sudo/redblack.c

/*
 * Copyright (c) 2003 Todd C. Miller <Todd.Miller@courtesan.com>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

#include <config.h>

#include <sys/types.h>
#include <sys/param.h>

#include <stdio.h>
#ifdef STDC_HEADERS
# include <stdlib.h>
# include <stddef.h>
#else
# ifdef HAVE_STDLIB_H
#  include <stdlib.h>
# endif
#endif /* STDC_HEADERS */

#include "sudo.h"
#include "redblack.h"

static void rbrepair		__P((struct rbtree *, struct rbnode *));
static void rotate_left		__P((struct rbtree *, struct rbnode *));
static void rotate_right	__P((struct rbtree *, struct rbnode *));
static void _rbdestroy		__P((struct rbtree *, struct rbnode *,
				    void (*)(VOID *)));

/*
 * Red-Black tree, see http://en.wikipedia.org/wiki/Red-black_tree
 *
 * A red-black tree is a binary search tree where each node has a color
 * attribute, the value of which is either red or black.  Essentially, it
 * is just a convenient way to express a 2-3-4 binary search tree where
 * the color indicates whether the node is part of a 3-node or a 4-node.
 * In addition to the ordinary requirements imposed on binary search
 * trees, we make the following additional requirements of any valid
 * red-black tree:
 *  1) The root is black.
 *  2) All leaves are black.
 *  3) Both children of each red node are black.
 *  4) The paths from each leaf up to the root each contain the same
 *     number of black nodes.
 */

/*
 * Create a red black tree struct using the specified compare routine.
 * Allocates and returns the initialized (empty) tree.
 */
struct rbtree *
rbcreate(compar)
    int (*compar)__P((const VOID *, const VOID*));
{
    struct rbtree *tree;

    tree = (struct rbtree *) emalloc(sizeof(*tree));
    tree->compar = compar;

    /*
     * We use a self-referencing sentinel node called nil to simplify the
     * code by avoiding the need to check for NULL pointers.
     */
    tree->nil.left = tree->nil.right = tree->nil.parent = &tree->nil;
    tree->nil.color = black;
    tree->nil.data = NULL;

    /*
     * Similarly, the fake root node keeps us from having to worry
     * about splitting the root.
     */
    tree->root.left = tree->root.right = tree->root.parent = &tree->nil;
    tree->root.color = black;
    tree->root.data = NULL;

    return(tree);
}

/*
 * Perform a left rotation starting at node.
 */
static void
rotate_left(tree, node)
    struct rbtree *tree;
    struct rbnode *node;
{
    struct rbnode *child;

    child = node->right;
    node->right = child->left;

    if (child->left != rbnil(tree))
        child->left->parent = node;
    child->parent = node->parent;

    if (node == node->parent->left)
	node->parent->left = child;
    else
	node->parent->right = child;
    child->left = node;
    node->parent = child;
}

/*
 * Perform a right rotation starting at node.
 */
static void
rotate_right(tree, node)
    struct rbtree *tree;
    struct rbnode *node;
{
    struct rbnode *child;

    child = node->left;
    node->left = child->right;

    if (child->right != rbnil(tree))
        child->right->parent = node;
    child->parent = node->parent;

    if (node == node->parent->left)
	node->parent->left = child;
    else
	node->parent->right = child;
    child->right = node;
    node->parent = child;
}

/*
 * Insert data pointer into a redblack tree.
 * Returns a NULL pointer on success.  If a node matching "data"
 * already exists, a pointer to the existant node is returned.
 */
struct rbnode *
rbinsert(tree, data)
    struct rbtree *tree;
    VOID *data;
{
    struct rbnode *node = rbfirst(tree);
    struct rbnode *parent = rbroot(tree);
    int res;

    /* Find correct insertion point. */
    while (node != rbnil(tree)) {
	parent = node;
	if ((res = tree->compar(data, node->data)) == 0)
	    return(node);
	node = res < 0 ? node->left : node->right;
    }

    node = (struct rbnode *) emalloc(sizeof(*node));
    node->data = data;
    node->left = node->right = rbnil(tree);
    node->parent = parent;
    if (parent == rbroot(tree) || tree->compar(data, parent->data) < 0)
	parent->left = node;
    else
	parent->right = node;
    node->color = red;

