--- /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_rbtree_oset.h"
+
+#include <stdlib.h>
+
+#include "xalloc.h"
+
+/* A red-black tree is a binary tree where every node is colored black or
+ red such that
+ 1. The root is black.
+ 2. No red node has a red parent.
+ Or equivalently: No red node has a red child.
+ 3. All paths from the root down to any NULL endpoint contain the same
+ number of black nodes.
+ Let's call this the "black-height" bh of the tree. It follows that every
+ such path contains exactly bh black and between 0 and bh red nodes. (The
+ extreme cases are a path containing only black nodes, and a path colored
+ alternatingly black-red-black-red-...-black-red.) The height of the tree
+ therefore is >= bh, <= 2*bh.
+ */
+
+/* -------------------------- gl_oset_t Data Type -------------------------- */
+
+/* Color of a node. */
+typedef enum color { BLACK, RED } color_t;
+
+/* 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;
+ color_t color; /* node's color */
+ 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 */
+};
+
+/* A red-black tree of height h has a black-height bh >= ceil(h/2) and
+ therefore at least 2^ceil(h/2) - 1 elements. So, h <= 116 (because a tree
+ of height h >= 117 would have at least 2^59 - 1 elements, and because even
+ on 64-bit machines,
+ sizeof (gl_oset_node_impl) * (2^59 - 1) > 2^64
+ this would exceed the address space of the machine. */
+#define MAXHEIGHT 116
+
+/* Rotate left a subtree.
+
+ B D
+ / \ / \
+ A D --> B E
+ / \ / \
+ C E A C
+
+ Change the tree structure, update the branch sizes.
+ The caller must update the colors and register D as child of its parent. */
+static inline gl_oset_node_t
+rotate_left (gl_oset_node_t b_node, gl_oset_node_t d_node)
+{
+ gl_oset_node_t c_node = d_node->left;
+
+ b_node->right = c_node;
+ d_node->left = b_node;
+
+ d_node->parent = b_node->parent;
+ b_node->parent = d_node;
+ if (c_node != NULL)
+ c_node->parent = b_node;
+
+ return d_node;
+}
+
+/* Rotate right a subtree.
+
+ D B
+ / \ / \
+ B E --> A D
+ / \ / \
+ A C C E
+
+ Change the tree structure, update the branch sizes.
+ The caller must update the colors and register B as child of its parent. */
+static inline gl_oset_node_t
+rotate_right (gl_oset_node_t b_node, gl_oset_node_t d_node)
+{
+ gl_oset_node_t c_node = b_node->right;
+
+ d_node->left = c_node;
+ b_node->right = d_node;
+
+ b_node->parent = d_node->parent;
+ d_node->parent = b_node;
+ if (c_node != NULL)
+ c_node->parent = d_node;
+
+ return b_node;
+}
+
+/* Ensure the tree is balanced, after an insertion operation.
+ Also assigns node->color.
+ parent is the given node's parent, known to be non-NULL. */
+static void
+rebalance_after_add (gl_oset_t set, gl_oset_node_t node, gl_oset_node_t parent)
+{
+ for (;;)
+ {
+ /* At this point, parent = node->parent != NULL.
+ Think of node->color being RED (although node->color is not yet
+ assigned.) */
+ gl_oset_node_t grandparent;
+ gl_oset_node_t uncle;
+
+ if (parent->color == BLACK)
+ {
+ /* A RED color for node is acceptable. */
+ node->color = RED;
+ return;
+ }
+
+ grandparent = parent->parent;
+ /* Since parent is RED, we know that
+ grandparent is != NULL and colored BLACK. */
+
+ if (grandparent->left == parent)
+ uncle = grandparent->right;
+ else if (grandparent->right == parent)
+ uncle = grandparent->left;
+ else
+ abort ();
+
+ if (uncle != NULL && uncle->color == RED)
+ {
+ /* Change grandparent from BLACK to RED, and
+ change parent and uncle from RED to BLACK.
+ This makes it acceptable for node to be RED. */
+ node->color = RED;
+ parent->color = uncle->color = BLACK;
+ node = grandparent;
+ }
+ else
+ {
+ /* grandparent and uncle are BLACK. parent is RED. node wants
+ to be RED too.
