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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) 2009-2021, 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);
+}
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