/* GLIB - Library of useful routines for C programming
 * Copyright (C) 1995-1997  Peter Mattis, Spencer Kimball and Josh MacDonald
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2 of the License, or (at your option) any later version.
 *
 * This library 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
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the
 * Free Software Foundation, Inc., 59 Temple Place - Suite 330,
 * Boston, MA 02111-1307, USA.
 */

/*
 * Modified by the GLib Team and others 1997-2000.  See the AUTHORS
 * file for a list of people on the GLib Team.  See the ChangeLog
 * files for a list of changes.  These files are distributed with
 * GLib at ftp://ftp.gtk.org/pub/gtk/. 
 */

/* 
 * MT safe
 */

#include "config.h"

#include "gtree.h"

#include "gatomic.h"
#include "gtestutils.h"

/**
 * SECTION: trees-binary
 * @title: Balanced Binary Trees
 * @short_description: a sorted collection of key/value pairs optimized
 *                     for searching and traversing in order
 *
 * The #GTree structure and its associated functions provide a sorted
 * collection of key/value pairs optimized for searching and traversing
 * in order.
 *
 * To create a new #GTree use g_tree_new().
 *
 * To insert a key/value pair into a #GTree use g_tree_insert().
 *
 * To lookup the value corresponding to a given key, use
 * g_tree_lookup() and g_tree_lookup_extended().
 *
 * To find out the number of nodes in a #GTree, use g_tree_nnodes(). To
 * get the height of a #GTree, use g_tree_height().
 *
 * To traverse a #GTree, calling a function for each node visited in
 * the traversal, use g_tree_foreach().
 *
 * To remove a key/value pair use g_tree_remove().
 *
 * To destroy a #GTree, use g_tree_destroy().
 **/

#undef G_TREE_DEBUG

#define MAX_GTREE_HEIGHT 40

typedef struct _GTreeNode  GTreeNode;

/**
 * GTree:
 *
 * The <structname>GTree</structname> struct is an opaque data
 * structure representing a <link
 * linkend="glib-Balanced-Binary-Trees">Balanced Binary Tree</link>. It
 * should be accessed only by using the following functions.
 **/
struct _GTree
{
  GTreeNode        *root;
  GCompareDataFunc  key_compare;
  GDestroyNotify    key_destroy_func;
  GDestroyNotify    value_destroy_func;
  gpointer          key_compare_data;
  guint             nnodes;
  gint              ref_count;
};

struct _GTreeNode
{
  gpointer   key;         /* key for this node */
  gpointer   value;       /* value stored at this node */
  GTreeNode *left;        /* left subtree */
  GTreeNode *right;       /* right subtree */
  gint8      balance;     /* height (left) - height (right) */
  guint8     left_child;  
  guint8     right_child;
};


static GTreeNode* g_tree_node_new                   (gpointer       key,
						     gpointer       value);
static void       g_tree_insert_internal            (GTree         *tree,
						     gpointer       key,
						     gpointer       value,
						     gboolean       replace);
static gboolean   g_tree_remove_internal            (GTree         *tree,
						     gconstpointer  key,
						     gboolean       steal);
static GTreeNode* g_tree_node_balance               (GTreeNode     *node);
static GTreeNode *g_tree_find_node                  (GTree         *tree,
						     gconstpointer  key);
static gint       g_tree_node_pre_order             (GTreeNode     *node,
						     GTraverseFunc  traverse_func,
						     gpointer       data);
static gint       g_tree_node_in_order              (GTreeNode     *node,
						     GTraverseFunc  traverse_func,
						     gpointer       data);
static gint       g_tree_node_post_order            (GTreeNode     *node,
						     GTraverseFunc  traverse_func,
						     gpointer       data);
static gpointer   g_tree_node_search                (GTreeNode     *node,
						     GCompareFunc   search_func,
						     gconstpointer  data);
static GTreeNode* g_tree_node_rotate_left           (GTreeNode     *node);
static GTreeNode* g_tree_node_rotate_right          (GTreeNode     *node);
#ifdef G_TREE_DEBUG
static void       g_tree_node_check                 (GTreeNode     *node);
#endif


static GTreeNode*
g_tree_node_new (gpointer key,
		 gpointer value)
{
  GTreeNode *node = g_slice_new (GTreeNode);

  node->balance = 0;
  node->left = NULL;
  node->right = NULL;
  node->left_child = FALSE;
  node->right_child = FALSE;
  node->key = key;
  node->value = value;