+ In this case, recoloring is not sufficient. Need to perform
+ one or two rotations. */
+ gl_oset_node_t *grandparentp;
+
+ if (grandparent->parent == NULL)
+ grandparentp = &set->root;
+ else if (grandparent->parent->left == grandparent)
+ grandparentp = &grandparent->parent->left;
+ else if (grandparent->parent->right == grandparent)
+ grandparentp = &grandparent->parent->right;
+ else
+ abort ();
+
+ if (grandparent->left == parent)
+ {
+ if (parent->right == node)
+ {
+ /* Rotation between node and parent. */
+ grandparent->left = rotate_left (parent, node);
+ node = parent;
+ parent = grandparent->left;
+ }
+ /* grandparent and uncle are BLACK. parent and node want to be
+ RED. parent = grandparent->left. node = parent->left.
+
+ grandparent parent
+ bh+1 bh+1
+ / \ / \
+ parent uncle --> node grandparent
+ bh bh bh bh
+ / \ / \
+ node C C uncle
+ bh bh bh bh
+ */
+ *grandparentp = rotate_right (parent, grandparent);
+ parent->color = BLACK;
+ node->color = grandparent->color = RED;
+ }
+ else /* grandparent->right == parent */
+ {
+ if (parent->left == node)
+ {
+ /* Rotation between node and parent. */
+ grandparent->right = rotate_right (node, parent);
+ node = parent;
+ parent = grandparent->right;
+ }
+ /* grandparent and uncle are BLACK. parent and node want to be
+ RED. parent = grandparent->right. node = parent->right.
+
+ grandparent parent
+ bh+1 bh+1
+ / \ / \
+ uncle parent --> grandparent node
+ bh bh bh bh
+ / \ / \
+ C node uncle C
+ bh bh bh bh
+ */
+ *grandparentp = rotate_left (grandparent, parent);
+ parent->color = BLACK;
+ node->color = grandparent->color = RED;
+ }
+ return;
+ }
+
+ /* Start again with a new (node, parent) pair. */
+ parent = node->parent;
+
+ if (parent == NULL)
+ {
+ /* Change node's color from RED to BLACK. This increases the
+ tree's black-height. */
+ node->color = BLACK;
+ return;
+ }
+ }
+}
+
+/* Ensure the tree is balanced, after a deletion operation.
+ CHILD was a grandchild of PARENT and is now its child. Between them,
+ a black node was removed. CHILD is also black, or NULL.
+ (CHILD can also be NULL. But PARENT is non-NULL.) */
+static void
+rebalance_after_remove (gl_oset_t set, gl_oset_node_t child, gl_oset_node_t parent)
+{
+ for (;;)
+ {
+ /* At this point, we reduced the black-height of the CHILD subtree by 1.
+ To make up, either look for a possibility to turn a RED to a BLACK
+ node, or try to reduce the black-height tree of CHILD's sibling
+ subtree as well. */
+ gl_oset_node_t *parentp;
+
+ if (parent->parent == NULL)
+ parentp = &set->root;
+ else if (parent->parent->left == parent)
+ parentp = &parent->parent->left;
+ else if (parent->parent->right == parent)
+ parentp = &parent->parent->right;
+ else
+ abort ();
+
+ if (parent->left == child)
+ {
+ gl_oset_node_t sibling = parent->right;
+ /* sibling's black-height is >= 1. In particular,
+ sibling != NULL.
+
+ parent
+ / \
+ child sibling
+ bh bh+1
+ */
+
+ if (sibling->color == RED)
+ {
+ /* sibling is RED, hence parent is BLACK and sibling's children
+ are non-NULL and BLACK.
+
+ parent sibling
+ bh+2 bh+2
+ / \ / \
+ child sibling --> parent SR
+ bh bh+1 bh+1 bh+1
+ / \ / \
+ SL SR child SL
+ bh+1 bh+1 bh bh+1
+ */
+ *parentp = rotate_left (parent, sibling);
+ parent->color = RED;
+ sibling->color = BLACK;
+
+ /* Concentrate on the subtree of parent. The new sibling is
+ one of the old sibling's children, and known to be BLACK. */
+ parentp = &sibling->left;
+ sibling = parent->right;
+ }
+ /* Now we know that sibling is BLACK.
