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<!DOCTYPE html><html lang="zh-CN" data-theme="light"><head><meta charset="UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0,viewport-fit=cover"><title>Hexo</title><meta name="author" content="mxrush"><meta name="copyright" content="mxrush"><meta name="format-detection" content="telephone=no"><meta name="theme-color" content="#ffffff"><meta property="og:type" content="website">
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<!-- hexo injector head_end end --><meta name="generator" content="Hexo 7.2.0"></head><body><div id="sidebar"><div id="menu-mask"></div><div id="sidebar-menus"><div class="avatar-img is-center"><img src="https://i.loli.net/2021/02/24/5O1day2nriDzjSu.png" onerror="onerror=null;src='/img/friend_404.gif'" alt="avatar"/></div><div class="sidebar-site-data site-data is-center"><a href="/archives/"><div class="headline">文章</div><div class="length-num">4</div></a><a href="/tags/"><div class="headline">标签</div><div class="length-num">2</div></a><a href="/categories/"><div class="headline">分类</div><div class="length-num">0</div></a></div><hr class="custom-hr"/></div></div><div class="page" id="body-wrap"><header class="full_page" id="page-header"><nav id="nav"><span id="blog-info"><a href="/" title="Hexo"><span class="site-name">Hexo</span></a></span><div id="menus"><div id="toggle-menu"><a class="site-page" href="javascript:void(0);"><i class="fas fa-bars fa-fw"></i></a></div></div></nav><div id="site-info"><h1 id="site-title">Hexo</h1></div><div id="scroll-down"><i class="fas fa-angle-down scroll-down-effects"></i></div></header><main class="layout" id="content-inner"><div class="recent-posts" id="recent-posts"><div class="recent-post-item"><div class="recent-post-info no-cover"><a class="article-title" href="/2024/05/01/CF1972D%E9%A2%98%E8%A7%A3/" title="CF1972D题解">CF1972D题解</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">发表于</span><time datetime="2024-05-01T11:14:59.000Z" title="发表于 2024-05-01 19:14:59">2024-05-01</time></span></div><div class="content">问题一
题面
给你两个正整数 \(n\) , \(m\) 。
计算满足以下条件的有序数对 \((a,
b)\) 的个数：
\(1\le a\le n\) , \(1\le b\le m\) ;
\(a+b\) 是 \(b \cdot \gcd(a,b)\) 的倍数。
思路
设\(d=\gcd(a,b)\). 有\(bd|a+b \Rightarrow qd^2|(p+q)d\Rightarrow
qd|p+q\), \(\gcd(p,q)=1\).
此时可以直接令\(kqd=p+q\Rightarrow
(kd-1)q=p\).
因为\(q,p\)是互质的. \(p\)可以表达为\(q\)和某个数的乘积\(q\)只能是1.
于是有\(kd=p+1\le
\lfloor\frac{n}{d}\rfloor+1\Rightarrow k\le
\frac{\lfloor\frac{n}{d}\rfloor+1}{d}\).
枚举\(d\)用上式计算每个贡献即可.
此外还有一种思路, 当发现\(q=1\)后可以知道\(d=b\).有\(b^2|a+b ...</div></div></div><div class="recent-post-item"><div class="recent-post-info no-cover"><a class="article-title" href="/2024/05/01/%E6%9D%82%E9%A2%98%E6%9C%88%E5%88%8A-2024-05/" title="杂题月刊(2024-05)">杂题月刊(2024-05)</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">发表于</span><time datetime="2024-05-01T03:19:14.000Z" title="发表于 2024-05-01 11:19:14">2024-05-01</time></span></div><div class="content">CF1777C(滑动窗口;极差;排序)
link
感觉十分EDU的一道题, 虽然很简单但还是被单防了一会儿.
太久没写这类题了忘记可以先sort一下了.
如果分析最后答案子序列的性质, 很难找到有用的信息.
此时从最后要求的东西入手. 因为要求极差只需要考虑两个极值,
对于有序数组的情况可以发现子序列问题可以转化为子区间问题,
因为要求极小值进一步变成求极短合法区间问题, 这个可以用滑动窗口解决.
又因为数组顺序不会影响答案(因为选的是子序列),
所以可以直接sort.
code or
tutorial
CF213C(网格图DP)
link
可转化为两个人同时从起点出发的路径和最大的问题.
用到了很典的的trick:
网格图上用(time, row/col)表示当前所处位置.
于是可以把f[x1][y1][x2][y2]的暴力dp定义优化为f[time][y1][y2]的定义,
压缩了状态并降低时间复杂度.
然鹅我没仔细想这样的暴力解再优化的方案, 开始去找路径性质.
似乎两条路径至多一个交点?
