rbtree.c

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/*-------------------------------------------------------------------------
 *
 * rbtree.c
 *    implementation for PostgreSQL generic Red-Black binary tree package
 *    Adopted from http://algolist.manual.ru/ds/rbtree.php
 *
 * This code comes from Thomas Niemann's "Sorting and Searching Algorithms:
 * a Cookbook".
 *
 * See http://www.cs.auckland.ac.nz/software/AlgAnim/niemann/s_man.htm for
 * license terms: "Source code, when part of a software project, may be used
 * freely without reference to the author."
 *
 * Red-black trees are a type of balanced binary tree wherein (1) any child of
 * a red node is always black, and (2) every path from root to leaf traverses
 * an equal number of black nodes.  From these properties, it follows that the
 * longest path from root to leaf is only about twice as long as the shortest,
 * so lookups are guaranteed to run in O(lg n) time.
 *
 * Copyright (c) 2009-2020, PostgreSQL Global Development Group
 *
 * IDENTIFICATION
 *    src/backend/lib/rbtree.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "lib/rbtree.h"


/*
 * Colors of nodes (values of RBTNode.color)
 */
#define RBTBLACK    (0)
#define RBTRED      (1)

/*
 * RBTree control structure
 */
struct RBTree
{
    RBTNode    *root;           /* root node, or RBTNIL if tree is empty */

    /* Remaining fields are constant after rbt_create */

    Size        node_size;      /* actual size of tree nodes */
    /* The caller-supplied manipulation functions */
    rbt_comparator comparator;
    rbt_combiner combiner;
    rbt_allocfunc allocfunc;
    rbt_freefunc freefunc;
    /* Passthrough arg passed to all manipulation functions */
    void       *arg;
};

/*
 * all leafs are sentinels, use customized NIL name to prevent
 * collision with system-wide constant NIL which is actually NULL
 */
#define RBTNIL (&sentinel)

static RBTNode sentinel =
{
    RBTBLACK, RBTNIL, RBTNIL, NULL
};


/*
 * rbt_create: create an empty RBTree
 *
 * Arguments are:
 *  node_size: actual size of tree nodes (> sizeof(RBTNode))
 *  The manipulation functions:
 *  comparator: compare two RBTNodes for less/equal/greater
 *  combiner: merge an existing tree entry with a new one
 *  allocfunc: allocate a new RBTNode
 *  freefunc: free an old RBTNode
 *  arg: passthrough pointer that will be passed to the manipulation functions
 *
 * Note that the combiner's righthand argument will be a "proposed" tree node,
 * ie the input to rbt_insert, in which the RBTNode fields themselves aren't
 * valid.  Similarly, either input to the comparator may be a "proposed" node.
 * This shouldn't matter since the functions aren't supposed to look at the
 * RBTNode fields, only the extra fields of the struct the RBTNode is embedded
 * in.
 *
 * The freefunc should just be pfree or equivalent; it should NOT attempt
 * to free any subsidiary data, because the node passed to it may not contain
 * valid data!  freefunc can be NULL if caller doesn't require retail
 * space reclamation.
 *
 * The RBTree node is palloc'd in the caller's memory context.  Note that
 * all contents of the tree are actually allocated by the caller, not here.
 *
 * Since tree contents are managed by the caller, there is currently not
 * an explicit "destroy" operation; typically a tree would be freed by
 * resetting or deleting the memory context it's stored in.  You can pfree
 * the RBTree node if you feel the urge.
 */
RBTree *
rbt_create(Size node_size,
           rbt_comparator comparator,
           rbt_combiner combiner,
           rbt_allocfunc allocfunc,
           rbt_freefunc freefunc,
           void *arg)
{
    RBTree     *tree = (RBTree *) palloc(sizeof(RBTree));

    Assert(node_size > sizeof(RBTNode));

    tree->root = RBTNIL;
    tree->node_size = node_size;
    tree->comparator = comparator;
    tree->combiner = combiner;
    tree->allocfunc = allocfunc;
    tree->freefunc = freefunc;

    tree->arg = arg;

    return tree;
}

/* Copy the additional data fields from one RBTNode to another */
static inline void
rbt_copy_data(RBTree *rbt, RBTNode *dest, const RBTNode *src)
{
    memcpy(dest + 1, src + 1, rbt->node_size - sizeof(RBTNode));
}