+
+ parent
+ / \
+ child sibling
+ bh bh+1
+ */
+ if (sibling->right != NULL && sibling->right->color == RED)
+ {
+ /*
+ parent sibling
+ bh+1|bh+2 bh+1|bh+2
+ / \ / \
+ child sibling --> parent SR
+ bh bh+1 bh+1 bh+1
+ / \ / \
+ SL SR child SL
+ bh bh bh bh
+ */
+ *parentp = rotate_left (parent, sibling);
+ sibling->color = parent->color;
+ parent->color = BLACK;
+ sibling->right->color = BLACK;
+ return;
+ }
+ else if (sibling->left != NULL && sibling->left->color == RED)
+ {
+ /*
+ parent parent
+ bh+1|bh+2 bh+1|bh+2
+ / \ / \
+ child sibling --> child SL
+ bh bh+1 bh bh+1
+ / \ / \
+ SL SR SLL sibling
+ bh bh bh bh
+ / \ / \
+ SLL SLR SLR SR
+ bh bh bh bh
+
+ where SLL, SLR, SR are all black.
+ */
+ parent->right = rotate_right (sibling->left, sibling);
+ /* Change sibling from BLACK to RED and SL from RED to BLACK. */
+ sibling->color = RED;
+ sibling = parent->right;
+ sibling->color = BLACK;
+
+ /* Now do as in the previous case. */
+ *parentp = rotate_left (parent, sibling);
+ sibling->color = parent->color;
+ parent->color = BLACK;
+ sibling->right->color = BLACK;
+ return;
+ }
+ else
+ {
+ if (parent->color == BLACK)
+ {
+ /* Change sibling from BLACK to RED. Then the entire
+ subtree at parent has decreased its black-height.
+ parent parent
+ bh+2 bh+1
+ / \ / \
+ child sibling --> child sibling
+ bh bh+1 bh bh
+ */
+ sibling->color = RED;
+
+ child = parent;
+ }
+ else
+ {
+ /* Change parent from RED to BLACK, but compensate by
+ changing sibling from BLACK to RED.
+ parent parent
+ bh+1 bh+1
+ / \ / \
+ child sibling --> child sibling
+ bh bh+1 bh bh
+ */
+ parent->color = BLACK;
+ sibling->color = RED;
+ return;
+ }
+ }
+ }
+ else if (parent->right == child)
+ {
+ gl_oset_node_t sibling = parent->left;
+ /* sibling's black-height is >= 1. In particular,
+ sibling != NULL.
+
+ parent
+ / \
+ sibling child
+ bh+1 bh
+ */
+
+ if (sibling->color == RED)
+ {
+ /* sibling is RED, hence parent is BLACK and sibling's children
+ are non-NULL and BLACK.
+
+ parent sibling
+ bh+2 bh+2
+ / \ / \
+ sibling child --> SR parent
+ bh+1 ch bh+1 bh+1
+ / \ / \
+ SL SR SL child
+ bh+1 bh+1 bh+1 bh
+ */
+ *parentp = rotate_right (sibling, parent);
+ parent->color = RED;
+ sibling->color = BLACK;
+
+ /* Concentrate on the subtree of parent. The new sibling is
+ one of the old sibling's children, and known to be BLACK. */
+ parentp = &sibling->right;
+ sibling = parent->left;
+ }
+ /* Now we know that sibling is BLACK.
+
+ parent
+ / \
+ sibling child
+ bh+1 bh
+ */
+ if (sibling->left != NULL && sibling->left->color == RED)
+ {
+ /*
+ parent sibling
+ bh+1|bh+2 bh+1|bh+2
+ / \ / \
+ sibling child --> SL parent
+ bh+1 bh bh+1 bh+1
+ / \ / \
+ SL SR SR child
+ bh bh bh bh
+ */
+ *parentp = rotate_right (sibling, parent);
+ sibling->color = parent->color;
+ parent->color = BLACK;
+ sibling->left->color = BLACK;
+ return;
+ }
+ else if (sibling->right != NULL && sibling->right->color == RED)
+ {
+ /*
+ parent parent
+ bh+1|bh+2 bh+1|bh+2
+ / \ / \
+ sibling child --> SR child
+ bh+1 bh bh+1 bh
+ / \ / \
+ SL SR sibling SRR
+ bh bh bh bh
+ / \ / \
+ SRL SRR SL SRL
+ bh bh bh bh
+
+ where SL, SRL, SRR are all black.
+ */
+ parent->left = rotate_left (sibling, sibling->right);
+ /* Change sibling from BLACK to RED and SL from RED to BLACK. */
+ sibling->color = RED;
+ sibling = parent->left;
+ sibling->color = BLACK;
+
+ /* Now do as in the previous case. */
+ *parentp = rotate_right (sibling, parent);
+ sibling->color = parent->color;
+ parent->color = BLACK;
+ sibling->left->color = BLACK;
+ return;
+ }
+ else
+ {
+ if (parent->color == BLACK)
+ {
+ /* Change sibling from BLACK to RED. Then the entire
+ subtree at parent has decreased its black-height.