  return node;
}

/**
 * g_tree_new:
 * @key_compare_func: the function used to order the nodes in the #GTree.
 *   It should return values similar to the standard strcmp() function -
 *   0 if the two arguments are equal, a negative value if the first argument 
 *   comes before the second, or a positive value if the first argument comes 
 *   after the second.
 * 
 * Creates a new #GTree.
 * 
 * Return value: a new #GTree.
 **/
GTree*
g_tree_new (GCompareFunc key_compare_func)
{
  g_return_val_if_fail (key_compare_func != NULL, NULL);

  return g_tree_new_full ((GCompareDataFunc) key_compare_func, NULL,
                          NULL, NULL);
}

/**
 * g_tree_new_with_data:
 * @key_compare_func: qsort()-style comparison function.
 * @key_compare_data: data to pass to comparison function.
 * 
 * Creates a new #GTree with a comparison function that accepts user data.
 * See g_tree_new() for more details.
 * 
 * Return value: a new #GTree.
 **/
GTree*
g_tree_new_with_data (GCompareDataFunc key_compare_func,
 		      gpointer         key_compare_data)
{
  g_return_val_if_fail (key_compare_func != NULL, NULL);
  
  return g_tree_new_full (key_compare_func, key_compare_data, 
 			  NULL, NULL);
}

/**
 * g_tree_new_full:
 * @key_compare_func: qsort()-style comparison function.
 * @key_compare_data: data to pass to comparison function.
 * @key_destroy_func: a function to free the memory allocated for the key 
 *   used when removing the entry from the #GTree or %NULL if you don't
 *   want to supply such a function.
 * @value_destroy_func: a function to free the memory allocated for the 
 *   value used when removing the entry from the #GTree or %NULL if you 
 *   don't want to supply such a function.
 * 
 * Creates a new #GTree like g_tree_new() and allows to specify functions 
 * to free the memory allocated for the key and value that get called when 
 * removing the entry from the #GTree.
 * 
 * Return value: a new #GTree.
 **/
GTree*	 
g_tree_new_full (GCompareDataFunc key_compare_func,
 		 gpointer         key_compare_data, 		 
                 GDestroyNotify   key_destroy_func,
 		 GDestroyNotify   value_destroy_func)
{
  GTree *tree;
  
  g_return_val_if_fail (key_compare_func != NULL, NULL);
  
  tree = g_slice_new (GTree);
  tree->root               = NULL;
  tree->key_compare        = key_compare_func;
  tree->key_destroy_func   = key_destroy_func;
  tree->value_destroy_func = value_destroy_func;
  tree->key_compare_data   = key_compare_data;
  tree->nnodes             = 0;
  tree->ref_count          = 1;
  
  return tree;
}

static inline GTreeNode *
g_tree_first_node (GTree *tree)
{
  GTreeNode *tmp;

  if (!tree->root)
    return NULL;

  tmp = tree->root;

  while (tmp->left_child)
    tmp = tmp->left;

  return tmp;
} 

static inline GTreeNode *
g_tree_node_previous (GTreeNode *node)
{
  GTreeNode *tmp;

  tmp = node->left;

  if (node->left_child)
    while (tmp->right_child)
      tmp = tmp->right;

  return tmp;
}
		  
static inline GTreeNode *
g_tree_node_next (GTreeNode *node)
{
  GTreeNode *tmp;

  tmp = node->right;

  if (node->right_child)
    while (tmp->left_child)
      tmp = tmp->left;

  return tmp;
}

static void
g_tree_remove_all (GTree *tree)
{
  GTreeNode *node;
  GTreeNode *next;

  g_return_if_fail (tree != NULL);

  node = g_tree_first_node (tree);

  while (node)
    {
      next = g_tree_node_next (node);

      if (tree->key_destroy_func)
	tree->key_destroy_func (node->key);
      if (tree->value_destroy_func)
	tree->value_destroy_func (node->value);
      g_slice_free (GTreeNode, node);

      node = next;
    }

  tree->root = NULL;
  tree->nnodes = 0;
}

/**
 * g_tree_ref:
 * @tree: a #GTree.
 *
 * Increments the reference count of @tree by one.  It is safe to call
 * this function from any thread.
 *
 * Return value: the passed in #GTree.
 *
 * Since: 2.22
 **/
GTree *
g_tree_ref (GTree *tree)
{
  g_return_val_if_fail (tree != NULL, NULL);

