/* avl.c

 * 

 * Copyright (C) 1998, 1999, 2000, 2001, 2002, 2004 Free Software

 * Foundation, Inc.

 * Copyright (C) 2014 Patrick Alken

 * 

 * This program is free software; you can redistribute it and/or modify

 * it under the terms of the GNU General Public License as published by

 * the Free Software Foundation; either version 3 of the License, or (at

 * your option) any later version.

 * 

 * This program is distributed in the hope that it will be useful, but

 * WITHOUT ANY WARRANTY; without even the implied warranty of

 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * General Public License for more details.

 * 

 * You should have received a copy of the GNU General Public License

 * along with this program; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

 */

/*

 * This code is originally from GNU libavl. The memory management

 * was slightly modified for use with preallocating GSL sparse matrices

 *

 * The allocator->libavl_malloc function is called only for creating

 * a new avl_node (tree node). This allows GSL to preallocate some number

 * of avl_node structs and then return pointers to them while the tree

 * is being assembled, avoiding multiple malloc calls

 */

#include <stdio.h>

#include <stdlib.h>

#include <stddef.h>

#include <string.h>

/* Function types. */

typedef int avl_comparison_func (const void *avl_a, const void *avl_b,

                                 void *avl_param);

typedef void avl_item_func (void *avl_item, void *avl_param);

typedef void *avl_copy_func (void *avl_item, void *avl_param);

/* Memory allocator. */

struct libavl_allocator

  {

    void *(*libavl_malloc) (size_t libavl_size, void *param);

    void (*libavl_free) (void *libavl_block, void *param);

  };

/* Default memory allocator. */

static struct libavl_allocator avl_allocator_default;

static void *avl_malloc (size_t, void *param);

static void avl_free (void *, void *param);

/* Maximum AVL tree height. */

#ifndef AVL_MAX_HEIGHT

#define AVL_MAX_HEIGHT 92

#endif

/* An AVL tree node. */

struct avl_node

  {

    struct avl_node *avl_link[2];  /* Subtrees. */

    void *avl_data;                /* Pointer to data. */

    signed char avl_balance;       /* Balance factor. */

  };

/* Tree data structure. */

struct avl_table

  {

    struct avl_node *avl_root;          /* Tree's root. */

    avl_comparison_func *avl_compare;   /* Comparison function. */

    void *avl_param;                    /* Extra argument to |avl_compare|. */

    struct libavl_allocator *avl_alloc; /* Memory allocator. */

    size_t avl_count;                   /* Number of items in tree. */

    unsigned long avl_generation;       /* Generation number. */

  };

/* Table functions. */

static struct avl_table *avl_create (avl_comparison_func *, void *,

                                     struct libavl_allocator *);

static struct avl_table *avl_copy (const struct avl_table *, avl_copy_func *,

                                   avl_item_func *, struct libavl_allocator *);

static void avl_empty (struct avl_table *, avl_item_func *);

static void avl_destroy (struct avl_table *, avl_item_func *);

static void **avl_probe (struct avl_table *, void *);

static void *avl_insert (struct avl_table *, void *);

static void *avl_replace (struct avl_table *, void *);

static void *avl_delete (struct avl_table *, const void *);

static void *avl_find (const struct avl_table *, const void *);

/* Creates and returns a new table

   with comparison function |compare| using parameter |param|

   and memory allocator |allocator|.

   Returns |NULL| if memory allocation failed. */

static struct avl_table *

avl_create (avl_comparison_func *compare, void *param,

            struct libavl_allocator *allocator)

{

  struct avl_table *tree;

  if (allocator == NULL)

    allocator = &avl_allocator_default;

  /*tree = allocator->libavl_malloc (allocator, sizeof *tree);*/

  tree = malloc(sizeof *tree);

  if (tree == NULL)

    return NULL;

  tree->avl_root = NULL;

  tree->avl_compare = compare;

  tree->avl_param = param;

  tree->avl_alloc = allocator;

  tree->avl_count = 0;

  tree->avl_generation = 0;

  return tree;

}

/* Search |tree| for an item matching |item|, and return it if found.

   Otherwise return |NULL|. */

static void *

avl_find (const struct avl_table *tree, const void *item)

{

  const struct avl_node *p;

  for (p = tree->avl_root; p != NULL; )

    {

      int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param);

      if (cmp < 0)

        p = p->avl_link[0];

      else if (cmp > 0)

        p = p->avl_link[1];

      else /* |cmp == 0| */

        return p->avl_data;

    }

  return NULL;

}

/* Inserts |item| into |tree| and returns a pointer to |item|'s address.

   If a duplicate item is found in the tree,

   returns a pointer to the duplicate without inserting |item|.

