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+/* tree.h -- AVL trees (in the spirit of BSD's 'queue.h') -*- C -*- */
+
+/* Copyright (c) 2005 Ian Piumarta
+ *
+ * All rights reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the 'Software'), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, and/or sell copies of the
+ * Software, and to permit persons to whom the Software is furnished to do so,
+ * provided that the above copyright notice(s) and this permission notice appear
+ * in all copies of the Software and that both the above copyright notice(s) and
+ * this permission notice appear in supporting documentation.
+ *
+ * THE SOFTWARE IS PROVIDED 'AS IS'. USE ENTIRELY AT YOUR OWN RISK.
+ */
+
+/* This file defines an AVL balanced binary tree [Georgii M. Adelson-Velskii and
+ * Evgenii M. Landis, 'An algorithm for the organization of information',
+ * Doklady Akademii Nauk SSSR, 146:263-266, 1962 (Russian). Also in Myron
+ * J. Ricci (trans.), Soviet Math, 3:1259-1263, 1962 (English)].
+ *
+ * An AVL tree is headed by pointers to the root node and to a function defining
+ * the ordering relation between nodes. Each node contains an arbitrary payload
+ * plus three fields per tree entry: the depth of the subtree for which it forms
+ * the root and two pointers to child nodes (singly-linked for minimum space, at
+ * the expense of direct access to the parent node given a pointer to one of the
+ * children). The tree is rebalanced after every insertion or removal. The
+ * tree may be traversed in two directions: forward (in-order left-to-right) and
+ * reverse (in-order, right-to-left).
+ *
+ * Because of the recursive nature of many of the operations on trees it is
+ * necessary to define a number of helper functions for each type of tree node.
+ * The macro TREE_DEFINE(node_tag, entry_name) defines these functions with
+ * unique names according to the node_tag. This macro should be invoked,
+ * thereby defining the necessary functions, once per node tag in the program.
+ *
+ * For details on the use of these macros, see the tree(3) manual page.
+ */
+
+#ifndef __tree_h
+#define __tree_h
+
+
+#define TREE_DELTA_MAX 1
+
+#define TREE_ENTRY(type) \
+ struct { \
+ struct type *avl_left; \
+ struct type *avl_right; \
+ int avl_height; \
+ }
+
+#define TREE_HEAD(name, type) \
+ struct name { \
+ struct type *th_root; \
+ int (*th_cmp)(struct type *lhs, struct type *rhs); \
+ }
+
+#define TREE_INITIALIZER(cmp) { 0, cmp }
+
+#define TREE_DELTA(self, field) \
+ (( (((self)->field.avl_left) ? (self)->field.avl_left->field.avl_height : 0)) \
+ - (((self)->field.avl_right) ? (self)->field.avl_right->field.avl_height : 0))
+
+/* Recursion prevents the following from being defined as macros. */
+
+#define TREE_DEFINE(node, field) \
+ \
+ struct node *TREE_BALANCE_##node##_##field(struct node *); \
+ \
+ struct node *TREE_ROTL_##node##_##field(struct node *self) \
+ { \
+ struct node *r= self->field.avl_right; \
+ self->field.avl_right= r->field.avl_left; \
+ r->field.avl_left= TREE_BALANCE_##node##_##field(self); \
+ return TREE_BALANCE_##node##_##field(r); \
+ } \
+ \
+ struct node *TREE_ROTR_##node##_##field(struct node *self) \
+ { \
+ struct node *l= self->field.avl_left; \
+ self->field.avl_left= l->field.avl_right; \
+ l->field.avl_right= TREE_BALANCE_##node##_##field(self); \
+ return TREE_BALANCE_##node##_##field(l); \
+ } \
+ \
+ struct node *TREE_BALANCE_##node##_##field(struct node *self) \
+ { \
+ int delta= TREE_DELTA(self, field); \
+ \
+ if (delta < -TREE_DELTA_MAX) \
+ { \
+ if (TREE_DELTA(self->field.avl_right, field) > 0) \
+ self->field.avl_right= TREE_ROTR_##node##_##field(self->field.avl_right); \
+ return TREE_ROTL_##node##_##field(self); \
+ } \
+ else if (delta > TREE_DELTA_MAX) \
+ { \
+ if (TREE_DELTA(self->field.avl_left, field) < 0) \
+ self->field.avl_left= TREE_ROTL_##node##_##field(self->field.avl_left); \
