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874 lines
20 KiB
C
874 lines
20 KiB
C
/*-------------------------------------------------------------------------
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*
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* rbtree.c
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* implementation for PostgreSQL generic Red-Black binary tree package
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* Adopted from http://algolist.manual.ru/ds/rbtree.php
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*
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* This code comes from Thomas Niemann's "Sorting and Searching Algorithms:
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* a Cookbook".
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*
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* See http://www.cs.auckland.ac.nz/software/AlgAnim/niemann/s_man.htm for
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* license terms: "Source code, when part of a software project, may be used
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* freely without reference to the author."
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*
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* Red-black trees are a type of balanced binary tree wherein (1) any child of
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* a red node is always black, and (2) every path from root to leaf traverses
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* an equal number of black nodes. From these properties, it follows that the
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* longest path from root to leaf is only about twice as long as the shortest,
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* so lookups are guaranteed to run in O(lg n) time.
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*
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* Copyright (c) 2009-2015, PostgreSQL Global Development Group
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*
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* IDENTIFICATION
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* src/backend/lib/rbtree.c
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*
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*-------------------------------------------------------------------------
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*/
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#include "postgres.h"
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#include "lib/rbtree.h"
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/*
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* Values of RBNode.iteratorState
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*
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* Note that iteratorState has an undefined value except in nodes that are
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* currently being visited by an active iteration.
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*/
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#define InitialState (0)
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#define FirstStepDone (1)
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#define SecondStepDone (2)
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#define ThirdStepDone (3)
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/*
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* Colors of nodes (values of RBNode.color)
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*/
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#define RBBLACK (0)
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#define RBRED (1)
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/*
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* RBTree control structure
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*/
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struct RBTree
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{
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RBNode *root; /* root node, or RBNIL if tree is empty */
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/* Iteration state */
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RBNode *cur; /* current iteration node */
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RBNode *(*iterate) (RBTree *rb);
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/* Remaining fields are constant after rb_create */
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Size node_size; /* actual size of tree nodes */
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/* The caller-supplied manipulation functions */
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rb_comparator comparator;
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rb_combiner combiner;
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rb_allocfunc allocfunc;
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rb_freefunc freefunc;
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/* Passthrough arg passed to all manipulation functions */
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void *arg;
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};
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/*
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* all leafs are sentinels, use customized NIL name to prevent
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* collision with system-wide constant NIL which is actually NULL
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*/
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#define RBNIL (&sentinel)
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static RBNode sentinel = {InitialState, RBBLACK, RBNIL, RBNIL, NULL};
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/*
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* rb_create: create an empty RBTree
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*
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* Arguments are:
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* node_size: actual size of tree nodes (> sizeof(RBNode))
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* The manipulation functions:
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* comparator: compare two RBNodes for less/equal/greater
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* combiner: merge an existing tree entry with a new one
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* allocfunc: allocate a new RBNode
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* freefunc: free an old RBNode
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* arg: passthrough pointer that will be passed to the manipulation functions
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*
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* Note that the combiner's righthand argument will be a "proposed" tree node,
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* ie the input to rb_insert, in which the RBNode fields themselves aren't
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* valid. Similarly, either input to the comparator may be a "proposed" node.
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* This shouldn't matter since the functions aren't supposed to look at the
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* RBNode fields, only the extra fields of the struct the RBNode is embedded
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* in.
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*
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* The freefunc should just be pfree or equivalent; it should NOT attempt
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* to free any subsidiary data, because the node passed to it may not contain
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* valid data! freefunc can be NULL if caller doesn't require retail
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* space reclamation.
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*
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* The RBTree node is palloc'd in the caller's memory context. Note that
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* all contents of the tree are actually allocated by the caller, not here.
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*
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* Since tree contents are managed by the caller, there is currently not
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* an explicit "destroy" operation; typically a tree would be freed by
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* resetting or deleting the memory context it's stored in. You can pfree
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* the RBTree node if you feel the urge.