  g_atomic_int_inc (&tree->ref_count);

  return tree;
}

/**
 * g_tree_unref:
 * @tree: a #GTree.
 *
 * Decrements the reference count of @tree by one.  If the reference count
 * drops to 0, all keys and values will be destroyed (if destroy
 * functions were specified) and all memory allocated by @tree will be
 * released.
 *
 * It is safe to call this function from any thread.
 *
 * Since: 2.22
 **/
void
g_tree_unref (GTree *tree)
{
  g_return_if_fail (tree != NULL);

  if (g_atomic_int_dec_and_test (&tree->ref_count))
    {
      g_tree_remove_all (tree);
      g_slice_free (GTree, tree);
    }
}

/**
 * g_tree_destroy:
 * @tree: a #GTree.
 * 
 * Removes all keys and values from the #GTree and decreases its
 * reference count by one. If keys and/or values are dynamically
 * allocated, you should either free them first or create the #GTree
 * using g_tree_new_full().  In the latter case the destroy functions
 * you supplied will be called on all keys and values before destroying
 * the #GTree.
 **/
void
g_tree_destroy (GTree *tree)
{
  g_return_if_fail (tree != NULL);

  g_tree_remove_all (tree);
  g_tree_unref (tree);
}

/**
 * g_tree_insert:
 * @tree: a #GTree.
 * @key: the key to insert.
 * @value: the value corresponding to the key.
 * 
 * Inserts a key/value pair into a #GTree. If the given key already exists 
 * in the #GTree its corresponding value is set to the new value. If you 
 * supplied a value_destroy_func when creating the #GTree, the old value is 
 * freed using that function. If you supplied a @key_destroy_func when 
 * creating the #GTree, the passed key is freed using that function.
 *
 * The tree is automatically 'balanced' as new key/value pairs are added,
 * so that the distance from the root to every leaf is as small as possible.
 **/
void
g_tree_insert (GTree    *tree,
	       gpointer  key,
	       gpointer  value)
{
  g_return_if_fail (tree != NULL);

  g_tree_insert_internal (tree, key, value, FALSE);

#ifdef G_TREE_DEBUG
  g_tree_node_check (tree->root);
#endif
}

/**
 * g_tree_replace:
 * @tree: a #GTree.
 * @key: the key to insert.
 * @value: the value corresponding to the key.
 * 
 * Inserts a new key and value into a #GTree similar to g_tree_insert(). 
 * The difference is that if the key already exists in the #GTree, it gets 
 * replaced by the new key. If you supplied a @value_destroy_func when 
 * creating the #GTree, the old value is freed using that function. If you 
 * supplied a @key_destroy_func when creating the #GTree, the old key is 
 * freed using that function. 
 *
 * The tree is automatically 'balanced' as new key/value pairs are added,
 * so that the distance from the root to every leaf is as small as possible.
 **/
void
g_tree_replace (GTree    *tree,
		gpointer  key,
		gpointer  value)
{
  g_return_if_fail (tree != NULL);

  g_tree_insert_internal (tree, key, value, TRUE);

#ifdef G_TREE_DEBUG
  g_tree_node_check (tree->root);
#endif
}

/* internal insert routine */
static void
g_tree_insert_internal (GTree    *tree,
                        gpointer  key,
                        gpointer  value,
                        gboolean  replace)
{
  GTreeNode *node;
  GTreeNode *path[MAX_GTREE_HEIGHT];
  int idx;

  g_return_if_fail (tree != NULL);

  if (!tree->root)
    {
      tree->root = g_tree_node_new (key, value);
      tree->nnodes++;
      return;
    }

  idx = 0;
  path[idx++] = NULL;
  node = tree->root;

  while (1)
    {
      int cmp = tree->key_compare (key, node->key, tree->key_compare_data);
      
      if (cmp == 0)
        {
          if (tree->value_destroy_func)
            tree->value_destroy_func (node->value);

          node->value = value;

          if (replace)
            {
              if (tree->key_destroy_func)
                tree->key_destroy_func (node->key);

              node->key = key;
            }
          else
            {
              /* free the passed key */
              if (tree->key_destroy_func)
                tree->key_destroy_func (key);
            }

          return;
        }
      else if (cmp < 0)
        {
          if (node->left_child)
            {
              path[idx++] = node;
              node = node->left;
            }
          else
            {
              GTreeNode *child = g_tree_node_new (key, value);