/**********************************************************************
 *                        Search                                      *
 **********************************************************************/

/*
 * rbt_find: search for a value in an RBTree
 *
 * data represents the value to try to find.  Its RBTNode fields need not
 * be valid, it's the extra data in the larger struct that is of interest.
 *
 * Returns the matching tree entry, or NULL if no match is found.
 */
RBTNode *
rbt_find(RBTree *rbt, const RBTNode *data)
{
    RBTNode    *node = rbt->root;

    while (node != RBTNIL)
    {
        int         cmp = rbt->comparator(data, node, rbt->arg);

        if (cmp == 0)
            return node;
        else if (cmp < 0)
            node = node->left;
        else
            node = node->right;
    }

    return NULL;
}

/*
 * rbt_leftmost: fetch the leftmost (smallest-valued) tree node.
 * Returns NULL if tree is empty.
 *
 * Note: in the original implementation this included an unlink step, but
 * that's a bit awkward.  Just call rbt_delete on the result if that's what
 * you want.
 */
RBTNode *
rbt_leftmost(RBTree *rbt)
{
    RBTNode    *node = rbt->root;
    RBTNode    *leftmost = rbt->root;

    while (node != RBTNIL)
    {
        leftmost = node;
        node = node->left;
    }

    if (leftmost != RBTNIL)
        return leftmost;

    return NULL;
}

/**********************************************************************
 *                            Insertion                               *
 **********************************************************************/

/*
 * Rotate node x to left.
 *
 * x's right child takes its place in the tree, and x becomes the left
 * child of that node.
 */
static void
rbt_rotate_left(RBTree *rbt, RBTNode *x)
{
    RBTNode    *y = x->right;

    /* establish x->right link */
    x->right = y->left;
    if (y->left != RBTNIL)
        y->left->parent = x;

    /* establish y->parent link */
    if (y != RBTNIL)
        y->parent = x->parent;
    if (x->parent)
    {
        if (x == x->parent->left)
            x->parent->left = y;
        else
            x->parent->right = y;
    }
    else
    {
        rbt->root = y;
    }

    /* link x and y */
    y->left = x;
    if (x != RBTNIL)
        x->parent = y;
}

/*
 * Rotate node x to right.
 *
 * x's left right child takes its place in the tree, and x becomes the right
 * child of that node.
 */
static void
rbt_rotate_right(RBTree *rbt, RBTNode *x)
{
    RBTNode    *y = x->left;

    /* establish x->left link */
    x->left = y->right;
    if (y->right != RBTNIL)
        y->right->parent = x;

    /* establish y->parent link */
    if (y != RBTNIL)
        y->parent = x->parent;
    if (x->parent)
    {
        if (x == x->parent->right)
            x->parent->right = y;
        else
            x->parent->left = y;
    }
    else
    {
        rbt->root = y;
    }

    /* link x and y */
    y->right = x;
    if (x != RBTNIL)
        x->parent = y;
}

/*
 * Maintain Red-Black tree balance after inserting node x.
 *
 * The newly inserted node is always initially marked red.  That may lead to
 * a situation where a red node has a red child, which is prohibited.  We can
 * always fix the problem by a series of color changes and/or "rotations",
 * which move the problem progressively higher up in the tree.  If one of the
 * two red nodes is the root, we can always fix the problem by changing the
 * root from red to black.
 *
 * (This does not work lower down in the tree because we must also maintain
 * the invariant that every leaf has equal black-height.)
 */
static void
rbt_insert_fixup(RBTree *rbt, RBTNode *x)
{
    /*
     * x is always a red node.  Initially, it is the newly inserted node. Each
     * iteration of this loop moves it higher up in the tree.
     */
    while (x != rbt->root && x->parent->color == RBTRED)
    {
        /*
         * x and x->parent are both red.  Fix depends on whether x->parent is
         * a left or right child.  In either case, we define y to be the
         * "uncle" of x, that is, the other child of x's grandparent.
         *
         * If the uncle is red, we flip the grandparent to red and its two
         * children to black.  Then we loop around again to check whether the
         * grandparent still has a problem.
         *
         * If the uncle is black, we will perform one or two "rotations" to
         * balance the tree.  Either x or x->parent will take the
         * grandparent's position in the tree and recolored black, and the
         * original grandparent will be recolored red and become a child of
         * that node. This always leaves us with a valid red-black tree, so
         * the loop will terminate.
         */
        if (x->parent == x->parent->parent->left)
        {
            RBTNode    *y = x->parent->parent->right;

