LaTeX\LaTeXLATE X 是一种基于 TeX\TeXTE X 的排版系统，能够方便地生成数学公式。 基础知识 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 行内公式与行间公式 行内公式（即穿插在文本中的公式）两侧分别使用一个美元 $ $ 符号定界。 例如 $x \cdot \sin(y)$ 显示为 x⋅sin⁡(y)x \cdot \sin(y)x⋅sin(y)。 行间公式（即独立成行的公式）两侧分别使用 $$ $$（每侧两个美元符号）定界，例如 $$ H_n = \sum_{i = 1}^{n} \frac{1}{i} $$ 显示为： Hn=∑i=1n1iH_n = \sum_{i = 1}^{n} \frac{1}{i} Hn =i=1∑n i1 行内公式的 “大小”（例如分数的大小、巨运算符上下标的位置）会比行间公式小，可以通过 \displaystyle 和 \textstyle 来切换两类模式： 对于行内公式，使用 \displaystyle 的效果： LaTeX 效果 \frac{1}{x} 1x\frac{1}{x}x1 \displaystyle \frac{1}{x} 1x\displaystyle \frac{1}{x}x1 对于行间公式，使用 textstyle 的效果： $$ \textstyle \int \frac{\mathop{}\!\mathrm{d} x}{x} = \ln(x) + C $$ 显示为： ∫ ⁣dxx=ln⁡(x)+C\textstyle \int \frac{\mathop{}\!\mathrm{d} x}{x} = \ln(x) + C ∫xdx =ln(x)+C LATEX 控制序列的概念（类似于函数） 控制序列可以视作为命令：以 \ 开头，参数：必需参数 {} 和可选参数 []。 控制序列可以实现特定功能，例如 \sin x 显示为 sin⁡x\sin xsinx、\color{red} x 显示为 x\color{red} xx。 LATEX 环境的概念 环境的格式为 \begin{环境名} 环境内部 \end{环境名}，即 \begin 和 \end 以及它们中间的部分。 环境有比控制序列更加灵活的用法，例如 \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} 显示为： [1234]\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}[13 24 ] 而 显示为： f(x)={2x∈Q1x∉Q∧x∈A0x∉Af(x) = \begin{cases} 2 & x \in \mathbb Q \\ 1 & x \notin \mathbb Q \land x \in \mathbb A \\ 0 & x \notin \mathbb A\end{cases}f(x)=⎩⎨⎧ 210 x∈Qx∈/Q∧x∈Ax∈/A 基本语法 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 二元关系 / 运算符 二元关系符： LaTeX 效果 x = y x=yx = yx=y x > y x>yx > yx>y x < y x<yx < yx<y x \ge y x≥yx \ge yx≥y x \le y x≤yx \le yx≤y x \perp y x⊥yx \perp yx⊥y x \parallel y x∥yx \parallel yx∥y x \mid y x∣yx \mid yx∣y x \nparallel y x∦yx \nparallel yx∦y x \nmid y x∤yx \nmid yx∤y x \approx y x≈yx \approx yx≈y x \in y x∈yx \in yx∈y x \ni y x∋yx \ni yx∋y x \ne y x≠yx \ne yx=y x \sim y x∼yx \sim yx∼y 二元运算符： LaTeX 效果 x + y x+yx + yx+y x - y x−yx - yx−y x \times y x×yx \times yx×y x \div y x÷yx \div yx÷y x \cdot y x⋅yx \cdot yx⋅y x \bmod y x mod yx \bmod yxmody x \circ y x∘yx \circ yx∘y x * y x∗yx * yx∗y x \ast y x∗yx \ast yx∗y x / y x/yx / yx/y x \oplus y x⊕yx \oplus yx⊕y x \otimes y x⊗yx \otimes yx⊗y 上标与下标 上标命令是 ^{角标}，下标命令是 _{角标}。当角标是单个字符时可以不用花括号（在 LaTeX\LaTeXLATE X 中，花括号是用于分组，即花括号内部文本为一组）。 例：x_1、x^2、x_1^2、x^2_1、x_{22}^{(n)}、{}^*\!x^* 的显示效果分别为：x1x_1x1 、x2x^2x2、x12x_1^2x12 、x12x^2_1x12 、x22(n)x_{22}^{(n)}x22(n) 、∗ ⁣x∗{}^*\!x^*∗x∗。 分式 输入较短的分式时，最简单的方法是使用斜线，譬如输入 $(x + y) / 2$，可得到 (x+y)/2(x + y) / 2(x+y)/2。 要输入带有水平分数线的公式，可用命令：\frac{分子}{分母}。 LaTeX 显示效果 \frac{x + y}{2} x+y2\frac{x + y}{2}2x+y \frac{1}{1 + \frac{1}{2}} 11+12\frac{1}{1 + \frac{1}{2}}1+21 1 根式 排版根式的命令是：开平方：\sqrt{表达式}；开 nnn 次方：\sqrt[n]{表达式}。 LaTeX 效果 \sqrt{2} < \sqrt[3]{3} 2<33\sqrt{2} < \sqrt[3]{3}2 <33 \sqrt{1 + \sqrt[p]{1 + a^2}} 1+1+a2p\sqrt{1 + \sqrt[p]{1 + a^2}}1+p1+a2 求和与积分 排版求和符号与积分符号的命令分别为 \sum 和 \int，它们通常都有上下限，在排版上就是上标和下标。 LaTeX 效果 \sum_{k = 1}^{n} \frac{1}{k} ∑k=1n1k\sum_{k = 1}^{n} \frac{1}{k}∑k=1n k1 \sum_{k = 1}^n \frac{1}{k} ∑k=1n1k\sum_{k = 1}^n \frac{1}{k}∑k=1n k1 \int_a^b f(x) d x ∫abf(x)dx\int_a^b f(x) d x∫ab f(x)dx \int_a^b f(x) \mathop{} \! \mathrm{d} x ∫abf(x) ⁣dx\int_a^b f(x) \mathop{} \! \mathrm{d} x∫ab f(x)dx 字体、字号与颜色 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 字体 对于英文的字体，LaTeX\LaTeXLATE X 给出了三个层级： 1. 族（family）：有罗马（roman）、无衬线（sans-serif）、打字机（teletype）三族，改变字体的基本外观。 2. 形状（shape）：有直立（upright）、意大利（italic）两种形状。 3. 重量（weight）：有中等（medium）、粗体（boldface）两种重量。 在某些时候，LaTeX\LaTeXLATE X 允许这些层级叠加使用： 直立中等 意大利中等 直立粗体 意大利粗体 \textup{\textmd \textit{\textmd \textup{\textbf \textit{\textbf 罗马 \textrm 无衬线 \textsf 打字机 \texttt 在文本模式下（即 \text 内部），默认情况下，族使用罗马、形状使用直立、重量使用中等。 在数学模式下（即 LaTeX\LaTeXLATE X 的默认），默认情况下，族使用罗马、形状使用意大利、重量使用中等。 \mathbb：ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}ABCDEFGHIJKLMNOPQRSTUVWXYZ 和 k\mathbb{k}k。 \mathcal：ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}ABCDEFGHIJKLMNOPQRSTUVWXYZ 和 0123456789\mathcal{0123456789}0123456789。 \mathscr：ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}ABCDEFGHIJKLMNOPQRSTUVWXYZ。 \mathfrak：ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789}ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789。 前文的改变字体的命令对这些特殊字体无效。