              child->left = node->left;
              child->right = node;
              node->left = child;
              node->left_child = TRUE;
              node->balance -= 1;

	      tree->nnodes++;

              break;
            }
        }
      else
        {
          if (node->right_child)
            {
              path[idx++] = node;
              node = node->right;
            }
          else
            {
              GTreeNode *child = g_tree_node_new (key, value);

              child->right = node->right;
              child->left = node;
              node->right = child;
              node->right_child = TRUE;
              node->balance += 1;

	      tree->nnodes++;

              break;
            }
        }
    }

  /* restore balance. This is the goodness of a non-recursive
     implementation, when we are done with balancing we 'break'
     the loop and we are done. */
  while (1)
    {
      GTreeNode *bparent = path[--idx];
      gboolean left_node = (bparent && node == bparent->left);
      g_assert (!bparent || bparent->left == node || bparent->right == node);

      if (node->balance < -1 || node->balance > 1)
        {
          node = g_tree_node_balance (node);
          if (bparent == NULL)
            tree->root = node;
          else if (left_node)
            bparent->left = node;
          else
            bparent->right = node;
        }

      if (node->balance == 0 || bparent == NULL)
        break;
      
      if (left_node)
        bparent->balance -= 1;
      else
        bparent->balance += 1;

      node = bparent;
    }
}

/**
 * g_tree_remove:
 * @tree: a #GTree.
 * @key: the key to remove.
 * 
 * Removes a key/value pair from a #GTree.
 *
 * If the #GTree was created using g_tree_new_full(), the key and value 
 * are freed using the supplied destroy functions, otherwise you have to 
 * make sure that any dynamically allocated values are freed yourself.
 * If the key does not exist in the #GTree, the function does nothing.
 *
 * Returns: %TRUE if the key was found (prior to 2.8, this function returned 
 *   nothing)
 **/
gboolean
g_tree_remove (GTree         *tree,
	       gconstpointer  key)
{
  gboolean removed;

  g_return_val_if_fail (tree != NULL, FALSE);

  removed = g_tree_remove_internal (tree, key, FALSE);

#ifdef G_TREE_DEBUG
  g_tree_node_check (tree->root);
#endif

  return removed;
}

/**
 * g_tree_steal:
 * @tree: a #GTree.
 * @key: the key to remove.
 * 
 * Removes a key and its associated value from a #GTree without calling 
 * the key and value destroy functions.
 *
 * If the key does not exist in the #GTree, the function does nothing.
 *
 * Returns: %TRUE if the key was found (prior to 2.8, this function returned 
 *    nothing)
 **/
gboolean
g_tree_steal (GTree         *tree,
              gconstpointer  key)
{
  gboolean removed;

  g_return_val_if_fail (tree != NULL, FALSE);

  removed = g_tree_remove_internal (tree, key, TRUE);

#ifdef G_TREE_DEBUG
  g_tree_node_check (tree->root);
#endif

  return removed;
}

/* internal remove routine */
static gboolean
g_tree_remove_internal (GTree         *tree,
                        gconstpointer  key,
                        gboolean       steal)
{
  GTreeNode *node, *parent, *balance;
  GTreeNode *path[MAX_GTREE_HEIGHT];
  int idx;
  gboolean left_node;

  g_return_val_if_fail (tree != NULL, FALSE);

  if (!tree->root)
    return FALSE;

  idx = 0;
  path[idx++] = NULL;
  node = tree->root;

  while (1)
    {
      int cmp = tree->key_compare (key, node->key, tree->key_compare_data);
      
      if (cmp == 0)
        break;
      else if (cmp < 0)
        {
          if (!node->left_child)
            return FALSE;
	  
	  path[idx++] = node;
	  node = node->left;
        }
      else
        {
          if (!node->right_child)
            return FALSE;
	  
	  path[idx++] = node;
	  node = node->right;
        }
    }

  /* the following code is almost equal to g_tree_remove_node,
     except that we do not have to call g_tree_node_parent. */
  balance = parent = path[--idx];
  g_assert (!parent || parent->left == node || parent->right == node);
  left_node = (parent && node == parent->left);

  if (!node->left_child)
    {
      if (!node->right_child)
        {
          if (!parent)
            tree->root = NULL;
          else if (left_node)
            {
              parent->left_child = FALSE;
              parent->left = node->left;
              parent->balance += 1;
            }
          else
            {
              parent->right_child = FALSE;
              parent->right = node->right;
              parent->balance -= 1;
            }
        }
      else /* node has a right child */
        {
          GTreeNode *tmp = g_tree_node_next (node);
	  tmp->left = node->left;

