rbtree.c

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/*!
 * \file rbtree.c
 *
 * \brief binary search tree 
 *
 * Generic balanced binary search tree (Red Black Tree) implementation
 *
 * (C) 2009 by the GRASS Development Team
 *
 * This program is free software under the GNU General Public License
 * (>=v2).  Read the file COPYING that comes with GRASS for details.
 *
 * \author Original author Julienne Walker 2003, 2008
 *         GRASS implementation Markus Metz, 2009
 */

/* balanced binary search tree implementation
 * 
 * this one is a Red Black Tree, no parent pointers, no threads
 * The core code comes from Julienne Walker's tutorials on binary search trees
 * original license: public domain
 * http://eternallyconfuzzled.com/tuts/datastructures/jsw_tut_rbtree.aspx
 * some ideas come from libavl (GPL >= 2)
 *
 * Red Black Trees are used to maintain a data structure with
 * search, insertion and deletion in O(log N) time
 */

#include <assert.h>
#include <stdlib.h>
#include <string.h>
#include <grass/gis.h>
#include <grass/glocale.h>
#include <grass/rbtree.h>

/* internal functions */
static struct RB_NODE *rbtree_single(struct RB_NODE *, int);
static struct RB_NODE *rbtree_double(struct RB_NODE *, int);
static void *rbtree_first(struct RB_TRAV *);
static void *rbtree_last(struct RB_TRAV *trav);
static void *rbtree_next(struct RB_TRAV *);
static void *rbtree_previous(struct RB_TRAV *);
static struct RB_NODE *rbtree_make_node(size_t, void *);
static int is_red(struct RB_NODE *);


/* create new tree and initialize
 * returns pointer to new tree, NULL for memory allocation error
 */
struct RB_TREE *rbtree_create(rb_compare_fn *compare, size_t rb_datasize)
{
    struct RB_TREE *tree = (struct RB_TREE *)malloc(sizeof(struct RB_TREE));

    if (tree == NULL) {
        G_warning("RB tree: Out of memory!");
        return NULL;
    }

    assert(compare);

    tree->datasize = rb_datasize;
    tree->rb_compare = compare;
    tree->count = 0;
    tree->root = NULL;

    return tree;
}

/* add an item to a tree
 * non-recursive top-down insertion
 * the algorithm does not allow duplicates and also does not warn about a duplicate
 * returns 1 on success, 0 on failure
 */
int rbtree_insert(struct RB_TREE *tree, void *data)
{
    assert(tree && data);

    if (tree->root == NULL) {
        /* create a new root node for tree */
        tree->root = rbtree_make_node(tree->datasize, data);
        if (tree->root == NULL)
            return 0;
    }
    else {
        struct RB_NODE head = { 0, 0, {0, 0} }; /* False tree root */
        struct RB_NODE *g, *t;  /* Grandparent & parent */
        struct RB_NODE *p, *q;  /* Iterator & parent */
        int dir = 0, last = 0;

        /* Set up helpers */
        t = &head;
        g = p = NULL;
        q = t->link[1] = tree->root;

        /* Search down the tree */
        for (;;) {
            if (q == NULL) {
                /* Insert new node at the bottom */
                p->link[dir] = q = rbtree_make_node(tree->datasize, data);
                if (q == NULL)
                    return 0;
            }
            else if (is_red(q->link[0]) && is_red(q->link[1])) {
                /* Color flip */
                q->red = 1;
                q->link[0]->red = 0;
                q->link[1]->red = 0;
            }

            /* Fix red violation */
            if (is_red(q) && is_red(p)) {
                int dir2 = t->link[1] == g;

                if (q == p->link[last])
                    t->link[dir2] = rbtree_single(g, !last);
                else
                    t->link[dir2] = rbtree_double(g, !last);
            }

            last = dir;
            dir = tree->rb_compare(q->data, data);

            /* Stop if found. This check also disallows duplicates in the tree */
            if (dir == 0)
                break;

            dir = dir < 0;