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*/
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RBTree *
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rb_create(Size node_size,
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rb_comparator comparator,
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rb_combiner combiner,
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rb_allocfunc allocfunc,
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rb_freefunc freefunc,
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void *arg)
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{
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RBTree *tree = (RBTree *) palloc(sizeof(RBTree));
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Assert(node_size > sizeof(RBNode));
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tree->root = RBNIL;
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tree->cur = RBNIL;
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tree->iterate = NULL;
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tree->node_size = node_size;
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tree->comparator = comparator;
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tree->combiner = combiner;
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tree->allocfunc = allocfunc;
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tree->freefunc = freefunc;
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tree->arg = arg;
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return tree;
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}
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/* Copy the additional data fields from one RBNode to another */
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static inline void
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rb_copy_data(RBTree *rb, RBNode *dest, const RBNode *src)
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{
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memcpy(dest + 1, src + 1, rb->node_size - sizeof(RBNode));
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}
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/**********************************************************************
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* Search *
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**********************************************************************/
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/*
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* rb_find: search for a value in an RBTree
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*
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* data represents the value to try to find. Its RBNode fields need not
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* be valid, it's the extra data in the larger struct that is of interest.
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*
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* Returns the matching tree entry, or NULL if no match is found.
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*/
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RBNode *
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rb_find(RBTree *rb, const RBNode *data)
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{
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RBNode *node = rb->root;
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while (node != RBNIL)
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{
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int cmp = rb->comparator(data, node, rb->arg);
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if (cmp == 0)
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return node;
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else if (cmp < 0)
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node = node->left;
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else
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node = node->right;
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}
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return NULL;
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}
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/*
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* rb_leftmost: fetch the leftmost (smallest-valued) tree node.
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* Returns NULL if tree is empty.
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*
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* Note: in the original implementation this included an unlink step, but
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* that's a bit awkward. Just call rb_delete on the result if that's what
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* you want.
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*/
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RBNode *
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rb_leftmost(RBTree *rb)
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{
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RBNode *node = rb->root;
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RBNode *leftmost = rb->root;
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while (node != RBNIL)
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{
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leftmost = node;
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node = node->left;
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}
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if (leftmost != RBNIL)
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return leftmost;
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return NULL;
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}
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/**********************************************************************
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* Insertion *
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**********************************************************************/
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/*
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* Rotate node x to left.
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*
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* x's right child takes its place in the tree, and x becomes the left
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* child of that node.
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*/
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static void
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rb_rotate_left(RBTree *rb, RBNode *x)
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{
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RBNode *y = x->right;
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/* establish x->right link */
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x->right = y->left;
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if (y->left != RBNIL)
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y->left->parent = x;
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/* establish y->parent link */
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if (y != RBNIL)
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y->parent = x->parent;
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if (x->parent)
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{
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if (x == x->parent->left)
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x->parent->left = y;
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else
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x->parent->right = y;
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}
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else
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{
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rb->root = y;
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}
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/* link x and y */
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y->left = x;
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if (x != RBNIL)
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x->parent = y;
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}
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/*
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* Rotate node x to right.
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*
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* x's left right child takes its place in the tree, and x becomes the right
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* child of that node.
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*/
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static void
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rb_rotate_right(RBTree *rb, RBNode *x)
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{
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RBNode *y = x->left;
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/* establish x->left link */
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x->left = y->right;
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if (y->right != RBNIL)
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y->right->parent = x;
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/* establish y->parent link */
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if (y != RBNIL)
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y->parent = x->parent;
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if (x->parent)
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{
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if (x == x->parent->right)
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x->parent->right = y;
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else
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x->parent->left = y;
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}
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else
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{
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rb->root = y;
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}
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/* link x and y */
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y->right = x;
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if (x != RBNIL)
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x->parent = y;
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}
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/*
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* Maintain Red-Black tree balance after inserting node x.
