801 lines
27 KiB
C
Executable File
801 lines
27 KiB
C
Executable File
/* Ordered {set,map} data type implemented by a binary tree.
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Copyright (C) 2006-2007, 2009-2024 Free Software Foundation, Inc.
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Written by Bruno Haible <bruno@clisp.org>, 2006.
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This file is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as
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published by the Free Software Foundation; either version 2.1 of the
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License, or (at your option) any later version.
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This file is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>. */
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/* A red-black tree is a binary tree where every node is colored black or
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red such that
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1. The root is black.
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2. No red node has a red parent.
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Or equivalently: No red node has a red child.
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3. All paths from the root down to any NULL endpoint contain the same
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number of black nodes.
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Let's call this the "black-height" bh of the tree. It follows that every
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such path contains exactly bh black and between 0 and bh red nodes. (The
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extreme cases are a path containing only black nodes, and a path colored
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alternately black-red-black-red-...-black-red.) The height of the tree
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therefore is >= bh, <= 2*bh.
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*/
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/* Color of a node. */
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typedef enum color { BLACK, RED } color_t;
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/* Tree node implementation, valid for this file only. */
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struct NODE_IMPL
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{
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struct NODE_IMPL *left; /* left branch, or NULL */
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struct NODE_IMPL *right; /* right branch, or NULL */
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/* Parent pointer, or NULL. The parent pointer is not needed for most
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operations. It is needed so that a NODE_T can be returned without
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memory allocation, on which the functions <container>_remove_node,
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<container>_add_before, <container>_add_after can be implemented. */
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struct NODE_IMPL *parent;
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color_t color; /* node's color */
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NODE_PAYLOAD_FIELDS
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};
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typedef struct NODE_IMPL * NODE_T;
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/* Concrete CONTAINER_IMPL type, valid for this file only. */
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struct CONTAINER_IMPL
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{
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struct CONTAINER_IMPL_BASE base;
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struct NODE_IMPL *root; /* root node or NULL */
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size_t count; /* number of nodes */
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};
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/* A red-black tree of height h has a black-height bh >= ceil(h/2) and
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therefore at least 2^ceil(h/2) - 1 elements. So, h <= 116 (because a tree
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of height h >= 117 would have at least 2^59 - 1 elements, and because even
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on 64-bit machines,
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sizeof (NODE_IMPL) * (2^59 - 1) > 2^64
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this would exceed the address space of the machine. */
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#define MAXHEIGHT 116
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/* Rotates left a subtree.
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B D
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/ \ / \
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A D --> B E
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/ \ / \
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C E A C
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Changes the tree structure, updates the branch sizes.
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The caller must update the colors and register D as child of its parent. */
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static NODE_T
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rotate_left (NODE_T b_node, NODE_T d_node)
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{
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NODE_T c_node = d_node->left;
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b_node->right = c_node;
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d_node->left = b_node;
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d_node->parent = b_node->parent;
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b_node->parent = d_node;
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if (c_node != NULL)
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c_node->parent = b_node;
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return d_node;
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}
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/* Rotates right a subtree.
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D B
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/ \ / \
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B E --> A D
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/ \ / \
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A C C E
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Changes the tree structure, updates the branch sizes.
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The caller must update the colors and register B as child of its parent. */
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static NODE_T
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rotate_right (NODE_T b_node, NODE_T d_node)
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{
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NODE_T c_node = b_node->right;
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d_node->left = c_node;
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b_node->right = d_node;
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b_node->parent = d_node->parent;
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d_node->parent = b_node;
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if (c_node != NULL)
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c_node->parent = d_node;
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return b_node;
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}
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/* Ensures the tree is balanced, after an insertion operation.
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Also assigns node->color.
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parent is the given node's parent, known to be non-NULL. */
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static void
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rebalance_after_add (CONTAINER_T container, NODE_T node, NODE_T parent)
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{
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for (;;)
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{
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/* At this point, parent = node->parent != NULL.
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Think of node->color being RED (although node->color is not yet
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assigned.) */
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NODE_T grandparent;
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NODE_T uncle;
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if (parent->color == BLACK)
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{
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/* A RED color for node is acceptable. */
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node->color = RED;
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return;
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}
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grandparent = parent->parent;
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/* Since parent is RED, we know that
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grandparent is != NULL and colored BLACK. */
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if (grandparent->left == parent)
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uncle = grandparent->right;
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else if (grandparent->right == parent)
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uncle = grandparent->left;
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else
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abort ();
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if (uncle != NULL && uncle->color == RED)
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{
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/* Change grandparent from BLACK to RED, and
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change parent and uncle from RED to BLACK.
