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 treeMaximum(Node x)
  {


  }
*/
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;
    }
  free(y);
}
Node treeSearch(Node u, int k)
{
  while((u!=NIL)&&(k!=u->key))
    {
      if(k<u->key)
	{
	  u=u->left;
	}
      else
	{
	  u=u->right;
	}
    }
  return u;
}
void insert(int k)
{
  Node y=NIL;
  Node x=root;
  Node z;
  z=malloc(sizeof(struct node));
  z->key=k;
  z->left=NIL;
  z->right=NIL;

  while (x!=NIL)
    {
      y=x; // 親を設定
      if (z->key<x->key)
	{
	  x=x->left; // 左の子へ移動
	}
      else
	{
	  x=x->right; // 右の子へ移動
	}
    }
  z->parent=y;
  if (y== NIL)
    {
      // T が空の場合
      root=z;
    }
  else if (z->key<y->key)
    {
      y->left=z; // z を y の左の子にする
    }
  else
    {
      y->right=z; // z を y の右の子にする
    }
}

void inorder(Node u)
{
  if(u==NIL)
    {
      return;
    }
  inorder(u->left);
  printf(" %d",u->key);
  inorder(u->right);
}
void preorder(Node u)
{
  if(u==NIL)
    {
      return;
    }
  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;
}
/*
  insert(T, z)
  {
  y = NIL; // x の親
  x = 'T の根';
  while (x ≠ NIL)
  {
  y = x; // 親を設定
  if (z.key < x.key)
  {
  x = x.left; // 左の子へ移動
  else
  {
  x = x.right; // 右の子へ移動
  z.p = y;
  }
  }
  if (y == NIL)
  {
  // T が空の場合
  'T の根' = z;
  }
  else if (z.key < y.key)
  {
  y.left = z; // z を y の左の子にする
  }
  else
  {
  y.right = z; // z を y の右の子にする
  }
  }
  }

  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));
  }
  }
 
*/