          if (!parent)
            tree->root = node->right;
          else if (left_node)
            {
              parent->left = node->right;
              parent->balance += 1;
            }
          else
            {
              parent->right = node->right;
              parent->balance -= 1;
            }
        }
    }
  else /* node has a left child */
    {
      if (!node->right_child)
        {
          GTreeNode *tmp = g_tree_node_previous (node);
          tmp->right = node->right;
	  
          if (parent == NULL)
            tree->root = node->left;
          else if (left_node)
            {
              parent->left = node->left;
              parent->balance += 1;
            }
          else
            {
              parent->right = node->left;
              parent->balance -= 1;
            }
        }
      else /* node has a both children (pant, pant!) */
        {
	  GTreeNode *prev = node->left;
	  GTreeNode *next = node->right;
	  GTreeNode *nextp = node;
	  int old_idx = idx + 1;
	  idx++;
	  
	  /* path[idx] == parent */
	  /* find the immediately next node (and its parent) */
	  while (next->left_child)
            {
	      path[++idx] = nextp = next;
	      next = next->left;
            }
 	  
	  path[old_idx] = next;
	  balance = path[idx];
	  
	  /* remove 'next' from the tree */
	  if (nextp != node)
	    {
	      if (next->right_child)
		nextp->left = next->right;
	      else
		nextp->left_child = FALSE;
	      nextp->balance += 1;
	      
	      next->right_child = TRUE;
	      next->right = node->right;
	    }
	  else
	    node->balance -= 1;
	    
	  /* set the prev to point to the right place */
	  while (prev->right_child)
	    prev = prev->right;
	  prev->right = next;
	    
	  /* prepare 'next' to replace 'node' */
	  next->left_child = TRUE;
	  next->left = node->left;
	  next->balance = node->balance;
	  
	  if (!parent)
	    tree->root = next;
	  else if (left_node)
	    parent->left = next;
	  else
	    parent->right = next;
        }
    }
  
  /* restore balance */
  if (balance)
    while (1)
      {
	GTreeNode *bparent = path[--idx];
	g_assert (!bparent || bparent->left == balance || bparent->right == balance);
	left_node = (bparent && balance == bparent->left);
			      
	if(balance->balance < -1 || balance->balance > 1)
	  {
	    balance = g_tree_node_balance (balance);
	    if (!bparent)
	      tree->root = balance;
	    else if (left_node)
	      bparent->left = balance;
	    else
	      bparent->right = balance;
	  }
	
	if (balance->balance != 0 || !bparent)
	  break;
	
	if (left_node)
	  bparent->balance += 1;
	else
	  bparent->balance -= 1;
	
	balance = bparent;
      }
  
  if (!steal)
    {
      if (tree->key_destroy_func)
        tree->key_destroy_func (node->key);
      if (tree->value_destroy_func)
        tree->value_destroy_func (node->value);
    }

  g_slice_free (GTreeNode, node);

  tree->nnodes--;

  return TRUE;
}

/**
 * g_tree_lookup:
 * @tree: a #GTree.
 * @key: the key to look up.
 * 
 * Gets the value corresponding to the given key. Since a #GTree is 
 * automatically balanced as key/value pairs are added, key lookup is very 
 * fast.
 *
 * Return value: the value corresponding to the key, or %NULL if the key was
 * not found.
 **/
gpointer
g_tree_lookup (GTree         *tree,
	       gconstpointer  key)
{
  GTreeNode *node;

  g_return_val_if_fail (tree != NULL, NULL);

  node = g_tree_find_node (tree, key);
  
  return node ? node->value : NULL;
}

/**
 * g_tree_lookup_extended:
 * @tree: a #GTree.
 * @lookup_key: the key to look up.
 * @orig_key: returns the original key.
 * @value: returns the value associated with the key.
 * 
 * Looks up a key in the #GTree, returning the original key and the
 * associated value and a #gboolean which is %TRUE if the key was found. This 
 * is useful if you need to free the memory allocated for the original key, 
 * for example before calling g_tree_remove().
 * 
 * Return value: %TRUE if the key was found in the #GTree.
 **/
gboolean
g_tree_lookup_extended (GTree         *tree,
                        gconstpointer  lookup_key,
                        gpointer      *orig_key,
                        gpointer      *value)
{
  GTreeNode *node;
  
  g_return_val_if_fail (tree != NULL, FALSE);
  
  node = g_tree_find_node (tree, lookup_key);
  
  if (node)
    {
      if (orig_key)
        *orig_key = node->key;
      if (value)
        *value = node->value;
      return TRUE;
    }
  else
    return FALSE;
}

