--- /dev/null
+/* Ordered set data type implemented by a binary tree.
+ Copyright (C) 2006 Free Software Foundation, Inc.
+ Written by Bruno Haible <bruno@clisp.org>, 2006.
+
+ 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 2, 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. */
+
+#ifdef HAVE_CONFIG_H
+# include <config.h>
+#endif
+
+/* Specification. */
+#include "gl_avltree_oset.h"
+
+#include <stdlib.h>
+
+#include "xalloc.h"
+
+/* An AVL tree is a binary tree where
+ 1. The height of each node is calculated as
+ heightof(node) = 1 + max (heightof(node.left), heightof(node.right)).
+ 2. The heights of the subtrees of each node differ by at most 1:
+ | heightof(right) - heightof(left) | <= 1.
+ 3. The index of the elements in the node.left subtree are smaller than
+ the index of node.
+ The index of the elements in the node.right subtree are larger than
+ the index of node.
+ */
+
+/* -------------------------- gl_oset_t Data Type -------------------------- */
+
+/* Tree node implementation, valid for this file only. */
+struct gl_oset_node_impl
+{
+ struct gl_oset_node_impl *left; /* left branch, or NULL */
+ struct gl_oset_node_impl *right; /* right branch, or NULL */
+ /* Parent pointer, or NULL. The parent pointer is not needed for most
+ operations. It is needed so that a gl_oset_node_t can be returned
+ without memory allocation, on which the functions gl_oset_remove_node,
+ gl_oset_add_before, gl_oset_add_after can be implemented. */
+ struct gl_oset_node_impl *parent;
+ int balance; /* heightof(right) - heightof(left),
+ always = -1 or 0 or 1 */
+ const void *value;
+};
+typedef struct gl_oset_node_impl * gl_oset_node_t;
+
+/* Concrete gl_oset_impl type, valid for this file only. */
+struct gl_oset_impl
+{
+ struct gl_oset_impl_base base;
+ struct gl_oset_node_impl *root; /* root node or NULL */
+ size_t count; /* number of nodes */
+};
+
+/* An AVL tree of height h has at least F_(h+2) [Fibonacci number] and at most
+ 2^h - 1 elements. So, h <= 84 (because a tree of height h >= 85 would have
+ at least F_87 elements, and because even on 64-bit machines,
+ sizeof (gl_oset_node_impl) * F_87 > 2^64
+ this would exceed the address space of the machine. */
+#define MAXHEIGHT 83
+
+/* Ensure the tree is balanced, after an insertion or deletion operation.
+ The height of NODE is incremented by HEIGHT_DIFF (1 or -1).
+ PARENT = NODE->parent. (NODE can also be NULL. But PARENT is non-NULL.)
+ Rotation operations are performed starting at PARENT (not NODE itself!). */
+static void
+rebalance (gl_oset_t set,
+ gl_oset_node_t node, int height_diff, gl_oset_node_t parent)
+{
+ for (;;)
+ {
+ gl_oset_node_t child;
+ int previous_balance;
+ int balance_diff;
+ gl_oset_node_t nodeleft;
+ gl_oset_node_t noderight;
+
+ child = node;
+ node = parent;
+
+ previous_balance = node->balance;
+
+ /* The balance of NODE is incremented by BALANCE_DIFF: +1 if the right
+ branch's height has increased by 1 or the left branch's height has
+ decreased by 1, -1 if the right branch's height has decreased by 1 or
+ the left branch's height has increased by 1, 0 if no height change. */
+ if (node->left != NULL || node->right != NULL)
+ balance_diff = (child == node->right ? height_diff : -height_diff);
+ else
+ /* Special case where above formula doesn't work, because the caller
+ didn't tell whether node's left or right branch shrunk from height 1
+ to NULL. */
+ balance_diff = - previous_balance;
+
+ node->balance += balance_diff;
+ if (balance_diff == previous_balance)
+ {
+ /* node->balance is outside the range [-1,1]. Must rotate. */
+ gl_oset_node_t *nodep;
+
+ if (node->parent == NULL)
+ /* node == set->root */
+ nodep = &set->root;
+ else if (node->parent->left == node)
+ nodep = &node->parent->left;
+ else if (node->parent->right == node)
+ nodep = &node->parent->right;
+ else
+ abort ();
+
+ nodeleft = node->left;
+ noderight = node->right;
+
+ if (balance_diff < 0)
+ {
+ /* node->balance = -2. The subtree is heavier on the left side.
