https://k4i.top/tags/small-to-large/Recent content in Small-to-Large on k4i's blogHugo -- gohugo.ioensky_io@outlook.com (K4i)sky_io@outlook.com (K4i)All content is subject to the license of <a rel="license noopener" href="https://creativecommons.org/licenses/by-nc-sa/4.0/" target="_blank">CC BY-NC-SA 4.0</a> .Fri, 16 Feb 2024 19:05:00 +0800https://k4i.top/posts/dsu-on-tree/Fri, 16 Feb 2024 19:05:00 +0800sky_io@outlook.com (K4i)Sun, 26 Apr 2026 16:08:06 +0800https://k4i.top/posts/dsu-on-tree/<h2 id="problem">the subtree-query problem</h2> <p>suppose every vertex of a rooted tree has a color. for every vertex \(v\), we want to answer:</p> <blockquote> <p>how many distinct colors appear in the subtree of \(v\)?</p> </blockquote> <p>a direct DFS for every query works, but it is too expensive. if we scan the whole subtree of each vertex independently, a chain of \(n\) vertices already costs</p> <p>\begin{equation}<br /> 1 + 2 + \cdots + n = O(n^2).<br /> \end{equation}</p>K4ifeatured imagedsu-on-treesacktreesmall-to-largeData-Structure-and-Algorithm