/src/postgres/src/backend/lib/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) 2009-2025, 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 =
{
  .color = RBTBLACK,.left = RBTNIL,.right = RBTNIL,.parent = 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_find_great: search for a greater value in an RBTree
 *
 * If equal_match is true, this will be a great or equal search.
 *
 * Returns the matching tree entry, or NULL if no match is found.
 */
RBTNode *
rbt_find_great(RBTree *rbt, const RBTNode *data, bool equal_match)
{
  RBTNode    *node = rbt->root;
  RBTNode    *greater = NULL;

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

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

  return greater;
}

/*
 * rbt_find_less: search for a lesser value in an RBTree
 *
 * If equal_match is true, this will be a less or equal search.
 *
 * Returns the matching tree entry, or NULL if no match is found.
 */
RBTNode *
rbt_find_less(RBTree *rbt, const RBTNode *data, bool equal_match)
{
  RBTNode    *node = rbt->root;
  RBTNode    *lesser = NULL;

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

    if (equal_match && cmp == 0)
      return node;
    else if (cmp > 0)
    {
      lesser = node;
      node = node->right;
    }
    else
      node = node->left;
  }

  return lesser;
}

/*
 * 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);
}

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Created: 2025-08-12 06:43