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){
  while(x->right != NIL)
    x = x->right;
  return x;
}

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;
}

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);
  }
}

  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;
      }
    else
      {
	y->right = z;
      }
  }

  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;
  }