<?xml version="1.0" encoding="utf-8" ?><rss version="2.0"><channel><title><![CDATA[aeiv52006的博客]]></title><description><![CDATA[]]></description><link>https://blog.youkuaiyun.com/aeiv52006</link><language>zh-cn</language><generator>https://blog.youkuaiyun.com/</generator><copyright><![CDATA[Copyright &copy; aeiv52006]]></copyright><item><title><![CDATA[知识点-数论进阶]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402433</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402433</guid><author>aeiv52006</author><pubDate>Fri, 06 Sep 2019 21:17:00 +0800</pubDate><description><![CDATA[知识点-数论进阶
abstract：整除分块，积性函数，线性筛，莫比乌斯反演，迪利克雷卷积，积性函数前缀和，
0.引入
Gym - 101485D debugging
（之后会发现，这道dp的转移方程和杜教筛的转移如出一辙。）
题意
有一份包含1个 bug 的n( 1≤????≤1e6)行代码，运行一次到崩溃需要的时间为 r( 1≤????≤1e9)。
你可以任意行添加 printf 语句来输出调试...]]></description><category></category></item><item><title><![CDATA[concrete maths ch2 求和]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402430</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402430</guid><author>aeiv52006</author><pubDate>Tue, 03 Sep 2019 20:43:00 +0800</pubDate><description><![CDATA[ch2 求和
1.sigma及相关符号

\(\sum\limits_{i=1}^{n}i\) 是确定式，\(\sum\limits_{1\le i\le n}i\)是一般式。 一般式进行下标换元不容易出错，确定式写代码的时候好写些。
边界问题：越简单越好。
Kenneth E. Iverson括号: \([p\ prime]\) 可以用于化简一般式：
\[
\sum\limits_{p...]]></description><category></category></item><item><title><![CDATA[concrete maths ch4 number theory]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402429</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402429</guid><author>aeiv52006</author><pubDate>Mon, 02 Sep 2019 22:12:00 +0800</pubDate><description><![CDATA[ch4 number theory
数论研究正数的性质
1.整除
gcd lcm 扩展欧几里得。
整除求和\(\sum_{n|m}\)的几个公式。ch2的知识会很有用。
2.质数
Fundamental Theorem of Arithmetic：
根据唯一分解定理，每个数可以用质数的次数数组表示：
\[
(n_2,n_3,n_5...)
\]
这样gcd lcm都有了新的定义。这种...]]></description><category></category></item><item><title><![CDATA[Aho-Corasick algorithm]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402428</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402428</guid><author>aeiv52006</author><pubDate>Tue, 20 Aug 2019 20:22:00 +0800</pubDate><description><![CDATA[Aho-Corasick algorithm
Let there be a set of strings with the total length \(m\) (sum of all lengths).
The Aho-Corasick algorithm constructs a data structure similar to a trie with some additiona...]]></description><category></category></item><item><title><![CDATA[Finding repetitions]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402427</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402427</guid><author>aeiv52006</author><pubDate>Tue, 20 Aug 2019 20:21:00 +0800</pubDate><description><![CDATA[Finding repetitions
Given a string \(s\) of length \(n\).
A repetition is two occurrences of a string in a row.
In other words a repetition can be described by a pair of indices \(i &lt; j\) suc...]]></description><category></category></item><item><title><![CDATA[Suffix Automaton]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402425</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402425</guid><author>aeiv52006</author><pubDate>Tue, 20 Aug 2019 20:20:00 +0800</pubDate><description><![CDATA[Suffix Automaton
A suffix automaton is a powerful data structure that allows solving many string-related problems.
For example, you can search for all occurrences of one string in another, or cou...]]></description><category></category></item><item><title><![CDATA[Z-function and its calculation]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402424</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402424</guid><author>aeiv52006</author><pubDate>Tue, 20 Aug 2019 20:19:00 +0800</pubDate><description><![CDATA[Z-function and its calculation
Suppose we are given a string \(s\) of length \(n\). The Z-function for this string is an array of length \(n\) where the \(i\)-th element is equal to the greatest ...]]></description><category></category></item><item><title><![CDATA[Prefix function. Knuth–Morris–Pratt algorithm]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402422</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402422</guid><author>aeiv52006</author><pubDate>Tue, 20 Aug 2019 20:18:00 +0800</pubDate><description><![CDATA[Prefix function. Knuth–Morris–Pratt algorithm
Prefix function definition
You are given a string \(s\) of length \(n\).
The prefix function for this string is defined as an array \(\pi\) of length...]]></description><category></category></item><item><title><![CDATA[Suffix Array]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402423</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402423</guid><author>aeiv52006</author><pubDate>Tue, 20 Aug 2019 20:16:00 +0800</pubDate><description><![CDATA[Suffix Array
Definition
Let \(s\) be a string of length \(n\). The \(i\)-th suffix of \(s\) is the substring \(s[i \ldots n - 1]\).
A suffix array will contain integers that represent the starti...]]></description><category></category></item><item><title><![CDATA[知识点 - 计算几何基础]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402420</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402420</guid><author>aeiv52006</author><pubDate>Sat, 17 Aug 2019 21:12:00 +0800</pubDate><description><![CDATA[知识点 - 计算几何基础
讲义
点
我们把点 \(\mathbf r\) 看成从 \(\mathbf 0\) 到 \(\mathbf r\)的向量 \(\vec{\mathbf r}\)
#define ftype long double
struct point2d {
    ftype x, y;
    point2d() {}
    point2d(ftype x, ftyp...]]></description><category></category></item><item><title><![CDATA[知识点 - 树状数组]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402421</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402421</guid><author>aeiv52006</author><pubDate>Fri, 16 Aug 2019 21:25:00 +0800</pubDate><description><![CDATA[知识点 - 树状数组
解决问题类型：
单点更新，前缀查询，很简单地拓展到2维
复杂度即代码：
//压行
#define lowbit(x) ((x)&amp;(-(x)))
void add(int x, int y) { for (; x &lt;= idx; x += lowbit(x)) f[x] += y; }
int sum(int x) { int ans = 0; for ...]]></description><category></category></item><item><title><![CDATA[知识点 - 线段树 权值 树套树 二维 可持续]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402419</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402419</guid><author>aeiv52006</author><pubDate>Fri, 16 Aug 2019 21:13:00 +0800</pubDate><description><![CDATA[知识点 - 线段树 权值 树套树 二维 可持续
//区间更新求和
inline int ls(int p) { return p &lt;&lt; 1; }//左儿子 
inline int rs(int p) { return p &lt;&lt; 1 | 1; }//右儿子 
void push_up(int p) {
    t[p] = t[ls(p)] + t[rs(p)];
...]]></description><category></category></item><item><title><![CDATA[Operations on polynomials and series]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402418</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402418</guid><author>aeiv52006</author><pubDate>Wed, 14 Aug 2019 16:39:00 +0800</pubDate><description><![CDATA[Operations on polynomials and series
In this article we will cover common operations that you will probably have to do if you deal with polynomials.
Basic Notion and Facts
Consider a polynomial \...]]></description><category></category></item><item><title><![CDATA[AtCoder 137 F 插值 差分 或构造]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402416</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402416</guid><author>aeiv52006</author><pubDate>Tue, 13 Aug 2019 22:24:00 +0800</pubDate><description><![CDATA[AtCoder 137 F 插值求系数 想法题
题意：AtCoder 137 F
已知：\(f(x)\)在p个点的值：\(f(i) \equiv a_i \pmod p\) \((0 \leq i \leq p-1)\)
求：\(f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \ldots + b_0\)的所有系数\(b_i\)
保证：\(2 \le...]]></description><category></category></item><item><title><![CDATA[Burnside's lemma / Pólya enumeration theorem]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402417</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402417</guid><author>aeiv52006</author><pubDate>Thu, 08 Aug 2019 22:21:00 +0800</pubDate><description><![CDATA[Burnside's lemma / Pólya enumeration theorem
Burnside's lemma
Burnside's lemma was formulated and proven by Burnside in 1897, but historically it was already discovered in 1887 by Frobenius, and ...]]></description><category></category></item><item><title><![CDATA[The Inclusion-Exclusion Principle]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402414</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402414</guid><author>aeiv52006</author><pubDate>Thu, 08 Aug 2019 22:05:00 +0800</pubDate><description><![CDATA[The Inclusion-Exclusion Principle
The inclusion-exclusion principle is an important combinatorial way to compute the size of a set or the probability of complex events. It relates the sizes of in...]]></description><category></category></item><item><title><![CDATA[图的联通性]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402415</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402415</guid><author>aeiv52006</author><pubDate>Thu, 25 Jul 2019 22:11:00 +0800</pubDate><description><![CDATA[图的联通性
0.【前置知识】 图上dfs相关概念
vis数组：在图的遍历中，往往设置了一个标记数组vis的bool值来记录顶点是否被访问过。但有些时候需要改变vis值的意义。令vis具有3种值并表示3种不同含义
vis = 0,表示该顶点没没有被访问
vis = 1,表示该顶点已经被访问，但其子孙后代还没被访问完，也就没从该点返回
vis = 2，表示该顶点已经被访问，其子孙后代也已经访...]]></description><category></category></item><item><title><![CDATA[数据结构入门]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402209</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402209</guid><author>aeiv52006</author><pubDate>Thu, 11 Apr 2019 17:13:00 +0800</pubDate><description><![CDATA[单调栈与单调队列 Minimum stack / Minimum queue
问题1：如何O(1)地访问一个栈的最小值？
Ans：我们给栈里的数附上第二个域，代表在这个数之前（包含这个数）的最小值。
stack&lt;pair&lt;int, int&gt;&gt; st;

