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 *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;

Node root;

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; 
      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; // 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);

}
Node findkey(int key)
{
  Node X=root;
  
  while(1)
  {
    
      if(X==NIL)return NIL;
      if(X->key==key)return X;
      if(X->key < key)X=X->right;
      else X=X->left;
    }
}

Node Successor(Node A)
{
  Node X;
  Node B;
 
  // if(A->right!=NIL)
  // {
      A=A->right;
      while(A->left!=NIL)A=A->left;

      return A;
      //}
      /*else
    {
      A=A->parent;
      while(1)
	{
	  if(A==A->parent->left)return A->parent;
	  A=A->parent;
	}
    }*/
}

void delete(Node X)
{
  
  Node B;
  Node child;

  

  if(X->right==NIL && X->left==NIL)///////>< ><//
    {
     
      if(X->parent->right==X)X->parent->right=NIL;
      else X->parent->left=NIL;
       free(X);

      
    }
  
  else if(X->right!=NIL && X->left!=NIL)//o o//ココがおかしい
    {
       B= Successor(X);
       
       X->key=B->key;
      
       delete(B);
    }


  else//o ><
    {
     
      
	
      if(X->right==NIL)child=X->left;
      else child=X->right;

      if(X->parent==NIL)
	{
	  child->parent=NIL;
	  return ;
	}
     
      if(X->parent->key < X->key)X->parent->right=child;
      else X->parent->left=child;

      child->parent=X->parent;

 free(X);

    }


 
}


int main()
{
  int n, i, x;
  char com[20];
  scanf("%d", &n);
  int count=0;
  
  for ( i = 0; i < n; i++ )
    {
      //printf("----%d\n",i);///////////////

      scanf("%s", com);
      if ( com[0] == 'i' )
        {
          scanf("%d", &x);
          insert(x);
        }
   else if (com[0] == 'f')//FIND
        {
          scanf("%d", &x);
          if(count)printf("\n");
          if(findkey(x)!=NIL)printf("yes\n");
          else printf("no\n");
        }
      else if(com[0] == 'd')
        {
          scanf("%d", &x);
          delete(findkey(x));

        }
      else if(com[0] == 'p')//PRINT
        {
	   inorder(root);
          printf("\n");
          preorder(root);
          printf("\n");
        }
    }
  return 0;
}