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

    avl.c - Source code for the AVL-tree library.

    Copyright (C) 1998  Michael H. Buselli <cosine@cosine.org>
    Copyright (C) 2000-2002  Wessel Dankers <wsl@nl.linux.org>

    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 2.1 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

    Augmented AVL-tree. Original by Michael H. Buselli <cosine@cosine.org>.

    Modified by Wessel Dankers <wsl@nl.linux.org> to add a bunch of bloat to
    the sourcecode, change the interface and squash a few bugs.
    Mail him if you find new bugs.

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

#include <stdio.h>
#include <stdlib.h>
#include <errno.h>
#include "avl.h"

static void avl_rebalance(avl_tree_t *, avl_node_t *);

#ifdef AVL_COUNT
#define NODE_COUNT(n)  ((n) ? (n)->count : 0)
#define L_COUNT(n)     (NODE_COUNT((n)->left))
#define R_COUNT(n)     (NODE_COUNT((n)->right))
#define CALC_COUNT(n)  (L_COUNT(n) + R_COUNT(n) + 1)
#endif

#ifdef AVL_DEPTH
#define NODE_DEPTH(n)  ((n) ? (n)->depth : 0)
#define L_DEPTH(n)     (NODE_DEPTH((n)->left))
#define R_DEPTH(n)     (NODE_DEPTH((n)->right))
#define CALC_DEPTH(n)  ((L_DEPTH(n)>R_DEPTH(n)?L_DEPTH(n):R_DEPTH(n)) + 1)
#endif

#ifndef AVL_DEPTH
/* Also known as ffs() (from BSD) */
static int lg(unsigned int u) {
	int r = 1;
	if(!u) return 0;
	if(u & 0xffff0000) { u >>= 16; r += 16; }
	if(u & 0x0000ff00) { u >>= 8; r += 8; }
	if(u & 0x000000f0) { u >>= 4; r += 4; }
	if(u & 0x0000000c) { u >>= 2; r += 2; }
	if(u & 0x00000002) r++;
	return r;
}
#endif

static int avl_check_balance(avl_node_t *avlnode) {
#ifdef AVL_DEPTH
	int d;
	d = R_DEPTH(avlnode) - L_DEPTH(avlnode);
	return d<-1?-1:d>1?1:0;
#else
/*	int d;
 *	d = lg(R_COUNT(avlnode)) - lg(L_COUNT(avlnode));
 *	d = d<-1?-1:d>1?1:0;
 */
#ifdef AVL_COUNT
	int pl, r;

	pl = lg(L_COUNT(avlnode));
	r = R_COUNT(avlnode);

	if(r>>pl+1)
		return 1;
	if(pl<2 || r>>pl-2)
		return 0;
	return -1;
#else
#error No balancing possible.
#endif
#endif
}

#ifdef AVL_COUNT
unsigned int avl_count(const avl_tree_t *avltree) {
	return NODE_COUNT(avltree->top);
}

avl_node_t *avl_at(const avl_tree_t *avltree, unsigned int index) {
	avl_node_t *avlnode;
	unsigned int c;

	avlnode = avltree->top;

	while(avlnode) {
		c = L_COUNT(avlnode);

		if(index < c) {
			avlnode = avlnode->left;
		} else if(index > c) {
			avlnode = avlnode->right;
			index -= c+1;
		} else {
			return avlnode;
		}
	}
	return NULL;
}

unsigned int avl_index(const avl_node_t *avlnode) {
	avl_node_t *next;
	unsigned int c;

	c = L_COUNT(avlnode);

	while((next = avlnode->parent)) {
		if(avlnode == next->right)
			c += L_COUNT(next) + 1;
		avlnode = next;
	}

	return c;
}
#endif

int avl_search_closest(const avl_tree_t *avltree, const void *item, avl_node_t **avlnode) {
	avl_node_t *node;
	avl_compare_t cmp;
	int c;

	if(!avlnode)
		avlnode = &node;

	node = avltree->top;

	if(!node)
		return *avlnode = NULL, 0;

	cmp = avltree->cmp;

	for(;;) {
		c = cmp(item, node->item);

		if(c < 0) {
			if(node->left)
				node = node->left;
			else
				return *avlnode = node, -1;
		} else if(c > 0) {
			if(node->right)
				node = node->right;
			else
				return *avlnode = node, 1;
		} else {
			return *avlnode = node, 0;
		}
	}
}