/**
 * g_tree_foreach:
 * @tree: a #GTree.
 * @func: the function to call for each node visited. If this function
 *   returns %TRUE, the traversal is stopped.
 * @user_data: user data to pass to the function.
 * 
 * Calls the given function for each of the key/value pairs in the #GTree.
 * The function is passed the key and value of each pair, and the given
 * @data parameter. The tree is traversed in sorted order.
 *
 * The tree may not be modified while iterating over it (you can't 
 * add/remove items). To remove all items matching a predicate, you need 
 * to add each item to a list in your #GTraverseFunc as you walk over 
 * the tree, then walk the list and remove each item.
 **/
void
g_tree_foreach (GTree         *tree,
                GTraverseFunc  func,
                gpointer       user_data)
{
  GTreeNode *node;

  g_return_if_fail (tree != NULL);
  
  if (!tree->root)
    return;

  node = g_tree_first_node (tree);
  
  while (node)
    {
      if ((*func) (node->key, node->value, user_data))
	break;
      
      node = g_tree_node_next (node);
    }
}

/**
 * g_tree_traverse:
 * @tree: a #GTree.
 * @traverse_func: the function to call for each node visited. If this 
 *   function returns %TRUE, the traversal is stopped.
 * @traverse_type: the order in which nodes are visited, one of %G_IN_ORDER,
 *   %G_PRE_ORDER and %G_POST_ORDER.
 * @user_data: user data to pass to the function.
 * 
 * Calls the given function for each node in the #GTree. 
 *
 * Deprecated:2.2: The order of a balanced tree is somewhat arbitrary. If you 
 * just want to visit all nodes in sorted order, use g_tree_foreach() 
 * instead. If you really need to visit nodes in a different order, consider
 * using an <link linkend="glib-N-ary-Trees">N-ary Tree</link>.
 **/
/**
 * GTraverseFunc:
 * @key: a key of a #GTree node.
 * @value: the value corresponding to the key.
 * @data: user data passed to g_tree_traverse().
 * @Returns: %TRUE to stop the traversal.
 *
 * Specifies the type of function passed to g_tree_traverse(). It is
 * passed the key and value of each node, together with the @user_data
 * parameter passed to g_tree_traverse(). If the function returns
 * %TRUE, the traversal is stopped.
 **/
/**
 * GTraverseType:
 * @G_IN_ORDER: vists a node's left child first, then the node itself,
 *              then its right child. This is the one to use if you
 *              want the output sorted according to the compare
 *              function.
 * @G_PRE_ORDER: visits a node, then its children.
 * @G_POST_ORDER: visits the node's children, then the node itself.
 * @G_LEVEL_ORDER: is not implemented for <link
 *                 linkend="glib-Balanced-Binary-Trees">Balanced Binary
 *                 Trees</link>.  For <link
 *                 linkend="glib-N-ary-Trees">N-ary Trees</link>, it
 *                 vists the root node first, then its children, then
 *                 its grandchildren, and so on. Note that this is less
 *                 efficient than the other orders.
 *
 * Specifies the type of traveral performed by g_tree_traverse(),
 * g_node_traverse() and g_node_find().
 **/
void
g_tree_traverse (GTree         *tree,
		 GTraverseFunc  traverse_func,
		 GTraverseType  traverse_type,
		 gpointer       user_data)
{
  g_return_if_fail (tree != NULL);

  if (!tree->root)
    return;

  switch (traverse_type)
    {
    case G_PRE_ORDER:
      g_tree_node_pre_order (tree->root, traverse_func, user_data);
      break;

    case G_IN_ORDER:
      g_tree_node_in_order (tree->root, traverse_func, user_data);
      break;

    case G_POST_ORDER:
      g_tree_node_post_order (tree->root, traverse_func, user_data);
      break;
    
    case G_LEVEL_ORDER:
      g_warning ("g_tree_traverse(): traverse type G_LEVEL_ORDER isn't implemented.");
      break;
    }
}