            if (y->color == RBTRED)
            {
                /* uncle is RBTRED */
                x->parent->color = RBTBLACK;
                y->color = RBTBLACK;
                x->parent->parent->color = RBTRED;

                x = x->parent->parent;
            }
            else
            {
                /* uncle is RBTBLACK */
                if (x == x->parent->right)
                {
                    /* make x a left child */
                    x = x->parent;
                    rbt_rotate_left(rbt, x);
                }

                /* recolor and rotate */
                x->parent->color = RBTBLACK;
                x->parent->parent->color = RBTRED;

                rbt_rotate_right(rbt, x->parent->parent);
            }
        }
        else
        {
            /* mirror image of above code */
            RBTNode    *y = x->parent->parent->left;

            if (y->color == RBTRED)
            {
                /* uncle is RBTRED */
                x->parent->color = RBTBLACK;
                y->color = RBTBLACK;
                x->parent->parent->color = RBTRED;

                x = x->parent->parent;
            }
            else
            {
                /* uncle is RBTBLACK */
                if (x == x->parent->left)
                {
                    x = x->parent;
                    rbt_rotate_right(rbt, x);
                }
                x->parent->color = RBTBLACK;
                x->parent->parent->color = RBTRED;

                rbt_rotate_left(rbt, x->parent->parent);
            }
        }
    }

    /*
     * The root may already have been black; if not, the black-height of every
     * node in the tree increases by one.
     */
    rbt->root->color = RBTBLACK;
}

/*
 * rbt_insert: insert a new value into the tree.
 *
 * data represents the value to insert.  Its RBTNode fields need not
 * be valid, it's the extra data in the larger struct that is of interest.
 *
 * If the value represented by "data" is not present in the tree, then
 * we copy "data" into a new tree entry and return that node, setting *isNew
 * to true.
 *
 * If the value represented by "data" is already present, then we call the
 * combiner function to merge data into the existing node, and return the
 * existing node, setting *isNew to false.
 *
 * "data" is unmodified in either case; it's typically just a local
 * variable in the caller.
 */
RBTNode *
rbt_insert(RBTree *rbt, const RBTNode *data, bool *isNew)
{
    RBTNode    *current,
               *parent,
               *x;
    int         cmp;

    /* find where node belongs */
    current = rbt->root;
    parent = NULL;
    cmp = 0;                    /* just to prevent compiler warning */

    while (current != RBTNIL)
    {
        cmp = rbt->comparator(data, current, rbt->arg);
        if (cmp == 0)
        {
            /*
             * Found node with given key.  Apply combiner.
             */
            rbt->combiner(current, data, rbt->arg);
            *isNew = false;
            return current;
        }
        parent = current;
        current = (cmp < 0) ? current->left : current->right;
    }

    /*
     * Value is not present, so create a new node containing data.
     */
    *isNew = true;

    x = rbt->allocfunc(rbt->arg);

    x->color = RBTRED;

    x->left = RBTNIL;
    x->right = RBTNIL;
    x->parent = parent;
    rbt_copy_data(rbt, x, data);

    /* insert node in tree */
    if (parent)
    {
        if (cmp < 0)
            parent->left = x;
        else
            parent->right = x;
    }
    else
    {
        rbt->root = x;
    }

    rbt_insert_fixup(rbt, x);

    return x;
}

/**********************************************************************
 *                          Deletion                                  *
 **********************************************************************/