/*
 * avl_search:
 * Return a pointer to a node with the given item in the tree.
 * If no such item is in the tree, then NULL is returned.
 */
avl_node_t *avl_search(const avl_tree_t *avltree, const void *item) {
	avl_node_t *node;
	return avl_search_closest(avltree, item, &node) ? NULL : node;
}

avl_tree_t *avl_init_tree(avl_tree_t *rc, avl_compare_t cmp, avl_freeitem_t freeitem) {
	if(rc) {
		rc->head = NULL;
		rc->tail = NULL;
		rc->top = NULL;
		rc->cmp = cmp;
		rc->freeitem = freeitem;
	}
	return rc;
}

avl_tree_t *avl_alloc_tree(avl_compare_t cmp, avl_freeitem_t freeitem) {
	return avl_init_tree(malloc(sizeof(avl_tree_t)), cmp, freeitem);
}

void avl_clear_tree(avl_tree_t *avltree) {
	avltree->top = avltree->head = avltree->tail = NULL;
}

void avl_free_nodes(avl_tree_t *avltree) {
	avl_node_t *node, *next;
	avl_freeitem_t freeitem;

	freeitem = avltree->freeitem;

	for(node = avltree->head; node; node = next) {
		next = node->next;
		if(freeitem)
			freeitem(node->item);
		free(node);
	}
	avl_clear_tree(avltree);
}

/*
 * avl_free_tree:
 * Free all memory used by this tree.  If freeitem is not NULL, then
 * it is assumed to be a destructor for the items referenced in the avl_
 * tree, and they are deleted as well.
 */
void avl_free_tree(avl_tree_t *avltree) {
	avl_free_nodes(avltree);
	free(avltree);
}

static void avl_clear_node(avl_node_t *newnode) {
	newnode->left = newnode->right = NULL;
	#ifdef AVL_COUNT
	newnode->count = 1;
	#endif
	#ifdef AVL_DEPTH
	newnode->depth = 1;
	#endif
}

avl_node_t *avl_init_node(avl_node_t *newnode, void *item) {
	if(newnode) {
	  avl_clear_node(newnode); 
	  newnode->item = item;
	}
	return newnode;
}

avl_node_t *avl_insert_top(avl_tree_t *avltree, avl_node_t *newnode) {
	avl_clear_node(newnode);
	newnode->prev = newnode->next = newnode->parent = NULL;
	avltree->head = avltree->tail = avltree->top = newnode;
	return newnode;
}

avl_node_t *avl_insert_before(avl_tree_t *avltree, avl_node_t *node, avl_node_t *newnode) {
	if(!node)
		return avltree->tail
			? avl_insert_after(avltree, avltree->tail, newnode)
			: avl_insert_top(avltree, newnode);

	if(node->left)
		return avl_insert_after(avltree, node->prev, newnode);

	avl_clear_node(newnode);

	newnode->next = node;
	newnode->parent = node;

	newnode->prev = node->prev;
	if(node->prev)
		node->prev->next = newnode;
	else
		avltree->head = newnode;
	node->prev = newnode;

	node->left = newnode;
	avl_rebalance(avltree, node);
	return newnode;
}

avl_node_t *avl_insert_after(avl_tree_t *avltree, avl_node_t *node, avl_node_t *newnode) {
	if(!node)
		return avltree->head
			? avl_insert_before(avltree, avltree->head, newnode)
			: avl_insert_top(avltree, newnode);

	if(node->right)
		return avl_insert_before(avltree, node->next, newnode);

	avl_clear_node(newnode);

	newnode->prev = node;
	newnode->parent = node;

	newnode->next = node->next;
	if(node->next)
		node->next->prev = newnode;
	else
		avltree->tail = newnode;
	node->next = newnode;

	node->right = newnode;
	avl_rebalance(avltree, node);
	return newnode;
}

avl_node_t *avl_insert_node(avl_tree_t *avltree, avl_node_t *newnode) {
	avl_node_t *node;