/**
 * g_tree_search:
 * @tree: a #GTree.
 * @search_func: a function used to search the #GTree. 
 * @user_data: the data passed as the second argument to the @search_func 
 * function.
 * 
 * Searches a #GTree using @search_func.
 *
 * The @search_func is called with a pointer to the key of a key/value pair in 
 * the tree, and the passed in @user_data. If @search_func returns 0 for a 
 * key/value pair, then g_tree_search_func() will return the value of that 
 * pair. If @search_func returns -1,  searching will proceed among the 
 * key/value pairs that have a smaller key; if @search_func returns 1, 
 * searching will proceed among the key/value pairs that have a larger key.
 *
 * Return value: the value corresponding to the found key, or %NULL if the key 
 * was not found.
 **/
gpointer
g_tree_search (GTree         *tree,
	       GCompareFunc   search_func,
	       gconstpointer  user_data)
{
  g_return_val_if_fail (tree != NULL, NULL);

  if (tree->root)
    return g_tree_node_search (tree->root, search_func, user_data);
  else
    return NULL;
}

/**
 * g_tree_height:
 * @tree: a #GTree.
 * 
 * Gets the height of a #GTree.
 *
 * If the #GTree contains no nodes, the height is 0.
 * If the #GTree contains only one root node the height is 1.
 * If the root node has children the height is 2, etc.
 * 
 * Return value: the height of the #GTree.
 **/
gint
g_tree_height (GTree *tree)
{
  GTreeNode *node;
  gint height;

  g_return_val_if_fail (tree != NULL, 0);

  if (!tree->root)
    return 0;

  height = 0;
  node = tree->root;

  while (1)
    {
      height += 1 + MAX(node->balance, 0);

      if (!node->left_child)
	return height;
      
      node = node->left;
    }
}

/**
 * g_tree_nnodes:
 * @tree: a #GTree.
 * 
 * Gets the number of nodes in a #GTree.
 * 
 * Return value: the number of nodes in the #GTree.
 **/
gint
g_tree_nnodes (GTree *tree)
{
  g_return_val_if_fail (tree != NULL, 0);

  return tree->nnodes;
}

static GTreeNode*
g_tree_node_balance (GTreeNode *node)
{
  if (node->balance < -1)
    {
      if (node->left->balance > 0)
	node->left = g_tree_node_rotate_left (node->left);
      node = g_tree_node_rotate_right (node);
    }
  else if (node->balance > 1)
    {
      if (node->right->balance < 0)
	node->right = g_tree_node_rotate_right (node->right);
      node = g_tree_node_rotate_left (node);
    }

  return node;
}

static GTreeNode *
g_tree_find_node (GTree        *tree,
		  gconstpointer key)
{
  GTreeNode *node;
  gint cmp;

  node = tree->root;
  if (!node)
    return NULL;

  while (1)
    {
      cmp = tree->key_compare (key, node->key, tree->key_compare_data);
      if (cmp == 0)
	return node;
      else if (cmp < 0)
	{
	  if (!node->left_child)
	    return NULL;

	  node = node->left;
	}
      else
	{
	  if (!node->right_child)
	    return NULL;

	  node = node->right;
	}
    }
}

static gint
g_tree_node_pre_order (GTreeNode     *node,
		       GTraverseFunc  traverse_func,
		       gpointer       data)
{
  if ((*traverse_func) (node->key, node->value, data))
    return TRUE;

  if (node->left_child)
    {
      if (g_tree_node_pre_order (node->left, traverse_func, data))
	return TRUE;
    }

  if (node->right_child)
    {
      if (g_tree_node_pre_order (node->right, traverse_func, data))
	return TRUE;
    }

  return FALSE;
}

static gint
g_tree_node_in_order (GTreeNode     *node,
		      GTraverseFunc  traverse_func,
		      gpointer       data)
{
  if (node->left_child)
    {
      if (g_tree_node_in_order (node->left, traverse_func, data))
	return TRUE;
    }

  if ((*traverse_func) (node->key, node->value, data))
    return TRUE;

  if (node->right_child)
    {
      if (g_tree_node_in_order (node->right, traverse_func, data))
	return TRUE;
    }
  
  return FALSE;
}

static gint
g_tree_node_post_order (GTreeNode     *node,
			GTraverseFunc  traverse_func,
			gpointer       data)
{
  if (node->left_child)
    {
      if (g_tree_node_post_order (node->left, traverse_func, data))
	return TRUE;
    }

