->right);
    }
  y = x->parent;

  while(y != NIL && x == y->right)
    {
      x = y;
      y = y->parent;
    }

  return y;
}
 
void treeDelete(Node z){
  Node y; // node to be deleted
  Node x; // child of y
 
  if(z->left == NIL || z->right == NIL) y = z;
  else y = treeSuccessor(z);
 
  if(y->left != NIL) x = y->left;
  else x = y->right;
 
  if(x != NIL) x->parent = y->parent;
 
  if(y->parent == NIL) root = x;
  else if(y == y->parent->left) y->parent->left = x;
  else y->parent->right = x;

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

}
 
void insert(int k){
  Node y = NIL; // parent of x
  Node x = root;
  Node z;
 
  z = malloc(sizeof(struct node));
  z->key = k;
  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; 
}
 
void inorder(Node u){
  if(u != NIL)
    {
      inorder(u->left);
      printf(" %d", u->key);
      inorder(u->right);
    }
}
 
void preorder(Node u){
  if(u != NIL)
    {
      printf(" %d", u->key);
      preorder(u->left);
      preorder(u->right);
    }
} 
 
int main()
{
  int n, i, x;
  char com[20];
  scanf("%d", &n);
   
  for ( i = 0; i < n; i++ )
    {
      scanf("%s", com);
      if ( com[0] == 'f' )
	{
	  scanf("%d", &x);
	  Node t = treeSearch(root, x);
	  if ( t != NIL ) printf("yes\n");
	  else printf("no\n");
	}
      else if ( com[0] == 'i' )
	{
	  scanf("%d", &x);
	  insert(x);
	} 
      else if ( com[0] == 'p' )
	{
	  inorder(root);
	  printf("\n");
	  preorder(root);
	  printf("\n");
	}
      else if ( com[0] == 'd' )
	{
	  scanf("%d", &x);
	  treeDelete(treeSearch(root, x));
	}
    }
   
  return 0;
}