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This makes it acceptable for node to be RED. */
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node->color = RED;
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parent->color = uncle->color = BLACK;
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node = grandparent;
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}
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else
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{
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/* grandparent and uncle are BLACK. parent is RED. node wants
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to be RED too.
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In this case, recoloring is not sufficient. Need to perform
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one or two rotations. */
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NODE_T *grandparentp;
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if (grandparent->parent == NULL)
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grandparentp = &container->root;
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else if (grandparent->parent->left == grandparent)
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grandparentp = &grandparent->parent->left;
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else if (grandparent->parent->right == grandparent)
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grandparentp = &grandparent->parent->right;
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else
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abort ();
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if (grandparent->left == parent)
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{
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if (parent->right == node)
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{
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/* Rotation between node and parent. */
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grandparent->left = rotate_left (parent, node);
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node = parent;
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parent = grandparent->left;
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}
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/* grandparent and uncle are BLACK. parent and node want to be
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RED. parent = grandparent->left. node = parent->left.
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grandparent parent
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bh+1 bh+1
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/ \ / \
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parent uncle --> node grandparent
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bh bh bh bh
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/ \ / \
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node C C uncle
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bh bh bh bh
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*/
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*grandparentp = rotate_right (parent, grandparent);
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parent->color = BLACK;
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node->color = grandparent->color = RED;
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}
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else /* grandparent->right == parent */
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{
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if (parent->left == node)
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{
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/* Rotation between node and parent. */
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grandparent->right = rotate_right (node, parent);
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node = parent;
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parent = grandparent->right;
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}
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/* grandparent and uncle are BLACK. parent and node want to be
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RED. parent = grandparent->right. node = parent->right.
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grandparent parent
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bh+1 bh+1
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/ \ / \
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uncle parent --> grandparent node
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bh bh bh bh
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/ \ / \
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C node uncle C
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bh bh bh bh
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*/
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*grandparentp = rotate_left (grandparent, parent);
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parent->color = BLACK;
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node->color = grandparent->color = RED;
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}
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return;
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}
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/* Start again with a new (node, parent) pair. */
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parent = node->parent;
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if (parent == NULL)
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{
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/* Change node's color from RED to BLACK. This increases the
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tree's black-height. */
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node->color = BLACK;
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return;
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}
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}
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}
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/* Ensures the tree is balanced, after a deletion operation.
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CHILD was a grandchild of PARENT and is now its child. Between them,
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a black node was removed. CHILD is also black, or NULL.
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(CHILD can also be NULL. But PARENT is non-NULL.) */
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static void
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rebalance_after_remove (CONTAINER_T container, NODE_T child, NODE_T parent)
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{
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for (;;)
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{
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/* At this point, we reduced the black-height of the CHILD subtree by 1.
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To make up, either look for a possibility to turn a RED to a BLACK
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node, or try to reduce the black-height tree of CHILD's sibling
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subtree as well. */
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NODE_T *parentp;
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if (parent->parent == NULL)
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parentp = &container->root;
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else if (parent->parent->left == parent)
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parentp = &parent->parent->left;
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else if (parent->parent->right == parent)
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parentp = &parent->parent->right;
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else
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abort ();
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if (parent->left == child)
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{
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NODE_T sibling = parent->right;
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/* sibling's black-height is >= 1. In particular,
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sibling != NULL.
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parent
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/ \
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child sibling
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bh bh+1
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*/
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if (sibling->color == RED)
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{
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/* sibling is RED, hence parent is BLACK and sibling's children
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are non-NULL and BLACK.
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parent sibling
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bh+2 bh+2
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/ \ / \
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child sibling --> parent SR
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bh bh+1 bh+1 bh+1
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/ \ / \
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SL SR child SL
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bh+1 bh+1 bh bh+1
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*/
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*parentp = rotate_left (parent, sibling);
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parent->color = RED;
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sibling->color = BLACK;
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/* Concentrate on the subtree of parent. The new sibling is
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one of the old sibling's children, and known to be BLACK. */
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parentp = &sibling->left;
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sibling = parent->right;
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}
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/* Now we know that sibling is BLACK.
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parent
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/ \
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child sibling
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bh bh+1
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*/
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if (sibling->right != NULL && sibling->right->color == RED)
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{
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/*
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parent sibling
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bh+1|bh+2 bh+1|bh+2
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/ \ / \
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child sibling --> parent SR
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bh bh+1 bh+1 bh+1
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/ \ / \
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SL SR child SL
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bh bh bh bh
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*/
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*parentp = rotate_left (parent, sibling);
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sibling->color = parent->color;
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parent->color = BLACK;
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sibling->right->color = BLACK;
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return;
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}
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else if (sibling->left != NULL && sibling->left->color == RED)
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{
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/*
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parent parent
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bh+1|bh+2 bh+1|bh+2
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/ \ / \
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child sibling --> child SL
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bh bh+1 bh bh+1
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/ \ / \
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SL SR SLL sibling
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bh bh bh bh
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/ \ / \
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SLL SLR SLR SR
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bh bh bh bh
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where SLL, SLR, SR are all black.