+ parent parent
+ bh+2 bh+1
+ / \ / \
+ sibling child --> sibling child
+ bh+1 bh bh bh
+ */
+ sibling->color = RED;
+
+ child = parent;
+ }
+ else
+ {
+ /* Change parent from RED to BLACK, but compensate by
+ changing sibling from BLACK to RED.
+ parent parent
+ bh+1 bh+1
+ / \ / \
+ sibling child --> sibling child
+ bh+1 bh bh bh
+ */
+ parent->color = BLACK;
+ sibling->color = RED;
+ return;
+ }
+ }
+ }
+ else
+ abort ();
+
+ /* Start again with a new (child, parent) pair. */
+ parent = child->parent;
+
+#if 0 /* Already handled. */
+ if (child != NULL && child->color == RED)
+ {
+ child->color = BLACK;
+ return;
+ }
+#endif
+
+ if (parent == NULL)
+ return;
+ }
+}
+
+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->value = elt;
+
+ /* Add it to the tree. */
+ if (set->root == NULL)
+ {
+ new_node->color = BLACK;
+ 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;
+
+ /* Color and rebalance. */
+ rebalance_after_add (set, new_node, node);
+ }
+
+ 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));
+
+ new_node->left = NULL;
+ new_node->right = NULL;
+ new_node->value = elt;
+
+ /* Add it to the tree. */
+ if (node->left == NULL)
+ node->left = new_node;
+ else
+ {
+ for (node = node->left; node->right != NULL; )
+ node = node->right;
+ node->right = new_node;
+ }
+ new_node->parent = node;
+
+ /* Color and rebalance. */
+ rebalance_after_add (set, new_node, node);
+
+ 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));
+
+ new_node->left = NULL;
+ new_node->right = NULL;
+ new_node->value = elt;
+
+ /* Add it to the tree. */
+ if (node->right == NULL)
+ node->right = new_node;
+ else
+ {
+ for (node = node->right; node->left != NULL; )
+ node = node->left;
+ node->left = new_node;
+ }
+ new_node->parent = node;
+
+ /* Color and rebalance. */
+ rebalance_after_add (set, new_node, node);
+
+ 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;
+ /* Since node->left == NULL, child must be RED and of height 1,
+ hence node must have been BLACK. Recolor the child. */
+ child->color = BLACK;
+ }
+ if (parent == NULL)
+ set->root = child;
+ else
+ {
+ if (parent->left == node)
+ parent->left = child;
+ else /* parent->right == node */
+ parent->right = child;
+
+ if (child == NULL && node->color == BLACK)
+ rebalance_after_remove (set, child, 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;
+ /* Since node->right == NULL, child must be RED and of height 1,
+ hence node must have been BLACK. Recolor the child. */
+ child->color = BLACK;
+ if (parent == NULL)
+ set->root = child;
+ else
+ {
+ if (parent->left == node)
+ parent->left = child;
+ else /* parent->right == node */
+ parent->right = child;
+ }
+ }
+ 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;
+ color_t removed_color;
+
+ for (subst = node->left; subst->right != NULL; )
+ subst = subst->right;
+
+ subst_parent = subst->parent;
+
+ child = subst->left;
+
+ removed_color = subst->color;
+
+ /* 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->color = node->color;
+ subst->parent = parent;
+ if (parent == NULL)
+ set->root = subst;
+ else if (parent->left == node)
+ parent->left = subst;
+ else /* parent->right == node */
+ parent->right = subst;
+
+ if (removed_color == BLACK)
+ {
+ if (child != NULL && child->color == RED)
+ /* Recolor the child. */
+ child->color = BLACK;
+ else
+ /* 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_after_remove (set, child,
+ 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_blackheight =
+ (node->left != NULL ? check_invariants (node->left, node, counterp) : 0);
+ unsigned int right_blackheight =
+ (node->right != NULL ? check_invariants (node->right, node, counterp) : 0);
+
+ if (!(node->parent == parent))
+ abort ();
+ if (!(node->color == BLACK || node->color == RED))
+ abort ();
+ if (parent == NULL && !(node->color == BLACK))
+ abort ();
+ if (!(left_blackheight == right_blackheight))
+ abort ();
+
+ (*counterp)++;
+
+ return left_blackheight + (node->color == BLACK ? 1 : 0);
+}
+void
+gl_rbtree_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_rbtree_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
+ };
projects / gnulib.git / blobdiff