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*
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* The newly inserted node is always initially marked red. That may lead to
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* a situation where a red node has a red child, which is prohibited. We can
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* always fix the problem by a series of color changes and/or "rotations",
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* which move the problem progressively higher up in the tree. If one of the
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* two red nodes is the root, we can always fix the problem by changing the
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* root from red to black.
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*
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* (This does not work lower down in the tree because we must also maintain
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* the invariant that every leaf has equal black-height.)
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*/
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static void
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rb_insert_fixup(RBTree *rb, RBNode *x)
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{
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/*
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* x is always a red node. Initially, it is the newly inserted node. Each
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* iteration of this loop moves it higher up in the tree.
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*/
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while (x != rb->root && x->parent->color == RBRED)
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{
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/*
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* x and x->parent are both red. Fix depends on whether x->parent is
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* a left or right child. In either case, we define y to be the
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* "uncle" of x, that is, the other child of x's grandparent.
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*
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* If the uncle is red, we flip the grandparent to red and its two
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* children to black. Then we loop around again to check whether the
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* grandparent still has a problem.
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*
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* If the uncle is black, we will perform one or two "rotations" to
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* balance the tree. Either x or x->parent will take the
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* grandparent's position in the tree and recolored black, and the
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* original grandparent will be recolored red and become a child of
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* that node. This always leaves us with a valid red-black tree, so
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* the loop will terminate.
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*/
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if (x->parent == x->parent->parent->left)
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{
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RBNode *y = x->parent->parent->right;
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if (y->color == RBRED)
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{
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/* uncle is RBRED */
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x->parent->color = RBBLACK;
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y->color = RBBLACK;
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x->parent->parent->color = RBRED;
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x = x->parent->parent;
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}
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else
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{
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/* uncle is RBBLACK */
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if (x == x->parent->right)
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{
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/* make x a left child */
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x = x->parent;
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rb_rotate_left(rb, x);
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}
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/* recolor and rotate */
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x->parent->color = RBBLACK;
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x->parent->parent->color = RBRED;
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rb_rotate_right(rb, x->parent->parent);
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}
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}
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else
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{
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/* mirror image of above code */
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RBNode *y = x->parent->parent->left;
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if (y->color == RBRED)
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{
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/* uncle is RBRED */
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x->parent->color = RBBLACK;
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y->color = RBBLACK;
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x->parent->parent->color = RBRED;
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x = x->parent->parent;
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}
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else
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{
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/* uncle is RBBLACK */
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if (x == x->parent->left)
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{
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x = x->parent;
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rb_rotate_right(rb, x);
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}
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x->parent->color = RBBLACK;
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x->parent->parent->color = RBRED;
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rb_rotate_left(rb, x->parent->parent);
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}
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}
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}
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/*
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* The root may already have been black; if not, the black-height of every
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* node in the tree increases by one.
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*/
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rb->root->color = RBBLACK;
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}
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/*
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* rb_insert: insert a new value into the tree.
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*
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* data represents the value to insert. Its RBNode fields need not
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* be valid, it's the extra data in the larger struct that is of interest.
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*
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* If the value represented by "data" is not present in the tree, then
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* we copy "data" into a new tree entry and return that node, setting *isNew
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* to true.
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*
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* If the value represented by "data" is already present, then we call the
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* combiner function to merge data into the existing node, and return the
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* existing node, setting *isNew to false.
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*
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* "data" is unmodified in either case; it's typically just a local
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* variable in the caller.
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*/
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RBNode *
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rb_insert(RBTree *rb, const RBNode *data, bool *isNew)
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{
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RBNode *current,
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*parent,
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*x;
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int cmp;
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/* find where node belongs */
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current = rb->root;
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parent = NULL;
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cmp = 0; /* just to prevent compiler warning */
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while (current != RBNIL)
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{
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cmp = rb->comparator(data, current, rb->arg);
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if (cmp == 0)
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{
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/*
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* Found node with given key. Apply combiner.