+ return TREE_ROTR_##node##_##field(self); \
+ } \
+ self->field.avl_height= 0; \
+ if (self->field.avl_left && (self->field.avl_left->field.avl_height > self->field.avl_height)) \
+ self->field.avl_height= self->field.avl_left->field.avl_height; \
+ if (self->field.avl_right && (self->field.avl_right->field.avl_height > self->field.avl_height)) \
+ self->field.avl_height= self->field.avl_right->field.avl_height; \
+ self->field.avl_height += 1; \
+ return self; \
+ } \
+ \
+ struct node *TREE_INSERT_##node##_##field \
+ (struct node *self, struct node *elm, int (*compare)(struct node *lhs, struct node *rhs)) \
+ { \
+ if (!self) \
+ return elm; \
+ if (compare(elm, self) < 0) \
+ self->field.avl_left= TREE_INSERT_##node##_##field(self->field.avl_left, elm, compare); \
+ else \
+ self->field.avl_right= TREE_INSERT_##node##_##field(self->field.avl_right, elm, compare); \
+ return TREE_BALANCE_##node##_##field(self); \
+ } \
+ \
+ struct node *TREE_FIND_##node##_##field \
+ (struct node *self, struct node *elm, int (*compare)(struct node *lhs, struct node *rhs)) \
+ { \
+ if (!self) \
+ return 0; \
+ if (compare(elm, self) == 0) \
+ return self; \
+ if (compare(elm, self) < 0) \
+ return TREE_FIND_##node##_##field(self->field.avl_left, elm, compare); \
+ else \
+ return TREE_FIND_##node##_##field(self->field.avl_right, elm, compare); \
+ } \
+ \
+ struct node *TREE_MOVE_RIGHT(struct node *self, struct node *rhs) \
+ { \
+ if (!self) \
+ return rhs; \
+ self->field.avl_right= TREE_MOVE_RIGHT(self->field.avl_right, rhs); \
+ return TREE_BALANCE_##node##_##field(self); \
+ } \
+ \
+ struct node *TREE_REMOVE_##node##_##field \
+ (struct node *self, struct node *elm, int (*compare)(struct node *lhs, struct node *rhs)) \
+ { \
+ if (!self) return 0; \
+ \
+ if (compare(elm, self) == 0) \
+ { \
+ struct node *tmp= TREE_MOVE_RIGHT(self->field.avl_left, self->field.avl_right); \
+ self->field.avl_left= 0; \
+ self->field.avl_right= 0; \
+ return tmp; \
+ } \
+ if (compare(elm, self) < 0) \
+ self->field.avl_left= TREE_REMOVE_##node##_##field(self->field.avl_left, elm, compare); \
+ else \
+ self->field.avl_right= TREE_REMOVE_##node##_##field(self->field.avl_right, elm, compare); \
+ return TREE_BALANCE_##node##_##field(self); \
+ } \
+ \
+ void TREE_FORWARD_APPLY_ALL_##node##_##field \
+ (struct node *self, void (*function)(struct node *node, void *data), void *data) \
+ { \
+ if (self) \
+ { \
+ TREE_FORWARD_APPLY_ALL_##node##_##field(self->field.avl_left, function, data); \
+ function(self, data); \
+ TREE_FORWARD_APPLY_ALL_##node##_##field(self->field.avl_right, function, data); \
+ } \
+ } \
+ \
+ void TREE_REVERSE_APPLY_ALL_##node##_##field \
+ (struct node *self, void (*function)(struct node *node, void *data), void *data) \
+ { \
+ if (self) \
+ { \
+ TREE_REVERSE_APPLY_ALL_##node##_##field(self->field.avl_right, function, data); \
+ function(self, data); \
+ TREE_REVERSE_APPLY_ALL_##node##_##field(self->field.avl_left, function, data); \
+ } \
+ }
+
+#define TREE_INSERT(head, node, field, elm) \
+ ((head)->th_root= TREE_INSERT_##node##_##field((head)->th_root, (elm), (head)->th_cmp))
+
+#define TREE_FIND(head, node, field, elm) \
+ (TREE_FIND_##node##_##field((head)->th_root, (elm), (head)->th_cmp))
+
+#define TREE_REMOVE(head, node, field, elm) \
+ ((head)->th_root= TREE_REMOVE_##node##_##field((head)->th_root, (elm), (head)->th_cmp))
+
+#define TREE_DEPTH(head, field) \
+ ((head)->th_root->field.avl_height)
+
+#define TREE_FORWARD_APPLY(head, node, field, function, data) \
+ TREE_FORWARD_APPLY_ALL_##node##_##field((head)->th_root, function, data)
+
+#define TREE_REVERSE_APPLY(head, node, field, function, data) \
+ TREE_REVERSE_APPLY_ALL_##node##_##field((head)->th_root, function, data)
+
+#define TREE_INIT(head, cmp) do { \
+ (head)->th_root= 0; \
+ (head)->th_cmp= (cmp); \
+ } while (0)
+
+
+#endif /* __tree_h */