挑战赛题解来喽！ T1、N - 立方数 T2、N - 9的倍数 T3、N - 平方数 T4、大盗杰瑞 T5、距离求和 T6、最小绝对差值和

ACGO悄咪咪上线了AC助手，不知道大家发现了没有~以下是AC君整理的几种AC助手正确使用方法，供大家参考 1、RUA它 包括不限于，用鼠标拖住它甩来谁去、把他反反复复的放在屏幕的上下左右各个方向 2、问它 * 询问解题思路 题目看不懂？直接戳AC助手，大胆问出“你可以给我一些解题思路吗？”，不用担心，它可不会嫌弃你的！准备好接收轻松易懂的解题小贴士吧，让那些高深莫测的题目变得亲切起来~ * 询问代码错误 代码又出错了？别急，问问AC助手：“我的代码错哪儿了？”，它会耐心地帮你一行行审视那些调皮的bug，不仅指出问题，还会提供修复建议。这就是你的私人代码侦探，搞定一切小麻烦！ * 询问更优解 代码虽然能跑，但你知道的，我们从不满足于此。向AC助手提出挑战：“是否还有更优解？”它会帮你榨出代码的最后一滴性能汁，教你如何用更少的行数、更优的方式完成题目~ 3、评价它 AC助手给到的回复有好有坏，你可以轻轻点击他说话内容下方的【有用/无用】小按钮，给到他客观的评价。你的每一次反馈，都是在帮助他不断地自我学习，从而更懂得如何协助你解决问题。这样一来，它就能变得更聪明，下次为你提供更精准的帮助了！ 另外，大家在使用AC助手过程中，遇到任何问题或bug，可以在本帖下方留言，我们会尽快处理的！