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*/
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rb->combiner(current, data, rb->arg);
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*isNew = false;
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return current;
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}
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parent = current;
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current = (cmp < 0) ? current->left : current->right;
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}
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/*
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* Value is not present, so create a new node containing data.
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*/
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*isNew = true;
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x = rb->allocfunc (rb->arg);
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x->iteratorState = InitialState;
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x->color = RBRED;
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x->left = RBNIL;
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x->right = RBNIL;
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x->parent = parent;
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rb_copy_data(rb, x, data);
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/* insert node in tree */
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if (parent)
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{
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if (cmp < 0)
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parent->left = x;
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else
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parent->right = x;
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}
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else
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{
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rb->root = x;
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}
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rb_insert_fixup(rb, x);
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return x;
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}
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/**********************************************************************
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* Deletion *
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**********************************************************************/
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/*
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* Maintain Red-Black tree balance after deleting a black node.
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*/
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static void
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rb_delete_fixup(RBTree *rb, RBNode *x)
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{
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/*
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* x is always a black node. Initially, it is the former child of the
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* deleted node. Each iteration of this loop moves it higher up in the
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* tree.
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*/
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while (x != rb->root && x->color == RBBLACK)
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{
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/*
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* Left and right cases are symmetric. Any nodes that are children of
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* x have a black-height one less than the remainder of the nodes in
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* the tree. We rotate and recolor nodes to move the problem up the
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* tree: at some stage we'll either fix the problem, or reach the root
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* (where the black-height is allowed to decrease).
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*/
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if (x == x->parent->left)
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{
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RBNode *w = x->parent->right;
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if (w->color == RBRED)
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{
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w->color = RBBLACK;
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x->parent->color = RBRED;
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rb_rotate_left(rb, x->parent);
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w = x->parent->right;
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}
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if (w->left->color == RBBLACK && w->right->color == RBBLACK)
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{
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w->color = RBRED;
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x = x->parent;
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}
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else
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{
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if (w->right->color == RBBLACK)
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{
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w->left->color = RBBLACK;
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w->color = RBRED;
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rb_rotate_right(rb, w);
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w = x->parent->right;
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}
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w->color = x->parent->color;
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x->parent->color = RBBLACK;
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w->right->color = RBBLACK;
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rb_rotate_left(rb, x->parent);
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x = rb->root; /* Arrange for loop to terminate. */
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}
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}
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else
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{
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RBNode *w = x->parent->left;
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if (w->color == RBRED)
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{
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w->color = RBBLACK;
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x->parent->color = RBRED;
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rb_rotate_right(rb, x->parent);
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w = x->parent->left;
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}
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if (w->right->color == RBBLACK && w->left->color == RBBLACK)
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{
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w->color = RBRED;
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x = x->parent;
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}
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else
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{
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if (w->left->color == RBBLACK)
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{
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w->right->color = RBBLACK;
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w->color = RBRED;
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rb_rotate_left(rb, w);
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w = x->parent->left;
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}
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w->color = x->parent->color;
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x->parent->color = RBBLACK;
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w->left->color = RBBLACK;
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rb_rotate_right(rb, x->parent);
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x = rb->root; /* Arrange for loop to terminate. */
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}
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}
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}
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x->color = RBBLACK;
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}
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/*
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* Delete node z from tree.
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*/
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static void
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rb_delete_node(RBTree *rb, RBNode *z)
|
|
{
|
|
RBNode *x,
|
|
*y;
|
|
|
|
if (!z || z == RBNIL)
|
|
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 == RBNIL || z->right == RBNIL)
|
|
{
|
|
/* y has a RBNIL node as a child */
|
|
y = z;
|
|
}
|
|
else
|
|
{
|
|
/* find tree successor */
|
|
y = z->right;
|
|
while (y->left != RBNIL)
|
|
y = y->left;
|
|
}
|
|
|
|
/* x is y's only child */
|
|
if (y->left != RBNIL)
|
|
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
|
|
{
|
|
rb->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)
|
|
rb_copy_data(rb, 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 == RBBLACK)
|
|
rb_delete_fixup(rb, x);
|
|
|
|
/* Now we can recycle the y node */
|
|
if (rb->freefunc)
|
|
rb->freefunc (y, rb->arg);
|
|
}
|
|
|
|
/*
|
|
* rb_delete: remove the given tree entry
|
|
*
|
|
* "node" must have previously been found via rb_find or rb_leftmost.