            /* Move the helpers down */
            if (g != NULL)
                t = g;

            g = p, p = q;
            q = q->link[dir];
        }

        /* Update root */
        tree->root = head.link[1];
    }

    /* Make root black */
    tree->root->red = 0;

    tree->count++;

    return 1;
}

/* remove an item from a tree that matches given data
 * non-recursive top-down removal
 * returns 1 on successful removal
 * returns 0 if data item was not found
 */
int rbtree_remove(struct RB_TREE *tree, const void *data)
{
    struct RB_NODE head = { 0, 0, {0, 0} };     /* False tree root */
    struct RB_NODE *q, *p, *g;  /* Helpers */
    struct RB_NODE *f = NULL;   /* Found item */
    int dir = 1, removed = 0;

    assert(tree && data);

    if (tree->root == NULL) {
        return 0;               /* empty tree, nothing to remove */
    }

    /* Set up helpers */
    q = &head;
    g = p = NULL;
    q->link[1] = tree->root;

    /* Search and push a red down */
    while (q->link[dir] != NULL) {
        int last = dir;

        /* Update helpers */
        g = p, p = q;
        q = q->link[dir];
        dir = tree->rb_compare(q->data, data);

        /* Save found node */
        if (dir == 0)
            f = q;

        dir = dir < 0;

        /* Push the red node down */
        if (!is_red(q) && !is_red(q->link[dir])) {
            if (is_red(q->link[!dir]))
                p = p->link[last] = rbtree_single(q, dir);
            else if (!is_red(q->link[!dir])) {
                struct RB_NODE *s = p->link[!last];

                if (s != NULL) {
                    if (!is_red(s->link[!last]) && !is_red(s->link[last])) {
                        /* Color flip */
                        p->red = 0;
                        s->red = 1;
                        q->red = 1;
                    }
                    else {
                        int dir2 = g->link[1] == p;

                        if (is_red(s->link[last]))
                            g->link[dir2] = rbtree_double(p, last);
                        else if (is_red(s->link[!last]))
                            g->link[dir2] = rbtree_single(p, last);

                        /* Ensure correct coloring */
                        q->red = g->link[dir2]->red = 1;
                        g->link[dir2]->link[0]->red = 0;
                        g->link[dir2]->link[1]->red = 0;
                    }
                }
            }
        }
    }

    /* Replace and remove if found */
    if (f != NULL) {
        free(f->data);
        f->data = q->data;
        p->link[p->link[1] == q] = q->link[q->link[0] == NULL];
        free(q);
        q = NULL;
        tree->count--;
        removed = 1;
    }
    else
        G_debug(2, "RB tree: data not found in search tree");

    /* Update root and make it black */
    tree->root = head.link[1];
    if (tree->root != NULL)
        tree->root->red = 0;

    return removed;
}

/* find data item in tree
 * returns pointer to data item if found else NULL
 */
void *rbtree_find(struct RB_TREE *tree, const void *data)
{
    struct RB_NODE *curr_node = tree->root;
    int cmp;

    assert(tree && data);

    while (curr_node != NULL) {
        cmp = tree->rb_compare(curr_node->data, data);
        if (cmp == 0)
            return curr_node->data;     /* found */

        curr_node = curr_node->link[cmp < 0];
    }
    return NULL;
}

/* initialize tree traversal
 * (re-)sets trav structure
 * returns 0
 */
int rbtree_init_trav(struct RB_TRAV *trav, struct RB_TREE *tree)
{
    assert(trav && tree);

    trav->tree = tree;
    trav->curr_node = tree->root;
    trav->first = 1;
    trav->top = 0;

    return 0;
}

/* traverse the tree in ascending order
 * useful to get all items in the tree non-recursively
 * struct RB_TRAV *trav needs to be initialized first
 * returns pointer to data, NULL when finished
 */
void *rbtree_traverse(struct RB_TRAV *trav)
{
    assert(trav);

    if (trav->curr_node == NULL) {
        if (trav->first)
            G_debug(1, "RB tree: empty tree");
        else
            G_debug(1, "RB tree: finished traversing");

        return NULL;
    }

    if (!trav->first)
        return rbtree_next(trav);
    else {
        trav->first = 0;
        return rbtree_first(trav);
    }
}

/* traverse the tree in descending order
 * useful to get all items in the tree non-recursively
 * struct RB_TRAV *trav needs to be initialized first
 * returns pointer to data, NULL when finished
 */
void *rbtree_traverse_backwd(struct RB_TRAV *trav)
{
    assert(trav);

    if (trav->curr_node == NULL) {
        if (trav->first)
            G_debug(1, "RB tree: empty tree");
        else
            G_debug(1, "RB tree: finished traversing");

        return NULL;
    }

    if (!trav->first)
        return rbtree_previous(trav);
    else {
        trav->first = 0;
        return rbtree_last(trav);
    }
}