   Returns |NULL| in case of memory allocation failure. */

static void **

avl_probe (struct avl_table *tree, void *item)

{

  struct avl_node *y, *z; /* Top node to update balance factor, and parent. */

  struct avl_node *p, *q; /* Iterator, and parent. */

  struct avl_node *n;     /* Newly inserted node. */

  struct avl_node *w;     /* New root of rebalanced subtree. */

  int dir;                /* Direction to descend. */

  unsigned char da[AVL_MAX_HEIGHT]; /* Cached comparison results. */

  int k = 0;              /* Number of cached results. */

  z = (struct avl_node *) &tree->avl_root;

  y = tree->avl_root;

  dir = 0;

  for (q = z, p = y; p != NULL; q = p, p = p->avl_link[dir])

    {

      int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param);

      if (cmp == 0)

        return &p->avl_data;

      if (p->avl_balance != 0)

        z = q, y = p, k = 0;

      da[k++] = dir = cmp > 0;

    }

  n = q->avl_link[dir] =

    tree->avl_alloc->libavl_malloc (sizeof *n, tree->avl_param);

  if (n == NULL)

    return NULL;

  tree->avl_count++;

  n->avl_data = item;

  n->avl_link[0] = n->avl_link[1] = NULL;

  n->avl_balance = 0;

  if (y == NULL)

    return &n->avl_data;

  for (p = y, k = 0; p != n; p = p->avl_link[da[k]], k++)

    if (da[k] == 0)

      p->avl_balance--;

    else

      p->avl_balance++;

  if (y->avl_balance == -2)

    {

      struct avl_node *x = y->avl_link[0];

      if (x->avl_balance == -1)

        {

          w = x;

          y->avl_link[0] = x->avl_link[1];

          x->avl_link[1] = y;

          x->avl_balance = y->avl_balance = 0;

        }

      else

        {

          w = x->avl_link[1];

          x->avl_link[1] = w->avl_link[0];

          w->avl_link[0] = x;

          y->avl_link[0] = w->avl_link[1];

          w->avl_link[1] = y;

          if (w->avl_balance == -1)

            x->avl_balance = 0, y->avl_balance = +1;

          else if (w->avl_balance == 0)

            x->avl_balance = y->avl_balance = 0;

          else /* |w->avl_balance == +1| */

            x->avl_balance = -1, y->avl_balance = 0;

          w->avl_balance = 0;

        }

    }

  else if (y->avl_balance == +2)

    {

      struct avl_node *x = y->avl_link[1];

      if (x->avl_balance == +1)

        {

          w = x;

          y->avl_link[1] = x->avl_link[0];

          x->avl_link[0] = y;

          x->avl_balance = y->avl_balance = 0;

        }

      else

        {

          w = x->avl_link[0];

          x->avl_link[0] = w->avl_link[1];

          w->avl_link[1] = x;

          y->avl_link[1] = w->avl_link[0];

          w->avl_link[0] = y;

          if (w->avl_balance == +1)

            x->avl_balance = 0, y->avl_balance = -1;

          else if (w->avl_balance == 0)

            x->avl_balance = y->avl_balance = 0;

          else /* |w->avl_balance == -1| */

            x->avl_balance = +1, y->avl_balance = 0;

          w->avl_balance = 0;

        }

    }

  else

    return &n->avl_data;

  z->avl_link[y != z->avl_link[0]] = w;

  tree->avl_generation++;

  return &n->avl_data;

}

/* Inserts |item| into |table|.

   Returns |NULL| if |item| was successfully inserted

   or if a memory allocation error occurred.

   Otherwise, returns the duplicate item. */

static void *

avl_insert (struct avl_table *table, void *item)

{

  void **p = avl_probe (table, item);

  return p == NULL || *p == item ? NULL : *p;

}

/* Inserts |item| into |table|, replacing any duplicate item.

   Returns |NULL| if |item| was inserted without replacing a duplicate,

   or if a memory allocation error occurred.

   Otherwise, returns the item that was replaced. */

static void *

avl_replace (struct avl_table *table, void *item)

{

  void **p = avl_probe (table, item);

  if (p == NULL || *p == item)

    return NULL;

  else

    {

      void *r = *p;

      *p = item;

      return r;

    }

}

/* Deletes from |tree| and returns an item matching |item|.

