红黑树

最新推荐文章于 2024-12-11 00:02:12 发布

panwanning

最新推荐文章于 2024-12-11 00:02:12 发布

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分类专栏：操作系统

本文链接：https://blog.youkuaiyun.com/panwanning/article/details/106464803

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红黑树是一种自平衡二叉查找树，它在插入、删除和查找操作上具有良好的性能。该数据结构通过特定的颜色属性和规则保持平衡，确保最坏情况下的时间复杂度为O(log n)。文章详细介绍了红黑树的性质、旋转操作以及在实际应用中的价值。

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static __always_inline void
__rb_insert(struct rb_node *node, struct rb_root *root,
	    void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
{
	struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;

	while (true) {
		/*
		 * Loop invariant: node is red.
		 */
		if (unlikely(!parent)) {
			/*
			 * The inserted node is root. Either this is the
			 * first node, or we recursed at Case 1 below and
			 * are no longer violating 4).
			 */
			rb_set_parent_color(node, NULL, RB_BLACK);
			break;
		}

		/*
		 * If there is a black parent, we are done.
		 * Otherwise, take some corrective action as,
		 * per 4), we don't want a red root or two
		 * consecutive red nodes.
		 */
		if(rb_is_black(parent))
			break;

		gparent = rb_red_parent(parent);

		tmp = gparent->rb_right;
		if (parent != tmp) {	/* parent == gparent->rb_left */
			if (tmp && rb_is_red(tmp)) {
				/*
				 * Case 1 - node's uncle is red (color flips).
				 *
				 *       G            g
				 *      / \          / \
				 *     p   u  -->   P   U
				 *    /            /
				 *   n            n
				 *
				 * However, since g's parent might be red, and
				 * 4) does not allow this, we need to recurse
				 * at g.
				 */
				rb_set_parent_color(tmp, gparent, RB_BLACK);
				rb_set_parent_color(parent, gparent, RB_BLACK);
				node = gparent;
				parent = rb_parent(node);
				rb_set_parent_color(node, parent, RB_RED);
				continue;
			}

			tmp = parent->rb_right;
			if (node == tmp) {
				/*
				 * Case 2 - node's uncle is black and node is
				 * the parent's right child (left rotate at parent).
				 *
				 *      G             G
				 *     / \           / \
				 *    p   U  -->    n   U
				 *     \           /
				 *      n         p
				 *
				 * This still leaves us in violation of 4), the
				 * continuation into Case 3 will fix that.
				 */
				tmp = node->rb_left;
				WRITE_ONCE(parent->rb_right, tmp);
				WRITE_ONCE(node->rb_left, parent);
				if (tmp)
					rb_set_parent_color(tmp, parent,
							    RB_BLACK);
				rb_set_parent_color(parent, node, RB_RED);
				augment_rotate(parent, node);
				parent = node;
				tmp = node->rb_right;
			}

			/*
			 * Case 3 - node's uncle is black and node is
			 * the parent's left child (right rotate at gparent).
			 *
			 *        G           P
			 *       / \         / \
			 *      p   U  -->  n   g
			 *     /                 \
			 *    n                   U
			 */
			WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
			WRITE_ONCE(parent->rb_right, gparent);
			if (tmp)
				rb_set_parent_color(tmp, gparent, RB_BLACK);
			__rb_rotate_set_parents(gparent, parent, root, RB_RED);
			augment_rotate(gparent, parent);
			break;
		} else {
			tmp = gparent->rb_left;
			if (tmp && rb_is_red(tmp)) {
				/* Case 1 - color flips */
				rb_set_parent_color(tmp, gparent, RB_BLACK);
				rb_set_parent_color(parent, gparent, RB_BLACK);
				node = gparent;
				parent = rb_parent(node);
				rb_set_parent_color(node, parent, RB_RED);
				continue;
			}

			tmp = parent->rb_left;
			if (node == tmp) {
				/* Case 2 - right rotate at parent */
				tmp = node->rb_right;
				WRITE_ONCE(parent->rb_left, tmp);
				WRITE_ONCE(node->rb_right, parent);
				if (tmp)
					rb_set_parent_color(tmp, parent,
							    RB_BLACK);
				rb_set_parent_color(parent, node, RB_RED);
				augment_rotate(parent, node);
				parent = node;
				tmp = node->rb_left;
			}

			/* Case 3 - left rotate at gparent */
			WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
			WRITE_ONCE(parent->rb_left, gparent);
			if (tmp)
				rb_set_parent_color(tmp, gparent, RB_BLACK);
			__rb_rotate_set_parents(gparent, parent, root, RB_RED);
			augment_rotate(gparent, parent);
			break;
		}
	}
}