/* find start point to traverse the tree in ascending order
 * useful to get a selection of items in the tree
 * magnitudes faster than traversing the whole tree
 * may return first item that's smaller or first item that's larger
 * struct RB_TRAV *trav needs to be initialized first
 * returns pointer to data, NULL when finished
 */
void *rbtree_traverse_start(struct RB_TRAV *trav, const void *data)
{
    int dir = 0;

    assert(trav && data);

    if (trav->curr_node == NULL) {
        if (trav->first)
            G_warning("RB tree: empty tree");
        else
            G_warning("RB tree: finished traversing");

        return NULL;
    }

    if (!trav->first)
        return rbtree_next(trav);

    /* else first time, get start node */

    trav->first = 0;
    trav->top = 0;

    while (trav->curr_node != NULL) {
        dir = trav->tree->rb_compare(trav->curr_node->data, data);
        /* exact match, great! */
        if (dir == 0)
            return trav->curr_node->data;
        else {
            dir = dir < 0;
            /* end of branch, also reached if
             * smallest item is larger than search template or
             * largest item is smaller than search template */
            if (trav->curr_node->link[dir] == NULL)
                return trav->curr_node->data;

            trav->up[trav->top++] = trav->curr_node;
            trav->curr_node = trav->curr_node->link[dir];
        }
    }

    return NULL;                /* should not happen */
}

/* two functions needed to fully traverse the tree: initialize and continue
 * useful to get all items in the tree non-recursively
 * this one here uses a stack
 * parent pointers or threads would also be possible
 * but these would need to be added to RB_NODE
 * -> more memory needed for standard operations
 */

/* start traversing the tree
 * returns pointer to smallest data item
 */
static void *rbtree_first(struct RB_TRAV *trav)
{
    /* get smallest item */
    while (trav->curr_node->link[0] != NULL) {
        trav->up[trav->top++] = trav->curr_node;
        trav->curr_node = trav->curr_node->link[0];
    }

    return trav->curr_node->data;       /* return smallest item */
}

/* start traversing the tree
 * returns pointer to largest data item
 */
static void *rbtree_last(struct RB_TRAV *trav)
{
    /* get smallest item */
    while (trav->curr_node->link[1] != NULL) {
        trav->up[trav->top++] = trav->curr_node;
        trav->curr_node = trav->curr_node->link[1];
    }

    return trav->curr_node->data;       /* return smallest item */
}

/* continue traversing the tree in ascending order
 * returns pointer to data item, NULL when finished
 */
void *rbtree_next(struct RB_TRAV *trav)
{
    if (trav->curr_node->link[1] != NULL) {
        /* something on the right side: larger item */
        trav->up[trav->top++] = trav->curr_node;
        trav->curr_node = trav->curr_node->link[1];

        /* go down, find smallest item in this branch */
        while (trav->curr_node->link[0] != NULL) {
            trav->up[trav->top++] = trav->curr_node;
            trav->curr_node = trav->curr_node->link[0];
        }
    }
    else {
        /* at smallest item in this branch, go back up */
        struct RB_NODE *last;

        do {
            if (trav->top == 0) {
                trav->curr_node = NULL;
                break;
            }
            last = trav->curr_node;
            trav->curr_node = trav->up[--trav->top];
        } while (last == trav->curr_node->link[1]);
    }

    if (trav->curr_node != NULL) {
        return trav->curr_node->data;
    }
    else
        return NULL;            /* finished traversing */
}

/* continue traversing the tree in descending order
 * returns pointer to data item, NULL when finished
 */
void *rbtree_previous(struct RB_TRAV *trav)
{
    if (trav->curr_node->link[0] != NULL) {
        /* something on the left side: smaller item */
        trav->up[trav->top++] = trav->curr_node;
        trav->curr_node = trav->curr_node->link[0];

