/*
**
** BU CAS CS520, Fall 2010
**
** Instructor: Hongwei Xi (hwxi AT cs DOT bu DOT edu)
**
** Exercise 3 in Assignment 1
**
*/

/* ****** ****** */

#define RED 1
#define BLK 0

//
// Here is the datatype for red-black trees
//
typedef struct rbtree_struct {
  int color ; /* RED: 1; BLK: 0 */
  int key ; char *itm ;
  struct rbtree_struct *parent ;
  struct rbtree_struct *left, *right ;
} rbtree ;

/* ****** ****** */

int rbtree_color (rbtree *rbt) {
  if (!rbt) return BLK ; else return rbt->color ;
} /* end of [rbtree_color] */


/*
// [rbtree_check] checks whether [rbt] meets all the
// required constraints for being a red-black tree.
//
// 1. the black height of [rbt] is returned if [rbt]
//    is a valid red-black tree
// 2. -1 is returned if [rbt] is not a valid red-black
//    tree
//
*/
int rbtree_check (rbtree *rbt) {
  int key ;
  int l_clr, r_clr ;
  int l_ret, r_ret ;
  rbtree *l_rbt, *r_rbt ;

  if (!rbt) return 0 ;

  key = rbt->key ;
  l_rbt = rbt->left ; r_rbt = rbt->right ;

  if (l_rbt) {
    if (l_rbt->parent != rbt) return -1 ;   
    if (l_rbt->key > key) return -1 ; // ill-ordered
  }

  if (r_rbt) {
    if (r_rbt->parent != rbt) return -1 ;   
    if (r_rbt->key < key) return -1 ; // ill-ordered
  }

  if (rbt->color == RED) {
    if (rbtree_color (l_rbt) == RED) return -1 ;
    if (rbtree_color (r_rbt) == RED) return -1 ;
  }

  l_ret = rbtree_check (l_rbt) ; if (l_ret < 0) return l_ret ;
  r_ret = rbtree_check (r_rbt) ; if (r_ret < 0) return r_ret ;

  if (l_ret != r_ret) return -1 ;

  if (rbt->color == BLK)
    return 1 + l_ret ; // inc only if [rbt] is black
  else
    return l_ret ;
  /* end of [if] */

} /* end of [rbtree_check] */

/* ****** ****** */

//
// [rbtree_insert] returns a null pointer if [key] is already in [rbt];
// otherwise, a red-black tree is returned that extends [rbt] with a mapping
// from [key] to [itm].
//
extern rbtree *rbtree_insert (rbtree *rbt, int key, char *itm) ;

/* ****** ****** */

//
// This one can be highly challenging!
//

//
// [rbtree_remove] returns a null pointer if [key] is not in [rbt];
// otherwise, a red-black tree is returned that removes from [rbt] a mapping
// from [key] to some item.
//
extern rbtree *rbtree_remove (rbtree *rbt, int key) ;

/* ****** ****** */

/* end of [rbtree.c] */