    /*
     * If the parent node is black we are all set, if it is red we have
     * the following possible cases to deal with.  We iterate through
     * the rest of the tree to make sure none of the required properties
     * is violated.
     *
     *	1) The uncle is red.  We repaint both the parent and uncle black
     *     and repaint the grandparent node red.
     *
     *  2) The uncle is black and the new node is the right child of its
     *     parent, and the parent in turn is the left child of its parent.
     *     We do a left rotation to switch the roles of the parent and
     *     child, relying on further iterations to fixup the old parent.
     *
     *  3) The uncle is black and the new node is the left child of its
     *     parent, and the parent in turn is the left child of its parent.
     *     We switch the colors of the parent and grandparent and perform
     *     a right rotation around the grandparent.  This makes the former
     *     parent the parent of the new node and the former grandparent.
     *
     * Note that because we use a sentinel for the root node we never
     * need to worry about replacing the root.
     */
    while (node->parent->color == red) {
	struct rbnode *uncle;
	if (node->parent == node->parent->parent->left) {
	    uncle = node->parent->parent->right;
	    if (uncle->color == red) {
		node->parent->color = black;
		uncle->color = black;
		node->parent->parent->color = red;
		node = node->parent->parent;
	    } else /* if (uncle->color == black) */ {
		if (node == node->parent->right) {
		    node = node->parent;
		    rotate_left(tree, node);
		}
		node->parent->color = black;
		node->parent->parent->color = red;
		rotate_right(tree, node->parent->parent);
	    }
	} else { /* if (node->parent == node->parent->parent->right) */
	    uncle = node->parent->parent->left;
	    if (uncle->color == red) {
		node->parent->color = black;
		uncle->color = black;
		node->parent->parent->color = red;
		node = node->parent->parent;
	    } else /* if (uncle->color == black) */ {
		if (node == node->parent->left) {
		    node = node->parent;
		    rotate_right(tree, node);
		}
		node->parent->color = black;
		node->parent->parent->color = red;
		rotate_left(tree, node->parent->parent);
	    }
	}
    }
    rbfirst(tree)->color = black;	/* first node is always black */
    return(NULL);
}

/*
 * Look for a node matching key in tree.
 * Returns a pointer to the node if found, else NULL.
 */
struct rbnode *
rbfind(tree, key)
    struct rbtree *tree;
    VOID *key;
{
    struct rbnode *node = rbfirst(tree);
    int res;

    while (node != rbnil(tree)) {
	if ((res = tree->compar(key, node->data)) == 0)
	    return(node);
	node = res < 0 ? node->left : node->right;
    }
    return(NULL);
}

/*
 * Call func() for each node, passing it the node data and a cookie;
 * If func() returns non-zero for a node, the traversal stops and the
 * error value is returned.  Returns 0 on successful traversal.
 */
int
rbapply_node(tree, node, func, cookie, order)
    struct rbtree *tree;
    struct rbnode *node;
    int (*func)__P((VOID *, VOID *));
    VOID *cookie;
    enum rbtraversal order;
{
    int error;

    if (node != rbnil(tree)) {
	if (order == preorder)
	    if ((error = func(node->data, cookie)) != 0)
		return(error);
	if ((error = rbapply_node(tree, node->left, func, cookie, order)) != 0)
	    return(error);
	if (order == inorder)
	    if ((error = func(node->data, cookie)) != 0)
		return(error);
	if ((error = rbapply_node(tree, node->right, func, cookie, order)) != 0)
	    return(error);
	if (order == postorder)
	    if ((error = func(node->data, cookie)) != 0)
		return(error);
    }
    return (0);
}

/*
 * Returns the successor of node, or nil if there is none.
 */
static struct rbnode *
rbsuccessor(tree, node)
    struct rbtree *tree;
    struct rbnode *node;
{
    struct rbnode *succ;

    if ((succ = node->right) != rbnil(tree)) {
	while (succ->left != rbnil(tree))
	    succ = succ->left;
    } else {
	/* No right child, move up until we find it or hit the root */
	for (succ = node->parent; node == succ->right; succ = succ->parent)
	    node = succ;
	if (succ == rbroot(tree))
	    succ = rbnil(tree);
    }
    return(succ);
}