   Returns a null pointer if no matching item found. */

static void *

avl_delete (struct avl_table *tree, const void *item)

{

  /* Stack of nodes. */

  struct avl_node *pa[AVL_MAX_HEIGHT]; /* Nodes. */

  unsigned char da[AVL_MAX_HEIGHT];    /* |avl_link[]| indexes. */

  int k;                               /* Stack pointer. */

  struct avl_node *p;   /* Traverses tree to find node to delete. */

  int cmp;              /* Result of comparison between |item| and |p|. */

  k = 0;

  p = (struct avl_node *) &tree->avl_root;

  for (cmp = -1; cmp != 0;

       cmp = tree->avl_compare (item, p->avl_data, tree->avl_param))

    {

      int dir = cmp > 0;

      pa[k] = p;

      da[k++] = dir;

      p = p->avl_link[dir];

      if (p == NULL)

        return NULL;

    }

  item = p->avl_data;

  if (p->avl_link[1] == NULL)

    pa[k - 1]->avl_link[da[k - 1]] = p->avl_link[0];

  else

    {

      struct avl_node *r = p->avl_link[1];

      if (r->avl_link[0] == NULL)

        {

          r->avl_link[0] = p->avl_link[0];

          r->avl_balance = p->avl_balance;

          pa[k - 1]->avl_link[da[k - 1]] = r;

          da[k] = 1;

          pa[k++] = r;

        }

      else

        {

          struct avl_node *s;

          int j = k++;

          for (;;)

            {

              da[k] = 0;

              pa[k++] = r;

              s = r->avl_link[0];

              if (s->avl_link[0] == NULL)

                break;

              r = s;

            }

          s->avl_link[0] = p->avl_link[0];

          r->avl_link[0] = s->avl_link[1];

          s->avl_link[1] = p->avl_link[1];

          s->avl_balance = p->avl_balance;

          pa[j - 1]->avl_link[da[j - 1]] = s;

          da[j] = 1;

          pa[j] = s;

        }

    }

  tree->avl_alloc->libavl_free (p, tree->avl_param);

  while (--k > 0)

    {

      struct avl_node *y = pa[k];

      if (da[k] == 0)

        {

          y->avl_balance++;

          if (y->avl_balance == +1)

            break;

          else if (y->avl_balance == +2)

            {

              struct avl_node *x = y->avl_link[1];

              if (x->avl_balance == -1)

                {

                  struct avl_node *w;

                  w = x->avl_link[0];

                  x->avl_link[0] = w->avl_link[1];

                  w->avl_link[1] = x;

                  y->avl_link[1] = w->avl_link[0];

                  w->avl_link[0] = y;

                  if (w->avl_balance == +1)

                    x->avl_balance = 0, y->avl_balance = -1;

                  else if (w->avl_balance == 0)

                    x->avl_balance = y->avl_balance = 0;

                  else /* |w->avl_balance == -1| */

                    x->avl_balance = +1, y->avl_balance = 0;

                  w->avl_balance = 0;

                  pa[k - 1]->avl_link[da[k - 1]] = w;

                }

              else

                {

                  y->avl_link[1] = x->avl_link[0];

                  x->avl_link[0] = y;

                  pa[k - 1]->avl_link[da[k - 1]] = x;

                  if (x->avl_balance == 0)

                    {

                      x->avl_balance = -1;

                      y->avl_balance = +1;

                      break;

                    }

                  else

                    x->avl_balance = y->avl_balance = 0;

                }

            }

        }

      else

        {

          y->avl_balance--;

          if (y->avl_balance == -1)

            break;

          else if (y->avl_balance == -2)

            {

              struct avl_node *x = y->avl_link[0];

              if (x->avl_balance == +1)

                {

                  struct avl_node *w;

                  w = x->avl_link[1];

                  x->avl_link[1] = w->avl_link[0];

                  w->avl_link[0] = x;

                  y->avl_link[0] = w->avl_link[1];

                  w->avl_link[1] = y;

                  if (w->avl_balance == -1)

                    x->avl_balance = 0, y->avl_balance = +1;

                  else if (w->avl_balance == 0)

                    x->avl_balance = y->avl_balance = 0;

                  else /* |w->avl_balance == +1| */

                    x->avl_balance = -1, y->avl_balance = 0;

                  w->avl_balance = 0;

                  pa[k - 1]->avl_link[da[k - 1]] = w;

                }

              else

                {

                  y->avl_link[0] = x->avl_link[1];

                  x->avl_link[1] = y;

                  pa[k - 1]->avl_link[da[k - 1]] = x;

                  if (x->avl_balance == 0)

                    {

                      x->avl_balance = +1;

                      y->avl_balance = -1;

                      break;

                    }

                  else

                    x->avl_balance = y->avl_balance = 0;

                }

            }

        }

    }

  tree->avl_count--;

  tree->avl_generation++;

  return (void *) item;

}

/* Destroys |new| with |avl_destroy (new, destroy)|,

   first setting right links of nodes in |stack| within |new|

   to null pointers to avoid touching uninitialized data. */

static void

copy_error_recovery (struct avl_node **stack, int height,

                     struct avl_table *new, avl_item_func *destroy)

{

  for (; height > 2; height -= 2)

    stack[height - 1]->avl_link[1] = NULL;

  avl_destroy (new, destroy);

}

/* Copies |org| to a newly created tree, which is returned.