void push(int new_elem){
    int new_min = st.empty() ? ...]]></description><category></category></item><item><title><![CDATA[数论函数补充  公式推导]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402207</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402207</guid><author>aeiv52006</author><pubDate>Mon, 08 Apr 2019 13:01:00 +0800</pubDate><description><![CDATA[\(\begin{array}{l} 考虑问题\sum\limits ^{n}_{i=1}\sum\limits ^{m}_{j=1} [gcd(i,j)=p]\ \ \ ( n,m\leqslant 1e7)\\ \\ \Leftrightarrow \sum\limits _{p}\sum\nolimits ^{\lfloor \frac{min( m,n)}{p} \rfloor...]]></description><category></category></item><item><title><![CDATA[几何入门合集 gym101968 problem F. Mirror + gym102082 Problem F Fair Chocolate-Cutting + gym101915 problem ...]]></title><link>https://blog.youkuaiyun.com/aeiv52006/article/details/102402206</link><guid>https://blog.youkuaiyun.com/aeiv52006/article/details/102402206</guid><author>aeiv52006</author><pubDate>Mon, 08 Apr 2019 12:41:00 +0800</pubDate><description><![CDATA[abstract:


V const &amp; a 加速

F. Mirror
题意
链接
问题：
有n个人在y=0的平面上(及xoz平面)。z=0平面上有一面镜子(边平行于坐标轴）。z=a平面上有q个点（保证a大于所有人的z坐标）。 所有人面朝镜子，且在镜子和q个点之间（即每个人的z坐标保证0&lt;z&lt;a）。
问对于某个点，让所有人能够通过镜子看到那个点的镜子的最小面积。...]]></description><category></category></item></channel></rss>