	if(!avltree->top)
		return avl_insert_top(avltree, newnode);

	switch(avl_search_closest(avltree, newnode->item, &node)) {
		case -1:
			return avl_insert_before(avltree, node, newnode);
		case 1:
			return avl_insert_after(avltree, node, newnode);
	}

	return NULL;
}

/*
 * avl_insert:
 * Create a new node and insert an item there.
 * Returns the new node on success or NULL if no memory could be allocated.
 */
avl_node_t *avl_insert(avl_tree_t *avltree, void *item) {
	avl_node_t *newnode;

	newnode = avl_init_node(malloc(sizeof(avl_node_t)), item);
	if(newnode) {
		if(avl_insert_node(avltree, newnode))
			return newnode;
		free(newnode);
		errno = EEXIST;
	}
	return NULL;
}

/*
 * avl_unlink_node:
 * Removes the given node.  Does not delete the item at that node.
 * The item of the node may be freed before calling avl_unlink_node.
 * (In other words, it is not referenced by this function.)
 */
void avl_unlink_node(avl_tree_t *avltree, avl_node_t *avlnode) {
	avl_node_t *parent;
	avl_node_t **superparent;
	avl_node_t *subst, *left, *right;
	avl_node_t *balnode;

	if(avlnode->prev)
		avlnode->prev->next = avlnode->next;
	else
		avltree->head = avlnode->next;

	if(avlnode->next)
		avlnode->next->prev = avlnode->prev;
	else
		avltree->tail = avlnode->prev;

	parent = avlnode->parent;

	superparent = parent
		? avlnode == parent->left ? &parent->left : &parent->right
		: &avltree->top;

	left = avlnode->left;
	right = avlnode->right;
	if(!left) {
		*superparent = right;
		if(right)
			right->parent = parent;
		balnode = parent;
	} else if(!right) {
		*superparent = left;
		left->parent = parent;
		balnode = parent;
	} else {
		subst = avlnode->prev;
		if(subst == left) {
			balnode = subst;
		} else {
			balnode = subst->parent;
			balnode->right = subst->left;
			if(balnode->right)
				balnode->right->parent = balnode;
			subst->left = left;
			left->parent = subst;
		}
		subst->right = right;
		subst->parent = parent;
		right->parent = subst;
		*superparent = subst;
	}

	avl_rebalance(avltree, balnode);
}

void *avl_delete_node(avl_tree_t *avltree, avl_node_t *avlnode) {
	void *item = NULL;
	if(avlnode) {
		item = avlnode->item;
		avl_unlink_node(avltree, avlnode);
		if(avltree->freeitem)
			avltree->freeitem(item);
		free(avlnode);
	}
	return item;
}

void *avl_delete(avl_tree_t *avltree, const void *item) {
	return avl_delete_node(avltree, avl_search(avltree, item));
}

avl_node_t *avl_fixup_node(avl_tree_t *avltree, avl_node_t *newnode) {
	avl_node_t *oldnode = NULL, *node;

	if(!avltree || !newnode)
		return NULL;

	node = newnode->prev;
	if(node) {
		oldnode = node->next;
		node->next = newnode;
	} else {
		avltree->head = newnode;
	}

	node = newnode->next;
	if(node) {
		oldnode = node->prev;
		node->prev = newnode;
	} else {
		avltree->tail = newnode;
	}

	node = newnode->parent;
	if(node) {
		if(node->left == oldnode)
			node->left = newnode;
		else
			node->right = newnode;
	} else {
		oldnode = avltree->top;
		avltree->top = newnode;
	}

	return oldnode;
}

/*
 * avl_rebalance:
 * Rebalances the tree if one side becomes too heavy.  This function
 * assumes that both subtrees are AVL-trees with consistant data.  The
 * function has the additional side effect of recalculating the count of
 * the tree at this node.  It should be noted that at the return of this
 * function, if a rebalance takes place, the top of this subtree is no
 * longer going to be the same node.
 */
void avl_rebalance(avl_tree_t *avltree, avl_node_t *avlnode) {
	avl_node_t *child;
	avl_node_t *gchild;
	avl_node_t *parent;
	avl_node_t **superparent;