|
|
* It is caller's responsibility to free any subsidiary data attached
|
|
* to the node before calling rb_delete. (Do *not* try to push that
|
|
* responsibility off to the freefunc, as some other physical node
|
|
* may be the one actually freed!)
|
|
*/
|
|
void
|
|
rb_delete(RBTree *rb, RBNode *node)
|
|
{
|
|
rb_delete_node(rb, node);
|
|
}
|
|
|
|
/**********************************************************************
|
|
* Traverse *
|
|
**********************************************************************/
|
|
|
|
/*
|
|
* The iterator routines were originally coded in tail-recursion style,
|
|
* which is nice to look at, but is trouble if your compiler isn't smart
|
|
* enough to optimize it. Now we just use looping.
|
|
*/
|
|
#define descend(next_node) \
|
|
do { \
|
|
(next_node)->iteratorState = InitialState; \
|
|
node = rb->cur = (next_node); \
|
|
goto restart; \
|
|
} while (0)
|
|
|
|
#define ascend(next_node) \
|
|
do { \
|
|
node = rb->cur = (next_node); \
|
|
goto restart; \
|
|
} while (0)
|
|
|
|
|
|
static RBNode *
|
|
rb_left_right_iterator(RBTree *rb)
|
|
{
|
|
RBNode *node = rb->cur;
|
|
|
|
restart:
|
|
switch (node->iteratorState)
|
|
{
|
|
case InitialState:
|
|
if (node->left != RBNIL)
|
|
{
|
|
node->iteratorState = FirstStepDone;
|
|
descend(node->left);
|
|
}
|
|
/* FALL THROUGH */
|
|
case FirstStepDone:
|
|
node->iteratorState = SecondStepDone;
|
|
return node;
|
|
case SecondStepDone:
|
|
if (node->right != RBNIL)
|
|
{
|
|
node->iteratorState = ThirdStepDone;
|
|
descend(node->right);
|
|
}
|
|
/* FALL THROUGH */
|
|
case ThirdStepDone:
|
|
if (node->parent)
|
|
ascend(node->parent);
|
|
break;
|
|
default:
|
|
elog(ERROR, "unrecognized rbtree node state: %d",
|
|
node->iteratorState);
|
|
}
|
|
|
|
return NULL;
|
|
}
|
|
|
|
static RBNode *
|
|
rb_right_left_iterator(RBTree *rb)
|
|
{
|
|
RBNode *node = rb->cur;
|
|
|
|
restart:
|
|
switch (node->iteratorState)
|
|
{
|
|
case InitialState:
|
|
if (node->right != RBNIL)
|
|
{
|
|
node->iteratorState = FirstStepDone;
|
|
descend(node->right);
|
|
}
|
|
/* FALL THROUGH */
|
|
case FirstStepDone:
|
|
node->iteratorState = SecondStepDone;
|
|
return node;
|
|
case SecondStepDone:
|
|
if (node->left != RBNIL)
|
|
{
|
|
node->iteratorState = ThirdStepDone;
|
|
descend(node->left);
|
|
}
|
|
/* FALL THROUGH */
|
|
case ThirdStepDone:
|
|
if (node->parent)
|
|
ascend(node->parent);
|
|
break;
|
|
default:
|
|
elog(ERROR, "unrecognized rbtree node state: %d",
|
|
node->iteratorState);
|
|
}
|
|
|
|
return NULL;
|
|
}
|
|
|
|
static RBNode *
|
|
rb_direct_iterator(RBTree *rb)
|
|
{
|
|
RBNode *node = rb->cur;
|
|
|
|
restart:
|
|
switch (node->iteratorState)
|
|
{
|
|
case InitialState:
|
|
node->iteratorState = FirstStepDone;
|
|