   If |copy != NULL|, each data item in |org| is first passed to |copy|,

   and the return values are inserted into the tree,

   with |NULL| return values taken as indications of failure.

   On failure, destroys the partially created new tree,

   applying |destroy|, if non-null, to each item in the new tree so far,

   and returns |NULL|.

   If |allocator != NULL|, it is used for allocation in the new tree.

   Otherwise, the same allocator used for |org| is used. */

static struct avl_table *

avl_copy (const struct avl_table *org, avl_copy_func *copy,

          avl_item_func *destroy, struct libavl_allocator *allocator)

{

  struct avl_node *stack[2 * (AVL_MAX_HEIGHT + 1)];

  int height = 0;

  struct avl_table *new;

  const struct avl_node *x;

  struct avl_node *y;

  new = avl_create (org->avl_compare, org->avl_param,

                    allocator != NULL ? allocator : org->avl_alloc);

  if (new == NULL)

    return NULL;

  new->avl_count = org->avl_count;

  if (new->avl_count == 0)

    return new;

  x = (const struct avl_node *) &org->avl_root;

  y = (struct avl_node *) &new->avl_root;

  for (;;)

    {

      while (x->avl_link[0] != NULL)

        {

          y->avl_link[0] =

            new->avl_alloc->libavl_malloc (sizeof *y->avl_link[0],

                                           new->avl_param);

          if (y->avl_link[0] == NULL)

            {

              if (y != (struct avl_node *) &new->avl_root)

                {

                  y->avl_data = NULL;

                  y->avl_link[1] = NULL;

                }

              copy_error_recovery (stack, height, new, destroy);

              return NULL;

            }

          stack[height++] = (struct avl_node *) x;

          stack[height++] = y;

          x = x->avl_link[0];

          y = y->avl_link[0];

        }

      y->avl_link[0] = NULL;

      for (;;)

        {

          y->avl_balance = x->avl_balance;

          if (copy == NULL)

            y->avl_data = x->avl_data;

          else

            {

              y->avl_data = copy (x->avl_data, org->avl_param);

              if (y->avl_data == NULL)

                {

                  y->avl_link[1] = NULL;

                  copy_error_recovery (stack, height, new, destroy);

                  return NULL;

                }

            }

          if (x->avl_link[1] != NULL)

            {

              y->avl_link[1] =

                new->avl_alloc->libavl_malloc (sizeof *y->avl_link[1],

                                               new->avl_param);

              if (y->avl_link[1] == NULL)

                {

                  copy_error_recovery (stack, height, new, destroy);

                  return NULL;

                }

              x = x->avl_link[1];

              y = y->avl_link[1];

              break;

            }

          else

            y->avl_link[1] = NULL;

          if (height <= 2)

            return new;

          y = stack[--height];

          x = stack[--height];

        }

    }

}

/* empty tree (delete all nodes) but do not free the tree itself */

static void

avl_empty (struct avl_table *tree, avl_item_func *destroy)

{

  struct avl_node *p, *q;

  for (p = tree->avl_root; p != NULL; p = q)

    if (p->avl_link[0] == NULL)

      {

        q = p->avl_link[1];

        if (destroy != NULL && p->avl_data != NULL)

          destroy (p->avl_data, tree->avl_param);

        tree->avl_alloc->libavl_free (p, tree->avl_param);

      }

    else

      {

        q = p->avl_link[0];

        p->avl_link[0] = q->avl_link[1];

        q->avl_link[1] = p;

      }

  tree->avl_root = NULL;

  tree->avl_count = 0;

  tree->avl_generation = 0;

}

/* Frees storage allocated for |tree|.

   If |destroy != NULL|, applies it to each data item in inorder. */

static void

avl_destroy (struct avl_table *tree, avl_item_func *destroy)

{

  avl_empty(tree, destroy);

  free(tree);

}

/* Allocates |size| bytes of space using |malloc()|.

   Returns a null pointer if allocation fails. */

static void *

avl_malloc (size_t size, void *param)

{

  (void)param; /* avoid unused parameter warning */

  return malloc (size);

}

/* Frees |block|. */

static void

avl_free (void *block, void *param)

{

  (void)param; /* avoid unused parameter warning */

  free (block);

}

/* Default memory allocator that uses |malloc()| and |free()|. */

static struct libavl_allocator avl_allocator_default =

  {

    avl_malloc,

    avl_free

  };