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*/
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parent->right = rotate_right (sibling->left, sibling);
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/* Change sibling from BLACK to RED and SL from RED to BLACK. */
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sibling->color = RED;
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sibling = parent->right;
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sibling->color = BLACK;
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/* Now do as in the previous case. */
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*parentp = rotate_left (parent, sibling);
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sibling->color = parent->color;
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parent->color = BLACK;
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sibling->right->color = BLACK;
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return;
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}
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else
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{
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if (parent->color == BLACK)
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{
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/* Change sibling from BLACK to RED. Then the entire
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subtree at parent has decreased its black-height.
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parent parent
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bh+2 bh+1
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/ \ / \
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child sibling --> child sibling
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bh bh+1 bh bh
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*/
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sibling->color = RED;
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child = parent;
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}
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else
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{
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/* Change parent from RED to BLACK, but compensate by
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changing sibling from BLACK to RED.
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parent parent
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bh+1 bh+1
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/ \ / \
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child sibling --> child sibling
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bh bh+1 bh bh
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*/
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parent->color = BLACK;
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sibling->color = RED;
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return;
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}
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}
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}
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else if (parent->right == child)
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{
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NODE_T sibling = parent->left;
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/* sibling's black-height is >= 1. In particular,
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sibling != NULL.
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parent
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/ \
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sibling child
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bh+1 bh
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*/
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if (sibling->color == RED)
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{
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/* sibling is RED, hence parent is BLACK and sibling's children
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are non-NULL and BLACK.
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parent sibling
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bh+2 bh+2
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/ \ / \
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sibling child --> SR parent
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bh+1 ch bh+1 bh+1
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/ \ / \
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SL SR SL child
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bh+1 bh+1 bh+1 bh
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*/
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*parentp = rotate_right (sibling, parent);
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parent->color = RED;
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sibling->color = BLACK;
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/* Concentrate on the subtree of parent. The new sibling is
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one of the old sibling's children, and known to be BLACK. */
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parentp = &sibling->right;
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sibling = parent->left;
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}
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/* Now we know that sibling is BLACK.
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parent
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/ \
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sibling child
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bh+1 bh
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*/
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if (sibling->left != NULL && sibling->left->color == RED)
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{
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/*
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parent sibling
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bh+1|bh+2 bh+1|bh+2
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/ \ / \
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sibling child --> SL parent
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bh+1 bh bh+1 bh+1
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/ \ / \
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SL SR SR child
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bh bh bh bh
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*/
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*parentp = rotate_right (sibling, parent);
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sibling->color = parent->color;
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parent->color = BLACK;
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sibling->left->color = BLACK;
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return;
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}
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else if (sibling->right != NULL && sibling->right->color == RED)
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{
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/*
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parent parent
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bh+1|bh+2 bh+1|bh+2
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/ \ / \
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sibling child --> SR child
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bh+1 bh bh+1 bh
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/ \ / \
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SL SR sibling SRR
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bh bh bh bh
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/ \ / \
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SRL SRR SL SRL
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bh bh bh bh
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where SL, SRL, SRR are all black.
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*/
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parent->left = rotate_left (sibling, sibling->right);
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/* Change sibling from BLACK to RED and SL from RED to BLACK. */
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sibling->color = RED;
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sibling = parent->left;
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sibling->color = BLACK;
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/* Now do as in the previous case. */
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*parentp = rotate_right (sibling, parent);
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sibling->color = parent->color;
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parent->color = BLACK;
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sibling->left->color = BLACK;
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return;
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}
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else
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{
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if (parent->color == BLACK)
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{
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/* Change sibling from BLACK to RED. Then the entire
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subtree at parent has decreased its black-height.
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parent parent
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bh+2 bh+1
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/ \ / \
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sibling child --> sibling child
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bh+1 bh bh bh
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*/
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sibling->color = RED;
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child = parent;
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}
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else
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{
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/* Change parent from RED to BLACK, but compensate by
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changing sibling from BLACK to RED.