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深度优先搜索 排列组合 加法原理：加步骤 乘法原理：乘步骤 排列：排列是指从给定的一组元素中，按照一定的顺序选择部分或全部元素所形成的线性排列(位置不同算不同) 公式：Pnk=n!/(n−k)!P_{n}^{k} = n! / (n-k)!Pnk =n!/(n−k)! 组合：组合是指从给定的一组元素中，选择部分或全部元素所形成的组合，不考虑元素的顺序(位置不同算同) 公式：Cnk=n!/(k!∗(n−k)!)C_{n}^{k} = n! / (k! * (n-k)!)Cnk =n!/(k!∗(n−k)!) 回溯 以下为排列输出 剪枝 可以剪掉一些状态，避免重复 减少搜索量 类型 可行性剪枝：得不到答案的去掉 最优性简直：更坏的去掉 连通性问题 走迷宫

AKSZ-DFS 深搜 > 回溯 > 剪枝 > 连通性判断 > 搜索解空间，找最优解 深搜加剪枝 经典八皇后 排列组合 加法原理 选a z+0 9=26+10=36a~z+0~9=26+10=36a z+0 9=26+10=36 乘法原理 20选3=20∗19∗1820选3=20*19*18 20选3=20∗19∗18

互关

<iostream>//数据流输入／输出 <istream>//数据流输入 <ostream>//数据流输出 <algorithm>//STL 通用算法 <bitset>//STL 位集容器 <cctype>//字符处理 <cerrno>//定义错误码 <cfloat>//浮点数处理 <ciso646>//对应各种运算符的宏 <climits>//定义各种数据类型最值的常量 <clocale>//定义本地化函数 <cmath>//定义数学函数 <complex>//复数类 <csignal>//信号机制支持 <csetjmp>//异常处理支持 <cstdarg>//不定参数列表支持 <cstddef>//常用常量 <cstdio>//定义输入／输出函数 <cstdlib>//定义杂项函数及内存分配函数 <cstring>//字符串处理 <ctime>//定义关于时间的函数 <cwchar>//宽字符处理及输入／输出 <cwctype>//宽字符分类 <deque>//STL 双端队列容器 <exception>//异常处理类 <fstream>//文件输入／输出 <functional>//STL 定义运算函数（代替运算符） <limits>//定义各种数据类型最值常量 <list>//STL 线性列表容器 <locale>//本地化特定信息 <map>//STL 映射容器 <memory>//STL通过分配器进行的内存分配 <new>//动态内存分配 <numeric>//STL常用的数字操作 <iomanip>//参数化输入／输出 <ios>//基本输入／输出支持 <iosfwd>//输入／输出系统使用的前置声明 <istream>//基本输入流 <iterator>//STL迭代器 <ostream>//基本输出流 <queue>//STL 队列容器 <set>//STL 集合容器 <sstream>//基于字符串的流 <stack>//STL 堆栈容器 <stdexcept>//标准异常类 <streambuf>//底层输入／输出支持 <string>//字符串类 <typeinfo>//运行期间类型信息 <utility>//STL 通用模板类 <valarray>//对包含值的数组的操作 <vector>//STL 动态数组容器 <bits/stdc++.h>//万能头文件 <windows.h>//调用windows系统 招人啦！！！

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> 声明：本人独立完成，非抄袭 > ACGO愚人节欢乐赛18题解完整版 第一题： 小明的魔力球 读题： 给定n个数，从中选出m个数，使得这些数中的最大值与最小值差最小 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 思路： 先输入这些数据，再排序，这样能够保证连续的m个数中最大值与最小值之差尽可能小，再擂台找到这些的最小值 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 代码： ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 第二题： 特工小明 读题： 输入一串字符串，把里面出现过的不同字符数统计出来 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 思路： 因为它要求字符不重复，所以我们可以用set（集合）来存储，最后输出集合的大小 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 代码： ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 第三题： 前行的拦截 读题： 给定一串数列，求至少将相邻两个数字交换几次，才能够让整个数列变成头最大、尾最小的数列 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 思路： 这是全场最难的题！ 想象一下，模拟做法假如超时该怎么办！（当然，由一只姜提供，模拟不会TLE） 那么我们可以转变为递推（像我给的新春欢乐赛第一题题解一样），找到一个规律 我们发现，能够擂台找到最大值的位置和最小值的位置，把最大值移到头需要abs(maxi-0)次，最小值移到尾需要abs(mini-(n-1))次 但是有没有想过最小的会在最大的前面？那如果这时我要把最大值放到最前面时，必须要和最小值交换一次，那么就需要减少一次！ 还有一个问题：当有并列最大值或最小值时，我们选哪一个？ 对于这个问题，我们再看一下题目：要求交换次数尽可能少，那么因为最大值要移到队首，所以我们最好选最靠前的最大值；同理，我们应该选最靠后的最小值。 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 代码： ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 本人做本类型题喜欢找到递推公式，请勿见怪 新思路：新思路： 新思路： 建议各位做题时不要局限于模拟的思路，也可以想想如何用二分、递推等思路去完成 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 第四题： 二进制运算异或 读题： 给两个二进制数，不进位相加 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 思路： 用字符串形式存储两个二进制数，如果两位相等，那么和的该位为0，否则为1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 代码： ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 第五题： 互送礼物 读题： 给你n个数，求哪个索引的数为当前的索引 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 思路： 用数组存储这些数，然后顺序查找查找，时间复杂度最高O(n2) ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 代码： 备注： 荧光 标注为考察知识点 下划线 标注为关键点 加粗体 标注为板块 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 分界线 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 标注为分界线 感兴趣的同志们，加入团队吧 还有团队分部 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 冷知识 如果你想要做出 加粗效果 那么： 如果你想要做出 倾斜效果 那么： 如果你想要做出 删除效果 那么： 如果你想要做出 下划线效果 那么： 如果你想要做出 荧光 效果，那么： 如果你想做出链接效果，那么： 如果你想做出 加粗大号效果 那么： 如果你想做出 居中效果居中效果 居中效果 那么： 如果你想做出 那么： 如果你想做出 下标效果 那么： 如果你想做出 上表效果 那么：