+ Rotate from left to right:
+
+ *
+ / \
+ h+2 h
+ */
+ gl_oset_node_t nodeleftright = nodeleft->right;
+ if (nodeleft->balance <= 0)
+ {
+ /*
+ * h+2|h+3
+ / \ / \
+ h+2 h --> / h+1|h+2
+ / \ | / \
+ h+1 h|h+1 h+1 h|h+1 h
+ */
+ node->left = nodeleftright;
+ nodeleft->right = node;
+
+ nodeleft->parent = node->parent;
+ node->parent = nodeleft;
+ if (nodeleftright != NULL)
+ nodeleftright->parent = node;
+
+ nodeleft->balance += 1;
+ node->balance = - nodeleft->balance;
+
+ *nodep = nodeleft;
+ height_diff = (height_diff < 0
+ ? /* noderight's height had been decremented from
+ h+1 to h. The subtree's height changes from
+ h+3 to h+2|h+3. */
+ nodeleft->balance - 1
+ : /* nodeleft's height had been incremented from
+ h+1 to h+2. The subtree's height changes from
+ h+2 to h+2|h+3. */
+ nodeleft->balance);
+ }
+ else
+ {
+ /*
+ * h+2
+ / \ / \
+ h+2 h --> h+1 h+1
+ / \ / \ / \
+ h h+1 h L R h
+ / \
+ L R
+
+ */
+ gl_oset_node_t L = nodeleft->right = nodeleftright->left;
+ gl_oset_node_t R = node->left = nodeleftright->right;
+ nodeleftright->left = nodeleft;
+ nodeleftright->right = node;
+
+ nodeleftright->parent = node->parent;
+ if (L != NULL)
+ L->parent = nodeleft;
+ if (R != NULL)
+ R->parent = node;
+ nodeleft->parent = nodeleftright;
+ node->parent = nodeleftright;
+
+ nodeleft->balance = (nodeleftright->balance > 0 ? -1 : 0);
+ node->balance = (nodeleftright->balance < 0 ? 1 : 0);
+ nodeleftright->balance = 0;
+
+ *nodep = nodeleftright;
+ height_diff = (height_diff < 0
+ ? /* noderight's height had been decremented from
+ h+1 to h. The subtree's height changes from
+ h+3 to h+2. */
+ -1
+ : /* nodeleft's height had been incremented from
+ h+1 to h+2. The subtree's height changes from
+ h+2 to h+2. */
+ 0);
+ }
+ }
+ else
+ {
+ /* node->balance = 2. The subtree is heavier on the right side.
+ Rotate from right to left:
+
+ *
+ / \
+ h h+2
+ */
+ gl_oset_node_t noderightleft = noderight->left;
+ if (noderight->balance >= 0)
+ {
+ /*
+ * h+2|h+3
+ / \ / \
+ h h+2 --> h+1|h+2 \
+ / \ / \ |
+ h|h+1 h+1 h h|h+1 h+1
+ */
+ node->right = noderightleft;
+ noderight->left = node;
+
+ noderight->parent = node->parent;
+ node->parent = noderight;
+ if (noderightleft != NULL)
+ noderightleft->parent = node;
+
+ noderight->balance -= 1;
+ node->balance = - noderight->balance;
+
+ *nodep = noderight;
+ height_diff = (height_diff < 0
+ ? /* nodeleft's height had been decremented from
+ h+1 to h. The subtree's height changes from
+ h+3 to h+2|h+3. */
+ - noderight->balance - 1
+ : /* noderight's height had been incremented from
+ h+1 to h+2. The subtree's height changes from
+ h+2 to h+2|h+3. */
+ - noderight->balance);
+ }
+ else
+ {
+ /*
+ * h+2
+ / \ / \
+ h h+2 --> h+1 h+1
+ / \ / \ / \
+ h+1 h h L R h
+ / \
+ L R
+
+ */
+ gl_oset_node_t L = node->right = noderightleft->left;
+ gl_oset_node_t R = noderight->left = noderightleft->right;
+ noderightleft->left = node;
+ noderightleft->right = noderight;
+
+ noderightleft->parent = node->parent;
+ if (L != NULL)
+ L->parent = node;
+ if (R != NULL)
+ R->parent = noderight;
+ node->parent = noderightleft;
+ noderight->parent = noderightleft;
+
+ node->balance = (noderightleft->balance > 0 ? -1 : 0);
+ noderight->balance = (noderightleft->balance < 0 ? 1 : 0);
+ noderightleft->balance = 0;
+
+ *nodep = noderightleft;
+ height_diff = (height_diff < 0
+ ? /* nodeleft's height had been decremented from
+ h+1 to h. The subtree's height changes from