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parent parent
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bh+1 bh+1
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/ \ / \
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sibling child --> sibling child
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bh+1 bh bh bh
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*/
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parent->color = BLACK;
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sibling->color = RED;
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return;
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}
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}
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}
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else
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abort ();
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/* Start again with a new (child, parent) pair. */
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parent = child->parent;
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#if 0 /* Already handled. */
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if (child != NULL && child->color == RED)
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{
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child->color = BLACK;
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return;
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}
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#endif
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if (parent == NULL)
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return;
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}
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}
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static NODE_T
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gl_tree_nx_add_first (CONTAINER_T container, NODE_PAYLOAD_PARAMS)
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{
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/* Create new node. */
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NODE_T new_node =
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(struct NODE_IMPL *) malloc (sizeof (struct NODE_IMPL));
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if (new_node == NULL)
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return NULL;
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new_node->left = NULL;
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new_node->right = NULL;
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NODE_PAYLOAD_ASSIGN(new_node)
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/* Add it to the tree. */
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if (container->root == NULL)
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{
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new_node->color = BLACK;
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container->root = new_node;
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new_node->parent = NULL;
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}
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else
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{
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NODE_T node;
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for (node = container->root; node->left != NULL; )
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node = node->left;
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node->left = new_node;
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new_node->parent = node;
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/* Color and rebalance. */
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rebalance_after_add (container, new_node, node);
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}
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container->count++;
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return new_node;
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}
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/* Adds the already allocated NEW_NODE to the tree, right before NODE. */
|
|
static void
|
|
gl_tree_add_node_before (CONTAINER_T container, NODE_T node, NODE_T new_node)
|
|
{
|
|
new_node->left = NULL;
|
|
new_node->right = NULL;
|
|
|
|
/* Add it to the tree. */
|
|
if (node->left == NULL)
|
|
node->left = new_node;
|
|
else
|
|
{
|
|
for (node = node->left; node->right != NULL; )
|
|
node = node->right;
|
|
node->right = new_node;
|
|
}
|
|
new_node->parent = node;
|
|
|
|
/* Color and rebalance. */
|
|
rebalance_after_add (container, new_node, node);
|
|
|
|
container->count++;
|
|
}
|
|
|
|
static NODE_T
|
|
gl_tree_nx_add_before (CONTAINER_T container, NODE_T node, NODE_PAYLOAD_PARAMS)
|
|
{
|
|
/* Create new node. */
|
|
NODE_T new_node =
|
|
(struct NODE_IMPL *) malloc (sizeof (struct NODE_IMPL));
|
|
|
|
if (new_node == NULL)
|
|
return NULL;
|
|
|
|
NODE_PAYLOAD_ASSIGN(new_node)
|
|
|
|
gl_tree_add_node_before (container, node, new_node);
|
|
return new_node;
|
|
}
|
|
|
|
/* Adds the already allocated NEW_NODE to the tree, right after NODE. */
|
|
static void
|
|