转成正负两次的网格图上不相交路径权值最大和的问题 ...</div></div></div><div class="recent-post-item"><div class="recent-post-info no-cover"><a class="article-title" href="/2024/04/29/%E6%9D%82%E9%A2%98%E6%9C%88%E5%88%8A-2024-04/" title="杂题月刊(2024-04)">杂题月刊(2024-04)</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">发表于</span><time datetime="2024-04-29T13:55:14.000Z" title="发表于 2024-04-29 21:55:14">2024-04-29</time></span></div><div class="content"> CF1365C(排列;shift;最大匹配数)
link
给左右shift操作求两个排列的最大匹配数. 很简单的一个题, 但是莫名奇妙被单防了.
code or tutorial
CF1401F(区间翻转;线段树)
link
用了比较常见的trick操作合并. 尝试将不同的操作用一种更简单的操作的若干次组合替代. 可以发现操作能够归约. 其次注意到二进制区间的翻转可以看作线段树子树的交换. 这个题的思路就很清晰了.
code or tutorial
牛客小白91G(树上字符串hash;回文串;lca)
link
思路比较简单, 做一个正反的树上字符串hash, 求出lca后减去计算重复的部分将两条链的哈希值对齐拼起来就是一条路径的hash了. 代码写起来略微折磨.
code or tutorial
24牛客寒营1H(位运算;枚举;分类讨论)
link
设最终重量为ccc, 枚举mmm中的所有1-bit, 令ccc该位为0, 对于这种类型的答案, 可以分为前后两部分讨论.
对更高位, 只能选择 mmm 二进制位的一个"子集".
对更低位, 可以任意选择.
...</div></div></div><div class="recent-post-item"><div class="recent-post-info no-cover"><a class="article-title" href="/2024/04/24/hello-world/" title="Hello World">Hello World</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">发表于</span><time datetime="2024-04-24T13:33:32.009Z" title="发表于 2024-04-24 21:33:32">2024-04-24</time></span></div><div class="content">这是一个测试.Welcome to Hexo! This is your very first post. Check documentation for more info. If you get any problems when using Hexo, you can find the answer in troubleshooting or you can ask me on GitHub.
Quick Start
Create a new post
1$ hexo new "My New Post"
More info: Writing
Run server
1$ hexo server
More info: Server
Generate static files
1$ hexo generate
More info: Generating
Deploy to remote sites
1$ hexo deploy
More info: Deployment
</div></div></div><nav id="pagination"><div class="pagination"><span class="page-number current">1</span></div></nav></div><div class="aside-content" id="aside-content"><div class="card-widget card-info"><div class="is-center"><div class="avatar-img"><img src="https://i.loli.net/2021/02/24/5O1day2nriDzjSu.png" onerror="this.onerror=null;this.src='/img/friend_404.gif'" alt="avatar"/></div><div class="author-info__name">mxrush</div><div class="author-info__description"></div></div><div class="card-info-data site-data is-center"><a href="/archives/"><div class="headline">文章</div><div class="length-num">4</div></a><a href="/tags/"><div class="headline">标签</div><div class="length-num">2</div></a><a href="/categories/"><div class="headline">分类</div><div class="length-num">0</div></a></div><a id="card-info-btn" target="_blank" rel="noopener" href="https://github.com/mxrush129"><i class="fab fa-github"></i><span>Follow Me</span></a></div><div class="card-widget card-announcement"><div class="item-headline"><i class="fas fa-bullhorn fa-shake"></i><span>公告</span></div><div class="announcement_content">This is my Blog</div></div><div class="sticky_layout"><div class="card-widget card-recent-post"><div class="item-headline"><i class="fas fa-history"></i><span>最新文章</span></div><div class="aside-list"><div class="aside-list-item no-cover"><div class="content"><a class="title" href="/2024/05/01/CF1972D%E9%A2%98%E8%A7%A3/" title="CF1972D题解">CF1972D题解</a><time datetime="2024-05-01T11:14:59.000Z" title="发表于 2024-05-01 19:14:59">2024-05-01</time></div></div><div class="aside-list-item no-cover"><div class="content"><a class="title" href="/2024/05/01/%E6%9D%82%E9%A2%98%E6%9C%88%E5%88%8A-2024-05/" title="杂题月刊(2024-05)">杂题月刊(2024-05)</a><time datetime="2024-05-01T03:19:14.000Z" title="发表于 2024-05-01 11:19:14">2024-05-01</time></div></div><div class="aside-list-item no-cover"><div class="content"><a class="title" href="/2024/04/29/%E6%9D%82%E9%A2%98%E6%9C%88%E5%88%8A-2024-04/" title="杂题月刊(2024-04)">杂题月刊(2024-04)</a><time datetime="2024-04-29T13:55:14.000Z" title="发表于 2024-04-29 21:55:14">2024-04-29</time></div></div><div class="aside-list-item no-cover"><div class="content"><a class="title" href="/2024/04/24/hello-world/" title="Hello World">Hello World</a><time datetime="2024-04-24T13:33:32.009Z" title="发表于 2024-04-24 21:33:32">2024-04-24</time></div></div></div></div><div class="card-widget card-tags"><div class="item-headline"><i class="fas fa-tags"></i><span>标签</span></div><div class="card-tag-cloud"><a href="/tags/%E9%A2%98%E8%A7%A3/" style="font-size: 1.5em; 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