        /* go down, find largest item in this branch */
        while (trav->curr_node->link[1] != NULL) {
            trav->up[trav->top++] = trav->curr_node;
            trav->curr_node = trav->curr_node->link[1];
        }
    }
    else {
        /* at largest item in this branch, go back up */
        struct RB_NODE *last;

        do {
            if (trav->top == 0) {
                trav->curr_node = NULL;
                break;
            }
            last = trav->curr_node;
            trav->curr_node = trav->up[--trav->top];
        } while (last == trav->curr_node->link[0]);
    }

    if (trav->curr_node != NULL) {
        return trav->curr_node->data;
    }
    else
        return NULL;            /* finished traversing */
}

/* clear the tree, removing all entries */
void rbtree_clear(struct RB_TREE *tree)
{
    struct RB_NODE *it;
    struct RB_NODE *save = tree->root;

    /*
    Rotate away the left links so that
    we can treat this like the destruction
    of a linked list
    */
    while((it = save) != NULL) {
        if (it->link[0] == NULL) {
            /* No left links, just kill the node and move on */
            save = it->link[1];
            free(it->data);
            it->data = NULL;
            free(it);
            it = NULL;
        }
        else {
            /* Rotate away the left link and check again */
            save = it->link[0];
            it->link[0] = save->link[1];
            save->link[1] = it;
        }
    }
    tree->root = NULL;
}

/* destroy the tree */
void rbtree_destroy(struct RB_TREE *tree)
{
    /* remove all entries */
    rbtree_clear(tree);

    free(tree);
    tree = NULL;
}

/* used for debugging: check for errors in tree structure */
int rbtree_debug(struct RB_TREE *tree, struct RB_NODE *root)
{
    int lh, rh;

    if (root == NULL)
        return 1;
    else {
        struct RB_NODE *ln = root->link[0];
        struct RB_NODE *rn = root->link[1];
        int lcmp = 0, rcmp = 0;

        /* Consecutive red links */
        if (is_red(root)) {
            if (is_red(ln) || is_red(rn)) {
                G_warning("Red Black Tree debugging: Red violation");
                return 0;
            }
        }

        lh = rbtree_debug(tree, ln);
        rh = rbtree_debug(tree, rn);

        if (ln) {
            lcmp = tree->rb_compare(ln->data, root->data);
        }

        if (rn) {
            rcmp = tree->rb_compare(rn->data, root->data);
        }

        /* Invalid binary search tree:
         * left node >= parent or right node <= parent */
        if ((ln != NULL && lcmp > -1)
            || (rn != NULL && rcmp < 1)) {
            G_warning("Red Black Tree debugging: Binary tree violation");
            return 0;
        }

        /* Black height mismatch */
        if (lh != 0 && rh != 0 && lh != rh) {
            G_warning("Red Black Tree debugging: Black violation");
            return 0;
        }

        /* Only count black links */
        if (lh != 0 && rh != 0)
            return is_red(root) ? lh : lh + 1;
        else
            return 0;
    }
}

/*******************************************************
 *                                                     *
 *  internal functions for Red Black Tree maintenance  *
 *                                                     *
 *******************************************************/

/* add a new node to the tree */
static struct RB_NODE *rbtree_make_node(size_t datasize, void *data)
{
    struct RB_NODE *new_node = (struct RB_NODE *)malloc(sizeof(*new_node));

    if (new_node == NULL)
        G_fatal_error("RB Search Tree: Out of memory!");

    new_node->data = malloc(datasize);
    if (new_node->data == NULL)
        G_fatal_error("RB Search Tree: Out of memory!");

    memcpy(new_node->data, data, datasize);
    new_node->red = 1;          /* 1 is red, 0 is black */
    new_node->link[0] = NULL;
    new_node->link[1] = NULL;

    return new_node;
}

/* check for red violation */
static int is_red(struct RB_NODE *root)
{
    if (root)
        return root->red == 1;

    return 0;
}

/* single rotation */
static struct RB_NODE *rbtree_single(struct RB_NODE *root, int dir)
{
    struct RB_NODE *newroot = root->link[!dir];

    root->link[!dir] = newroot->link[dir];
    newroot->link[dir] = root;

    root->red = 1;
    newroot->red = 0;

    return newroot;
}

/* double rotation */
static struct RB_NODE *rbtree_double(struct RB_NODE *root, int dir)
{
    root->link[!dir] = rbtree_single(root->link[!dir], !dir);
    return rbtree_single(root, dir);
}