+ h+3 to h+2. */
+ -1
+ : /* noderight's height had been incremented from
+ h+1 to h+2. The subtree's height changes from
+ h+2 to h+2. */
+ 0);
+ }
+ }
+ node = *nodep;
+ }
+ else
+ {
+ /* No rotation needed. Only propagation of the height change to the
+ next higher level. */
+ if (height_diff < 0)
+ height_diff = (previous_balance == 0 ? 0 : -1);
+ else
+ height_diff = (node->balance == 0 ? 0 : 1);
+ }
+
+ if (height_diff == 0)
+ break;
+
+ parent = node->parent;
+ if (parent == NULL)
+ break;
+ }
+}
+
+static gl_oset_node_t
+gl_tree_add_first (gl_oset_t set, const void *elt)
+{
+ /* Create new node. */
+ gl_oset_node_t new_node =
+ (struct gl_oset_node_impl *) xmalloc (sizeof (struct gl_oset_node_impl));
+
+ new_node->left = NULL;
+ new_node->right = NULL;
+ new_node->balance = 0;
+ new_node->value = elt;
+
+ /* Add it to the tree. */
+ if (set->root == NULL)
+ {
+ set->root = new_node;
+ new_node->parent = NULL;
+ }
+ else
+ {
+ gl_oset_node_t node;
+
+ for (node = set->root; node->left != NULL; )
+ node = node->left;
+
+ node->left = new_node;
+ new_node->parent = node;
+ node->balance--;
+
+ /* Rebalance. */
+ if (node->right == NULL && node->parent != NULL)
+ rebalance (set, node, 1, node->parent);
+ }
+
+ set->count++;
+ return new_node;
+}
+
+static gl_oset_node_t
+gl_tree_add_before (gl_oset_t set, gl_oset_node_t node, const void *elt)
+{
+ /* Create new node. */
+ gl_oset_node_t new_node =
+ (struct gl_oset_node_impl *) xmalloc (sizeof (struct gl_oset_node_impl));
+ bool height_inc;
+
+ new_node->left = NULL;
+ new_node->right = NULL;
+ new_node->balance = 0;
+ new_node->value = elt;
+
+ /* Add it to the tree. */
+ if (node->left == NULL)
+ {
+ node->left = new_node;
+ node->balance--;
+ height_inc = (node->right == NULL);
+ }
+ else
+ {
+ for (node = node->left; node->right != NULL; )
+ node = node->right;
+ node->right = new_node;
+ node->balance++;
+ height_inc = (node->left == NULL);
+ }
+ new_node->parent = node;
+
+ /* Rebalance. */
+ if (height_inc && node->parent != NULL)
+ rebalance (set, node, 1, node->parent);
+
+ set->count++;
+ return new_node;
+}
+
+static gl_oset_node_t
+gl_tree_add_after (gl_oset_t set, gl_oset_node_t node, const void *elt)
+{
+ /* Create new node. */
+ gl_oset_node_t new_node =
+ (struct gl_oset_node_impl *) xmalloc (sizeof (struct gl_oset_node_impl));
+ bool height_inc;
+
+ new_node->left = NULL;
+ new_node->right = NULL;
+ new_node->balance = 0;
+ new_node->value = elt;
+
+ /* Add it to the tree. */
+ if (node->right == NULL)
+ {
+ node->right = new_node;
+ node->balance++;
+ height_inc = (node->left == NULL);
+ }
+ else
+ {
+ for (node = node->right; node->left != NULL; )
+ node = node->left;
+ node->left = new_node;
+ node->balance--;
+ height_inc = (node->right == NULL);
+ }
+ new_node->parent = node;
+
+ /* Rebalance. */
+ if (height_inc && node->parent != NULL)
+ rebalance (set, node, 1, node->parent);
+
+ set->count++;
+ return new_node;
+}
+
+static bool
+gl_tree_remove_node (gl_oset_t set, gl_oset_node_t node)
+{
+ gl_oset_node_t parent = node->parent;
+
+ if (node->left == NULL)
+ {
+ /* Replace node with node->right. */
+ gl_oset_node_t child = node->right;
+
+ if (child != NULL)
+ child->parent = parent;
+ if (parent == NULL)
+ set->root = child;
+ else
+ {
+ if (parent->left == node)
+ parent->left = child;
+ else /* parent->right == node */
+ parent->right = child;
+
+ rebalance (set, child, -1, parent);
+ }
+ }