/*
 * Recursive portion of rbdestroy().
 */
static void
_rbdestroy(tree, node, destroy)
    struct rbtree *tree;
    struct rbnode *node;
    void (*destroy)__P((VOID *));
{
    if (node != rbnil(tree)) {
	_rbdestroy(tree, node->left, destroy);
	_rbdestroy(tree, node->right, destroy);
	if (destroy != NULL)
	    destroy(node->data);
	free(node);
    }
}

/*
 * Destroy the specified tree, calling the destructor destroy
 * for each node and then freeing the tree itself.
 */
void
rbdestroy(tree, destroy)
    struct rbtree *tree;
    void (*destroy)__P((VOID *));
{
    _rbdestroy(tree, rbfirst(tree), destroy);
    free(tree);
}

/*
 * Delete victim from tree and return its data pointer.
 */
VOID *
rbdelete(tree, victim)
    struct rbtree *tree;
    struct rbnode *victim;
{
    struct rbnode *pred, *succ;
    VOID *data;

    if (victim->left != rbnil(tree) && victim->right != rbnil(tree)) {
	succ = rbsuccessor(tree, victim);
	pred = succ->left == rbnil(tree) ? succ->right : succ->left;
	if (succ->parent == rbroot(tree)) {
	    pred->parent = rbroot(tree);
	    rbfirst(tree) = pred;
	} else {
	    if (succ == succ->parent->left)
		succ->parent->left = pred;
	    else
		succ->parent->right = pred;
	}
	if ((succ->color == black))
	    rbrepair(tree, pred);

	succ->left = victim->left;
	succ->right = victim->right;
	succ->parent = victim->parent;
	succ->color = victim->color;
	victim->left->parent = victim->right->parent = succ;
	if (victim == victim->parent->left)
	    victim->parent->left = succ;
	else
	    victim->parent->right = succ;
	data = victim->data;
	free(victim);
    } else {
	pred = victim->left == rbnil(tree) ? victim->right : victim->left;
	if (victim->parent == rbroot(tree)) {
	    pred->parent = rbroot(tree);
	    rbfirst(tree) = pred;
	} else {
	    if (victim == victim->parent->left)
		victim->parent->left = pred;
	    else
		victim->parent->right = pred;
	}
	if (victim->color == black)
	    rbrepair(tree, pred);
	data = victim->data;
	free(victim);
    }
    return(data);
}

/*
 * Repair the tree after a node has been deleted by rotating and repainting
 * colors to restore the 4 properties inherent in red-black trees.
 */
static void
rbrepair(tree, node)
    struct rbtree *tree;
    struct rbnode *node;
{
    struct rbnode *sibling;

    while (node->color == black && node != rbfirst(tree)) {
	if (node == node->parent->left) {
	    sibling = node->parent->right;
	    if (sibling->color == red) {
		sibling->color = black;
		node->parent->color = red;
		rotate_left(tree, node->parent);
		sibling = node->parent->right;
	    }
	    if (sibling->right->color == black && sibling->left->color == black) {
		sibling->color = red;
		node = node->parent;
	    } else {
		if (sibling->right->color == black) {
		      sibling->left->color = black;
		      sibling->color = red;
		      rotate_right(tree, sibling);
		      sibling = node->parent->right;
		}
		sibling->color = node->parent->color;
		node->parent->color = black;
		sibling->right->color = black;
		rotate_left(tree, node->parent);
		return;	/* XXX */
	    }
	} else { /* if (node == node->parent->right) */
	    sibling = node->parent->left;
	    if (sibling->color == red) {
		sibling->color = black;
		node->parent->color = red;
		rotate_right(tree, node->parent);
		sibling = node->parent->left;
	    }
	    if (sibling->right->color == black && sibling->left->color == black) {
		sibling->color = red;
		node = node->parent;
	    } else {
		if (sibling->left->color == black) {
		    sibling->right->color = black;
		    sibling->color = red;
		    rotate_left(tree, sibling);
		    sibling = node->parent->left;
		}
		sibling->color = node->parent->color;
		node->parent->color = black;
		sibling->left->color = black;
		rotate_right(tree, node->parent);
		return; /* XXX */
	    }
	}
    }
    node->color = black;
}