  if (node->right_child)
    {
      if (g_tree_node_post_order (node->right, traverse_func, data))
	return TRUE;
    }

  if ((*traverse_func) (node->key, node->value, data))
    return TRUE;

  return FALSE;
}

static gpointer
g_tree_node_search (GTreeNode     *node,
		    GCompareFunc   search_func,
		    gconstpointer  data)
{
  gint dir;

  if (!node)
    return NULL;

  while (1) 
    {
      dir = (* search_func) (node->key, data);
      if (dir == 0)
	return node->value;
      else if (dir < 0) 
	{ 
	  if (!node->left_child)
	    return NULL;

	  node = node->left;
	}
      else
	{
	  if (!node->right_child)
	    return NULL;
	  
	  node = node->right;
	}
    }
}

static GTreeNode*
g_tree_node_rotate_left (GTreeNode *node)
{
  GTreeNode *right;
  gint a_bal;
  gint b_bal;

  right = node->right;

  if (right->left_child)
    node->right = right->left;
  else
    {
      node->right_child = FALSE;
      node->right = right;
      right->left_child = TRUE;
    }
  right->left = node;

  a_bal = node->balance;
  b_bal = right->balance;

  if (b_bal <= 0)
    {
      if (a_bal >= 1)
	right->balance = b_bal - 1;
      else
	right->balance = a_bal + b_bal - 2;
      node->balance = a_bal - 1;
    }
  else
    {
      if (a_bal <= b_bal)
	right->balance = a_bal - 2;
      else
	right->balance = b_bal - 1;
      node->balance = a_bal - b_bal - 1;
    }

  return right;
}

static GTreeNode*
g_tree_node_rotate_right (GTreeNode *node)
{
  GTreeNode *left;
  gint a_bal;
  gint b_bal;

  left = node->left;

  if (left->right_child)
    node->left = left->right;
  else
    {
      node->left_child = FALSE;
      node->left = left;
      left->right_child = TRUE;
    }
  left->right = node;

  a_bal = node->balance;
  b_bal = left->balance;

  if (b_bal <= 0)
    {
      if (b_bal > a_bal)
	left->balance = b_bal + 1;
      else
	left->balance = a_bal + 2;
      node->balance = a_bal - b_bal + 1;
    }
  else
    {
      if (a_bal <= -1)
	left->balance = b_bal + 1;
      else
	left->balance = a_bal + b_bal + 2;
      node->balance = a_bal + 1;
    }

  return left;
}

#ifdef G_TREE_DEBUG
static gint
g_tree_node_height (GTreeNode *node)
{
  gint left_height;
  gint right_height;

  if (node)
    {
      left_height = 0;
      right_height = 0;

      if (node->left_child)
	left_height = g_tree_node_height (node->left);

      if (node->right_child)
	right_height = g_tree_node_height (node->right);

      return MAX (left_height, right_height) + 1;
    }

  return 0;
}

static void
g_tree_node_check (GTreeNode *node)
{
  gint left_height;
  gint right_height;
  gint balance;
  GTreeNode *tmp;

  if (node)
    {
      if (node->left_child)
	{
	  tmp = g_tree_node_previous (node);
	  g_assert (tmp->right == node);
	}

      if (node->right_child)
	{
	  tmp = g_tree_node_next (node);
	  g_assert (tmp->left == node);
	}

      left_height = 0;
      right_height = 0;
      
      if (node->left_child)
	left_height = g_tree_node_height (node->left);
      if (node->right_child)
	right_height = g_tree_node_height (node->right);
      
      balance = right_height - left_height;
      g_assert (balance == node->balance);
      
      if (node->left_child)
	g_tree_node_check (node->left);
      if (node->right_child)
	g_tree_node_check (node->right);
    }
}

static void
g_tree_node_dump (GTreeNode *node, 
		  gint       indent)
{
  g_print ("%*s%c\n", indent, "", *(char *)node->key);

  if (node->left_child)
    g_tree_node_dump (node->left, indent + 2);
  else if (node->left)
    g_print ("%*s<%c\n", indent + 2, "", *(char *)node->left->key);

  if (node->right_child)
    g_tree_node_dump (node->right, indent + 2);
  else if (node->right)
    g_print ("%*s>%c\n", indent + 2, "", *(char *)node->right->key);
}


void
g_tree_dump (GTree *tree)
{
  if (tree->root)
    g_tree_node_dump (tree->root, 0);
}
#endif