	parent = avlnode;

	while(avlnode) {
		parent = avlnode->parent;

		superparent = parent
			? avlnode == parent->left ? &parent->left : &parent->right
			: &avltree->top;

		switch(avl_check_balance(avlnode)) {
		case -1:
			child = avlnode->left;
			#ifdef AVL_DEPTH
			if(L_DEPTH(child) >= R_DEPTH(child)) {
			#else
			#ifdef AVL_COUNT
			if(L_COUNT(child) >= R_COUNT(child)) {
			#else
			#error No balancing possible.
			#endif
			#endif
				avlnode->left = child->right;
				if(avlnode->left)
					avlnode->left->parent = avlnode;
				child->right = avlnode;
				avlnode->parent = child;
				*superparent = child;
				child->parent = parent;
				#ifdef AVL_COUNT
				avlnode->count = CALC_COUNT(avlnode);
				child->count = CALC_COUNT(child);
				#endif
				#ifdef AVL_DEPTH
				avlnode->depth = CALC_DEPTH(avlnode);
				child->depth = CALC_DEPTH(child);
				#endif
			} else {
				gchild = child->right;
				avlnode->left = gchild->right;
				if(avlnode->left)
					avlnode->left->parent = avlnode;
				child->right = gchild->left;
				if(child->right)
					child->right->parent = child;
				gchild->right = avlnode;
				if(gchild->right)
					gchild->right->parent = gchild;
				gchild->left = child;
				if(gchild->left)
					gchild->left->parent = gchild;
				*superparent = gchild;
				gchild->parent = parent;
				#ifdef AVL_COUNT
				avlnode->count = CALC_COUNT(avlnode);
				child->count = CALC_COUNT(child);
				gchild->count = CALC_COUNT(gchild);
				#endif
				#ifdef AVL_DEPTH
				avlnode->depth = CALC_DEPTH(avlnode);
				child->depth = CALC_DEPTH(child);
				gchild->depth = CALC_DEPTH(gchild);
				#endif
			}
		break;
		case 1:
			child = avlnode->right;
			#ifdef AVL_DEPTH
			if(R_DEPTH(child) >= L_DEPTH(child)) {
			#else
			#ifdef AVL_COUNT
			if(R_COUNT(child) >= L_COUNT(child)) {
			#else
			#error No balancing possible.
			#endif
			#endif
				avlnode->right = child->left;
				if(avlnode->right)
					avlnode->right->parent = avlnode;
				child->left = avlnode;
				avlnode->parent = child;
				*superparent = child;
				child->parent = parent;
				#ifdef AVL_COUNT
				avlnode->count = CALC_COUNT(avlnode);
				child->count = CALC_COUNT(child);
				#endif
				#ifdef AVL_DEPTH
				avlnode->depth = CALC_DEPTH(avlnode);
				child->depth = CALC_DEPTH(child);
				#endif
			} else {
				gchild = child->left;
				avlnode->right = gchild->left;
				if(avlnode->right)
					avlnode->right->parent = avlnode;
				child->left = gchild->right;
				if(child->left)
					child->left->parent = child;
				gchild->left = avlnode;
				if(gchild->left)
					gchild->left->parent = gchild;
				gchild->right = child;
				if(gchild->right)
					gchild->right->parent = gchild;
				*superparent = gchild;
				gchild->parent = parent;
				#ifdef AVL_COUNT
				avlnode->count = CALC_COUNT(avlnode);
				child->count = CALC_COUNT(child);
				gchild->count = CALC_COUNT(gchild);
				#endif
				#ifdef AVL_DEPTH
				avlnode->depth = CALC_DEPTH(avlnode);
				child->depth = CALC_DEPTH(child);
				gchild->depth = CALC_DEPTH(gchild);
				#endif
			}
		break;
		default:
			#ifdef AVL_COUNT
			avlnode->count = CALC_COUNT(avlnode);
			#endif
			#ifdef AVL_DEPTH
			avlnode->depth = CALC_DEPTH(avlnode);
			#endif
		}
		avlnode = parent;
	}
}