/*
 * Maintain Red-Black tree balance after deleting a black node.
 */
static void
rbt_delete_fixup(RBTree *rbt, RBTNode *x)
{
    /*
     * x is always a black node.  Initially, it is the former child of the
     * deleted node.  Each iteration of this loop moves it higher up in the
     * tree.
     */
    while (x != rbt->root && x->color == RBTBLACK)
    {
        /*
         * Left and right cases are symmetric.  Any nodes that are children of
         * x have a black-height one less than the remainder of the nodes in
         * the tree.  We rotate and recolor nodes to move the problem up the
         * tree: at some stage we'll either fix the problem, or reach the root
         * (where the black-height is allowed to decrease).
         */
        if (x == x->parent->left)
        {
            RBTNode    *w = x->parent->right;

            if (w->color == RBTRED)
            {
                w->color = RBTBLACK;
                x->parent->color = RBTRED;

                rbt_rotate_left(rbt, x->parent);
                w = x->parent->right;
            }

            if (w->left->color == RBTBLACK && w->right->color == RBTBLACK)
            {
                w->color = RBTRED;

                x = x->parent;
            }
            else
            {
                if (w->right->color == RBTBLACK)
                {
                    w->left->color = RBTBLACK;
                    w->color = RBTRED;

                    rbt_rotate_right(rbt, w);
                    w = x->parent->right;
                }
                w->color = x->parent->color;
                x->parent->color = RBTBLACK;
                w->right->color = RBTBLACK;

                rbt_rotate_left(rbt, x->parent);
                x = rbt->root;  /* Arrange for loop to terminate. */
            }
        }
        else
        {
            RBTNode    *w = x->parent->left;

            if (w->color == RBTRED)
            {
                w->color = RBTBLACK;
                x->parent->color = RBTRED;

                rbt_rotate_right(rbt, x->parent);
                w = x->parent->left;
            }

            if (w->right->color == RBTBLACK && w->left->color == RBTBLACK)
            {
                w->color = RBTRED;

                x = x->parent;
            }
            else
            {
                if (w->left->color == RBTBLACK)
                {
                    w->right->color = RBTBLACK;
                    w->color = RBTRED;

                    rbt_rotate_left(rbt, w);
                    w = x->parent->left;
                }
                w->color = x->parent->color;
                x->parent->color = RBTBLACK;
                w->left->color = RBTBLACK;

                rbt_rotate_right(rbt, x->parent);
                x = rbt->root;  /* Arrange for loop to terminate. */
            }
        }
    }
    x->color = RBTBLACK;
}

/*
 * Delete node z from tree.
 */
static void
rbt_delete_node(RBTree *rbt, RBTNode *z)
{
    RBTNode    *x,
               *y;

    /* This is just paranoia: we should only get called on a valid node */
    if (!z || z == RBTNIL)
        return;

    /*
     * y is the node that will actually be removed from the tree.  This will
     * be z if z has fewer than two children, or the tree successor of z
     * otherwise.
     */
    if (z->left == RBTNIL || z->right == RBTNIL)
    {
        /* y has a RBTNIL node as a child */
        y = z;
    }
    else
    {
        /* find tree successor */
        y = z->right;
        while (y->left != RBTNIL)
            y = y->left;
    }

    /* x is y's only child */
    if (y->left != RBTNIL)
        x = y->left;
    else
        x = y->right;

    /* Remove y from the tree. */
    x->parent = y->parent;
    if (y->parent)
    {
        if (y == y->parent->left)
            y->parent->left = x;
        else
            y->parent->right = x;
    }
    else
    {
        rbt->root = x;
    }

    /*
     * If we removed the tree successor of z rather than z itself, then move
     * the data for the removed node to the one we were supposed to remove.
     */
    if (y != z)
        rbt_copy_data(rbt, z, y);

    /*
     * Removing a black node might make some paths from root to leaf contain
     * fewer black nodes than others, or it might make two red nodes adjacent.
     */
    if (y->color == RBTBLACK)
        rbt_delete_fixup(rbt, x);