gl_tree_add_node_after (CONTAINER_T container, NODE_T node, NODE_T new_node)
|
|
{
|
|
new_node->left = NULL;
|
|
new_node->right = NULL;
|
|
|
|
/* Add it to the tree. */
|
|
if (node->right == NULL)
|
|
node->right = new_node;
|
|
else
|
|
{
|
|
for (node = node->right; node->left != NULL; )
|
|
node = node->left;
|
|
node->left = new_node;
|
|
}
|
|
new_node->parent = node;
|
|
|
|
/* Color and rebalance. */
|
|
rebalance_after_add (container, new_node, node);
|
|
|
|
container->count++;
|
|
}
|
|
|
|
static NODE_T
|
|
gl_tree_nx_add_after (CONTAINER_T container, NODE_T node, NODE_PAYLOAD_PARAMS)
|
|
{
|
|
/* Create new node. */
|
|
NODE_T new_node =
|
|
(struct NODE_IMPL *) malloc (sizeof (struct NODE_IMPL));
|
|
|
|
if (new_node == NULL)
|
|
return NULL;
|
|
|
|
NODE_PAYLOAD_ASSIGN(new_node)
|
|
|
|
gl_tree_add_node_after (container, node, new_node);
|
|
return new_node;
|
|
}
|
|
|
|
static void
|
|
gl_tree_remove_node_no_free (CONTAINER_T container, NODE_T node)
|
|
{
|
|
NODE_T parent = node->parent;
|
|
|
|
if (node->left == NULL)
|
|
{
|
|
/* Replace node with node->right. */
|
|
NODE_T child = node->right;
|
|
|
|
if (child != NULL)
|
|
{
|
|
child->parent = parent;
|
|
/* Since node->left == NULL, child must be RED and of height 1,
|
|
hence node must have been BLACK. Recolor the child. */
|
|
child->color = BLACK;
|
|
}
|
|
if (parent == NULL)
|
|
container->root = child;
|
|
else
|
|
{
|
|
if (parent->left == node)
|
|
parent->left = child;
|
|
else /* parent->right == node */
|
|
parent->right = child;
|
|
|
|
if (child == NULL && node->color == BLACK)
|
|
rebalance_after_remove (container, child, parent);
|
|
}
|
|
}
|
|
else if (node->right == NULL)
|
|
{
|
|
/* It is not absolutely necessary to treat this case. But the more
|
|
general case below is more complicated, hence slower. */
|
|
/* Replace node with node->left. */
|
|
NODE_T child = node->left;
|
|
|
|
child->parent = parent;
|
|
/* Since node->right == NULL, child must be RED and of height 1,
|
|
hence node must have been BLACK. Recolor the child. */
|
|
child->color = BLACK;
|
|
if (parent == NULL)
|
|
container->root = child;
|
|
else
|
|
{
|
|
if (parent->left == node)
|
|
parent->left = child;
|
|
else /* parent->right == node */
|
|
parent->right = child;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* Replace node with the rightmost element of the node->left subtree. */
|
|
NODE_T subst;
|
|
NODE_T subst_parent;
|
|
NODE_T child;
|
|
color_t removed_color;
|
|
|
|
for (subst = node->left; subst->right != NULL; )
|
|
subst = subst->right;
|
|
|
|
subst_parent = subst->parent;
|
|
|
|
child = subst->left;
|
|
|
|
removed_color = subst->color;
|
|
|
|
/* The case subst_parent == node is special: If we do nothing special,
|
|
we get confusion about node->left, subst->left and child->parent.
|
|
subst_parent == node
|
|
<==> The 'for' loop above terminated immediately.
|
|
<==> subst == subst_parent->left
|
|
[otherwise subst == subst_parent->right]
|
|
In this case, we would need to first set
|
|
child->parent = node; node->left = child;
|
|
and later - when we copy subst into node's position - again
|
|
child->parent = subst; subst->left = child;
|
|
Altogether a no-op. */
|
|
if (subst_parent != node)
|
|
{
|
|
if (child != NULL)
|
|
child->parent = subst_parent;
|
|
subst_parent->right = child;
|
|
}
|
|
|
|
/* Copy subst into node's position.
|
|
(This is safer than to copy subst's value into node, keep node in
|
|
place, and free subst.) */
|
|
if (subst_parent != node)
|
|
{
|
|
subst->left = node->left;
|
|
subst->left->parent = subst;
|
|
}
|
|
subst->right = node->right;
|
|
subst->right->parent = subst;
|
|
subst->color = node->color;
|
|
subst->parent = parent;
|
|
if (parent == NULL)
|
|
container->root = subst;
|
|
else if (parent->left == node)
|
|
parent->left = subst;
|
|
else /* parent->right == node */
|
|
parent->right = subst;
|
|
|
|
if (removed_color == BLACK)
|
|
{
|
|
if (child != NULL && child->color == RED)
|
|
/* Recolor the child. */
|
|
child->color = BLACK;
|
|
else
|
|
/* Rebalancing starts at child's parent, that is subst_parent -
|
|
except when subst_parent == node. In this case, we need to use
|
|
its replacement, subst. */
|
|
rebalance_after_remove (container, child,
|
|
subst_parent != node ? subst_parent : subst);
|
|
}
|
|
}
|
|
|
|
container->count--;
|
|
}
|
|
|
|
static bool
|
|
gl_tree_remove_node (CONTAINER_T container, NODE_T node)
|
|
{
|
|
gl_tree_remove_node_no_free (container, node);
|
|
NODE_PAYLOAD_DISPOSE (container, node)
|
|
free (node);
|
|
return true;
|
|
}
|
|
|
|
/* For debugging. */
|
|
static unsigned int
|
|
check_invariants (NODE_T node, NODE_T parent, size_t *counterp)
|
|
{
|
|
unsigned int left_blackheight =
|
|
(node->left != NULL ? check_invariants (node->left, node, counterp) : 0);
|
|
unsigned int right_blackheight =
|
|
(node->right != NULL ? check_invariants (node->right, node, counterp) : 0);
|
|
|
|
if (!(node->parent == parent))
|
|
abort ();
|
|
if (!(node->color == BLACK || node->color == RED))
|
|
abort ();
|
|
if (parent == NULL && !(node->color == BLACK))
|
|
abort ();
|
|
if (!(left_blackheight == right_blackheight))
|
|
abort ();
|
|
|
|
(*counterp)++;
|
|
|
|
return left_blackheight + (node->color == BLACK ? 1 : 0);
|
|
}
|