IAKIOIIAKIOIAKIOIIAKIOIIAKIOIIAKIOIIAKIOIIAKIOIIAKIOIIAKIOIIAKIOIIAKIOIIAKIOI，快%我！！！！！！我明天就去黑AC君当站长！！！

AKDAY8 搜索算法——深度优先搜索(DFS) > * 回溯 > * 剪枝 > * 连通性判断 排列组合 加法原理与乘法原理 加法原理：(0∼9+a∼z)(0\sim 9+a\sim z)(0∼9+a∼z)任选一个共有多少种可能性 10+26=36种 乘法原理： Anm=n∗(n−1)∗......∗(n−m+1)A^m_n=n*(n-1)*......*(n-m+1)Anm =n∗(n−1)∗......∗(n−m+1) ***=Anm÷AmmC^m_n=A^m_n\div A^m_mCnm =Anm ÷Amm “排列”例题 洛谷B3621B3621B3621——枚举元组 寻找题目链接 “组合”例题 洛谷B3623B3623B3623——枚举排列 寻找题目链接 综合例题 洛谷B3622B3622B3622——枚举子集 寻找题目链接 剪枝 剪枝条件 当题目上出现w[i]w[i]w[i]在范围内均匀随机生成 可运用剪枝的例题 洛谷B3624 猫粮规划 八皇后问题 题目描述 一个如下的 6×66 \times 66×6 的跳棋棋盘，有六个棋子被放置在棋盘上，使得每行、每列有且只有一个，每条对角线（包括两条主对角线的所有平行线）上至多有一个棋子。 上面的布局可以用序列 2 4 6 1 3 52\ 4\ 6\ 1\ 3\ 52 4 6 1 3 5 来描述，第 iii 个数字表示在第 iii 行的相应位置有一个棋子，如下： 行号 1 2 3 4 5 61\ 2\ 3\ 4\ 5\ 61 2 3 4 5 6 列号 2 4 6 1 3 52\ 4\ 6\ 1\ 3\ 52 4 6 1 3 5 这只是棋子放置的一个解。请编一个程序找出所有棋子放置的解。 并把它们以上面的序列方法输出，解按字典顺序排列。 请输出前 333 个解。最后一行是解的总个数。 输入格式 一行一个正整数 nnn，表示棋盘是 n×nn \times nn×n 大小的。 输出格式 前三行为前三个解，每个解的两个数字之间用一个空格隔开。第四行只有一个数字，表示解的总数。 样例 #1 样例输入 #1 样例输出 #1 提示 【数据范围】 对于 100%100\%100% 的数据，6≤n≤136 \le n \le 136≤n≤13。 题目翻译来自NOCOW。 USACO Training Section 1.5 ANSWERANSWERANSWER

RT 第0关： this is 链接 in luogu,the patse in this: 提示： 00110101 01110111 01100010 01110100 00111001 01111010 00110010 00110000 upd 2024/5/19 @钱某 成功猜出第0关答案 现公布第0关答案：https://www.luogu.com.cn/paste/5wbt9z20 请复制此链接到下一关。

ahduoebuidbuabbooaeebemoji

#include<bits/stdc++.h> using namespace std; int n,a[110]; int main(){ cin >> n; for(int i=1;i<=n;i++){ cin >> a[i]; } sort(a+1,a+n+1);sort//(a数组+a的第1项，a数组+a的上限n+1) for(int i=1;i<=n;i++){ cout<< a[i]<< " "; } return 0; }

我和“联合国”的小伙伴都在ACGO等你，快用这个专属链接加入我们吧！https://www.acgo.cn/application/1761564296288649216

已AC

a \Lleftarrow b