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<li>限制操作：一些思维题不允许选手直接读取数据，而是要求选手做特定询问获取详细内容；或者可能限制操作次数。</li>
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<a href="/post/inv/">乘法逆元</a>
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数论基础第三弹！
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<time datetime="2024-07-18T22:09:36+08:00">
Jul 18, 2024
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math
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<a href="/post/odt/">珂朵莉树</a>
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<p>珂朵莉树（Chtholly Tree），又名老司机树 ODT（Old Driver Tree）。起源自 <a
class="gblog-markdown__link"
href="https://codeforces.com/problemset/problem/896/C"
>CF896C</a>。</p>
<p>实际上，这种想法的本质是基于数据随机的「颜色段均摊」，而不是一种数据结构。</p>
<p>使用 <code>set</code> 实现的珂朵莉树的 <code>assign</code>、<code>add</code>、<code>sum</code> 操作复杂度为 $O(n\log\log n)$.</p>
<p>ODT 的核心思想是将值相同的区间合并为一个结点维护，只要有区间赋值的题目都可以用 ODT 骗分。</p>
<p>ODT 在随机数据上表现良好，但是不保证数据随机时，会被构造数据卡到 T 飞。</p>
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<time datetime="2024-06-24T15:45:44+08:00">
Jun 24, 2024
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<a href="/post/fresh_seg/">小清新线段树</a>
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<p>通常来说，在使用线段树维护区间操作时，需要使操作在区间上能被快速计算，经典的区间加-区间求和是一个简单的例子。</p>
<p>但是，这里也有一个看似难以维护的反例：</p>
<blockquote>
<p><a
class="gblog-markdown__link"
href="https://vjudge.net/problem/bzoj-3211"
><strong>bzoj 3211 花神游历各国</strong></a></p>
<p>维护一个序列 $A$，初始值为 $A=(a_1,a_2,a_3,\cdots,a_n)$，支持以下操作 $q$ 次：</p>
<ol>
<li>区间求和</li>
<li>对区间每个数求平方根（向下取整）</li>
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<p>$1\le n,q\le 1\times 10^5,0\le a_i\le 10^{12}.$</p>
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