return node;
|
|
case FirstStepDone:
|
|
if (node->left != RBNIL)
|
|
{
|
|
node->iteratorState = SecondStepDone;
|
|
descend(node->left);
|
|
}
|
|
/* FALL THROUGH */
|
|
case SecondStepDone:
|
|
if (node->right != RBNIL)
|
|
{
|
|
node->iteratorState = ThirdStepDone;
|
|
descend(node->right);
|
|
}
|
|
/* FALL THROUGH */
|
|
case ThirdStepDone:
|
|
if (node->parent)
|
|
ascend(node->parent);
|
|
break;
|
|
default:
|
|
elog(ERROR, "unrecognized rbtree node state: %d",
|
|
node->iteratorState);
|
|
}
|
|
|
|
return NULL;
|
|
}
|
|
|
|
static RBNode *
|
|
rb_inverted_iterator(RBTree *rb)
|
|
{
|
|
RBNode *node = rb->cur;
|
|
|
|
restart:
|
|
switch (node->iteratorState)
|
|
{
|
|
case InitialState:
|
|
if (node->left != RBNIL)
|
|
{
|
|
node->iteratorState = FirstStepDone;
|
|
descend(node->left);
|
|
}
|
|
/* FALL THROUGH */
|
|
case FirstStepDone:
|
|
if (node->right != RBNIL)
|
|
{
|
|
node->iteratorState = SecondStepDone;
|
|
descend(node->right);
|
|
}
|
|
/* FALL THROUGH */
|
|
case SecondStepDone:
|
|
node->iteratorState = ThirdStepDone;
|
|
return node;
|
|
case ThirdStepDone:
|
|
if (node->parent)
|
|
ascend(node->parent);
|
|
break;
|
|
default:
|
|
elog(ERROR, "unrecognized rbtree node state: %d",
|
|
node->iteratorState);
|
|
}
|
|
|
|
return NULL;
|
|
}
|
|
|
|
/*
|
|
* rb_begin_iterate: prepare to traverse the tree in any of several orders
|
|
*
|
|
* After calling rb_begin_iterate, call rb_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
|
|
* rb_iterate are unspecified.
|
|
*
|
|
* Note: this used to return a separately palloc'd iterator control struct,
|
|
* but that's a bit pointless since the data structure is incapable of
|
|
* supporting multiple concurrent traversals. Now we just keep the state
|
|
* in RBTree.
|
|
*/
|
|
void
|
|
rb_begin_iterate(RBTree *rb, RBOrderControl ctrl)
|
|
{
|
|
rb->cur = rb->root;
|
|
if (rb->cur != RBNIL)
|
|
rb->cur->iteratorState = InitialState;
|
|
|
|
switch (ctrl)
|
|
{
|
|
case LeftRightWalk: /* visit left, then self, then right */
|
|
rb->iterate = rb_left_right_iterator;
|
|
break;
|
|
case RightLeftWalk: /* visit right, then self, then left */
|
|
rb->iterate = rb_right_left_iterator;
|
|
break;
|
|
case DirectWalk: /* visit self, then left, then right */
|
|
rb->iterate = rb_direct_iterator;
|
|
break;
|
|
case InvertedWalk: /* visit left, then right, then self */
|
|
rb->iterate = rb_inverted_iterator;
|
|
break;
|
|
default:
|
|
elog(ERROR, "unrecognized rbtree iteration order: %d", ctrl);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* rb_iterate: return the next node in traversal order, or NULL if no more
|
|
*/
|
|
RBNode *
|
|
rb_iterate(RBTree *rb)
|
|
{
|
|
if (rb->cur == RBNIL)
|
|
return NULL;
|
|
|
|
return rb->iterate(rb);
|
|
}
|