+ else if (node->right == NULL)
+ {
+ /* It is not absolutely necessary to treat this case. But the more
+ general case below is more complicated, hence slower. */
+ /* Replace node with node->left. */
+ gl_oset_node_t child = node->left;
+
+ child->parent = parent;
+ if (parent == NULL)
+ set->root = child;
+ else
+ {
+ if (parent->left == node)
+ parent->left = child;
+ else /* parent->right == node */
+ parent->right = child;
+
+ rebalance (set, child, -1, parent);
+ }
+ }
+ else
+ {
+ /* Replace node with the rightmost element of the node->left subtree. */
+ gl_oset_node_t subst;
+ gl_oset_node_t subst_parent;
+ gl_oset_node_t child;
+
+ for (subst = node->left; subst->right != NULL; )
+ subst = subst->right;
+
+ subst_parent = subst->parent;
+
+ child = subst->left;
+
+ /* The case subst_parent == node is special: If we do nothing special,
+ we get confusion about node->left, subst->left and child->parent.
+ subst_parent == node
+ <==> The 'for' loop above terminated immediately.
+ <==> subst == subst_parent->left
+ [otherwise subst == subst_parent->right]
+ In this case, we would need to first set
+ child->parent = node; node->left = child;
+ and later - when we copy subst into node's position - again
+ child->parent = subst; subst->left = child;
+ Altogether a no-op. */
+ if (subst_parent != node)
+ {
+ if (child != NULL)
+ child->parent = subst_parent;
+ subst_parent->right = child;
+ }
+
+ /* Copy subst into node's position.
+ (This is safer than to copy subst's value into node, keep node in
+ place, and free subst.) */
+ if (subst_parent != node)
+ {
+ subst->left = node->left;
+ subst->left->parent = subst;
+ }
+ subst->right = node->right;
+ subst->right->parent = subst;
+ subst->balance = node->balance;
+ subst->parent = parent;
+ if (parent == NULL)
+ set->root = subst;
+ else if (parent->left == node)
+ parent->left = subst;
+ else /* parent->right == node */
+ parent->right = subst;
+
+ /* Rebalancing starts at child's parent, that is subst_parent -
+ except when subst_parent == node. In this case, we need to use
+ its replacement, subst. */
+ rebalance (set, child, -1, subst_parent != node ? subst_parent : subst);
+ }
+
+ set->count--;
+ free (node);
+ return true;
+}
+
+/* Generic binary tree code. */
+#include "gl_anytree_oset.h"
+
+/* For debugging. */
+static unsigned int
+check_invariants (gl_oset_node_t node, gl_oset_node_t parent, size_t *counterp)
+{
+ unsigned int left_height =
+ (node->left != NULL ? check_invariants (node->left, node, counterp) : 0);
+ unsigned int right_height =
+ (node->right != NULL ? check_invariants (node->right, node, counterp) : 0);
+ int balance = (int)right_height - (int)left_height;
+
+ if (!(node->parent == parent))
+ abort ();
+ if (!(balance >= -1 && balance <= 1))
+ abort ();
+ if (!(node->balance == balance))
+ abort ();
+
+ (*counterp)++;
+
+ return 1 + (left_height > right_height ? left_height : right_height);
+}
+void
+gl_avltree_oset_check_invariants (gl_oset_t set)
+{
+ size_t counter = 0;
+ if (set->root != NULL)
+ check_invariants (set->root, NULL, &counter);
+ if (!(set->count == counter))
+ abort ();
+}
+
+const struct gl_oset_implementation gl_avltree_oset_implementation =
+ {
+ gl_tree_create_empty,
+ gl_tree_size,
+ gl_tree_search,
+ gl_tree_add,
+ gl_tree_remove,
+ gl_tree_oset_free,
+ gl_tree_iterator,
+ gl_tree_iterator_next,
+ gl_tree_iterator_free
+ };
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