    /* Now we can recycle the y node */
    if (rbt->freefunc)
        rbt->freefunc(y, rbt->arg);
}

/*
 * rbt_delete: remove the given tree entry
 *
 * "node" must have previously been found via rbt_find or rbt_leftmost.
 * It is caller's responsibility to free any subsidiary data attached
 * to the node before calling rbt_delete.  (Do *not* try to push that
 * responsibility off to the freefunc, as some other physical node
 * may be the one actually freed!)
 */
void
rbt_delete(RBTree *rbt, RBTNode *node)
{
    rbt_delete_node(rbt, node);
}

/**********************************************************************
 *                        Traverse                                    *
 **********************************************************************/

static RBTNode *
rbt_left_right_iterator(RBTreeIterator *iter)
{
    if (iter->last_visited == NULL)
    {
        iter->last_visited = iter->rbt->root;
        while (iter->last_visited->left != RBTNIL)
            iter->last_visited = iter->last_visited->left;

        return iter->last_visited;
    }

    if (iter->last_visited->right != RBTNIL)
    {
        iter->last_visited = iter->last_visited->right;
        while (iter->last_visited->left != RBTNIL)
            iter->last_visited = iter->last_visited->left;

        return iter->last_visited;
    }

    for (;;)
    {
        RBTNode    *came_from = iter->last_visited;

        iter->last_visited = iter->last_visited->parent;
        if (iter->last_visited == NULL)
        {
            iter->is_over = true;
            break;
        }

        if (iter->last_visited->left == came_from)
            break;              /* came from left sub-tree, return current
                                 * node */

        /* else - came from right sub-tree, continue to move up */
    }

    return iter->last_visited;
}

static RBTNode *
rbt_right_left_iterator(RBTreeIterator *iter)
{
    if (iter->last_visited == NULL)
    {
        iter->last_visited = iter->rbt->root;
        while (iter->last_visited->right != RBTNIL)
            iter->last_visited = iter->last_visited->right;

        return iter->last_visited;
    }

    if (iter->last_visited->left != RBTNIL)
    {
        iter->last_visited = iter->last_visited->left;
        while (iter->last_visited->right != RBTNIL)
            iter->last_visited = iter->last_visited->right;

        return iter->last_visited;
    }

    for (;;)
    {
        RBTNode    *came_from = iter->last_visited;

        iter->last_visited = iter->last_visited->parent;
        if (iter->last_visited == NULL)
        {
            iter->is_over = true;
            break;
        }

        if (iter->last_visited->right == came_from)
            break;              /* came from right sub-tree, return current
                                 * node */

        /* else - came from left sub-tree, continue to move up */
    }

    return iter->last_visited;
}

/*
 * rbt_begin_iterate: prepare to traverse the tree in any of several orders
 *
 * After calling rbt_begin_iterate, call rbt_iterate repeatedly until it
 * returns NULL or the traversal stops being of interest.
 *
 * If the tree is changed during traversal, results of further calls to
 * rbt_iterate are unspecified.  Multiple concurrent iterators on the same
 * tree are allowed.
 *
 * The iterator state is stored in the 'iter' struct.  The caller should
 * treat it as an opaque struct.
 */
void
rbt_begin_iterate(RBTree *rbt, RBTOrderControl ctrl, RBTreeIterator *iter)
{
    /* Common initialization for all traversal orders */
    iter->rbt = rbt;
    iter->last_visited = NULL;
    iter->is_over = (rbt->root == RBTNIL);

    switch (ctrl)
    {
        case LeftRightWalk:     /* visit left, then self, then right */
            iter->iterate = rbt_left_right_iterator;
            break;
        case RightLeftWalk:     /* visit right, then self, then left */
            iter->iterate = rbt_right_left_iterator;
            break;
        default:
            elog(ERROR, "unrecognized rbtree iteration order: %d", ctrl);
    }
}

/*
 * rbt_iterate: return the next node in traversal order, or NULL if no more
 */
RBTNode *
rbt_iterate(RBTreeIterator *iter)
{
    if (iter->is_over)
        return NULL;

    return iter->iterate(iter);
}