学习笔记
根据NOI不知道第几年的大纲开的目录，学（复习）到哪写到哪，颜色代表知识点难度（与Luogu意义相同）
点击Link即可传送，文章在Luogu与博客园同步更新喵~
图论
最短路
| \(\textcolor{#52C41A}{SPFA}\) |
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\(\textcolor{#52C41A}{dijkstra}\) |
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\(\textcolor{#3498DB}{Floyd}\) |
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| \(\textcolor{#9D3DCF}{K短路}\) |
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\(\textcolor{#52C41A}{最长路}\) |
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\(\textcolor{#3498DB}{差分约束}\) |
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Tarjan
| \(\textcolor{#3498DB}{强联通分量、缩点}\) |
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\(\textcolor{#3498DB}{双联通分量（点、边）}\) |
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\(\textcolor{#3498DB}{割边、割点、桥}\) |
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| \(\textcolor{#3498DB}{2-SAT}\) |
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拓扑排序
| \(\textcolor{#52C41A}{拓扑排序}\) |
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二分图
| \(\textcolor{#3498DB}{二分图最大匹配（匈牙利）}\) |
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\(\textcolor{#3498DB}{二分图最大权匹配（KM）}\) |
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网络流
| \(\textcolor{#9D3DCF}{最大流、最小割}\) |
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\(\textcolor{#9D3DCF}{最小费用最大流}\) |
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\(\textcolor{#9D3DCF}{有上下界的网络流}\) |
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| \(\textcolor{#9D3DCF}{数据结构优化网络流}\) |
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\(\textcolor{#3498DB}{分数规划}\) |
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欧拉图
| \(\textcolor{#3498DB}{欧拉图}\) |
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树论（大哥）
| \(\textcolor{#3498DB}{生成树}\) |
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\(\textcolor{#3498DB}{LCA}\) |
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\(\textcolor{9D3DCF}{虚树}\) |
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| \(\textcolor{#3498DB}{基环树}\) |
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\(\textcolor{#3498DB}{树链剖分}\) |
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\(\textcolor{#9D3DCF}{Prufer序列}\) |
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| \(\textcolor{#3498DB}{括号序列}\) |
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\(\textcolor{#3498DB}{dfs序}\) |
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\(\textcolor{52C41A}{树的遍历}\) |
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| \(\textcolor{#3498DB}{树上倍增}\) |
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\(\textcolor{#52C41A}{树的直径}\) |
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\(\textcolor{#52C41A}{树的重心}\) |
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| \(\textcolor{#9D3DCF}{树分治}\) |
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\(\textcolor{#9D3DCF}{Link-Cut-Tree}\) |
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\(\textcolor{#9D3DCF}{树分块}\) |
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区间图与弦图
| \(\textcolor{#9D3DCF}{区间图与弦图}\) |
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平面图与对偶图
| \(\textcolor{#9D3DCF}{平面图与对偶图}\) |
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最小树形图（朱刘算法）
| \(\textcolor{#9D3DCF}{最小树形图（朱刘算法）}\) |
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仙人掌
| \(\textcolor{#9D3DCF}{仙人掌}\) |
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数据结构
队列
| \(\textcolor{#52C41A}{队列}\) |
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栈
| \(\textcolor{#52C41A}{栈}\) |
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堆
| \(\textcolor{#52C41A}{堆}\) |
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\(\textcolor{#9D3DCF}{可并堆}\) |
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并查集
| \(\textcolor{#52C41A}{并查集}\) |
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\(\textcolor{#3498DB}{带权并查集}\) |
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\(\textcolor{#9D3DCF}{可持久化并查集}\) |
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hash表
| \(\textcolor{#52C41A}{hash表}\) |
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链表
| \(\textcolor{#52C41A}{链表}\) |
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\(\textcolor{#9D3DCF}{块状链表}\) |
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\(\textcolor{#9D3DCF}{十字链表}\) |
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| \(\textcolor{#52C41A}{双向链表}\) |
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st表
| \(\textcolor{#3498DB}{st表}\) |
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块状树
| \(\textcolor{#9D3DCF}{块状树}\) |
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树状数组
| \(\textcolor{#3498DB}{树状数组}\) |
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\(\textcolor{#3498DB}{多维树状数组}\) |
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\(\textcolor{#3498DB}{树状数组求逆序对}\) |
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线段树（男一号）
| \(\textcolor{#3498DB}{普通线段树}\) |
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\(\textcolor{#3498DB}{线段树合并}\) |
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\(\textcolor{#3498DB}{权值线段树}\) |
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| \(\textcolor{#3498DB}{zkw线段树}\) |
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\(\textcolor{#3498DB}{二维线段树（线段树套线段树）}\) |
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\(\textcolor{#3498DB}{可持久化线段树（主席树）}\) |
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| \(\textcolor{#3498DB}{扫描线}\) |
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平衡树（女一号）
| \(\textcolor{#3498DB}{Treap}\) |
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\(\textcolor{#3498DB}{Splay}\) |
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\(\textcolor{#9D3DCF}{fhq-treap（无旋treap）}\) |
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| \(\textcolor{#9D3DCF}{替罪羊树}\) |
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\(\textcolor{#9D3DCF}{红黑树}\) |
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\(\textcolor{#9D3DCF}{AVL树}\) |
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| \(\textcolor{#9D3DCF}{SBT}\) |
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\(\textcolor{#9D3DCF}{朝鲜树}\) |
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KDtree
| \(\textcolor{#9D3DCF}{KDtree}\) |
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划分数
| \(\textcolor{#9D3DCF}{划分数}\) |
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四分树
| \(\textcolor{#9D3DCF}{四分树}\) |
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笛卡尔树
| \(\textcolor{#9D3DCF}{笛卡尔树}\) |
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树套树（男一和女一的孩子）
| \(\textcolor{#9D3DCF}{线段树套平衡树}\) |
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\(\textcolor{#9D3DCF}{平衡树套线段树}\) |
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\(\textcolor{#9D3DCF}{其他平衡树}\) |
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STL（真正的主角）
| \(\textcolor{#52C41A}{map}\) |
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\(\textcolor{#52C41A}{set}\) |
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\(\textcolor{#52C41A}{stack}\) |
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| \(\textcolor{#52C41A}{queue}\) |
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\(\textcolor{#52C41A}{pritority} \textcolor{#52C41A}{\_} \textcolor{#52C41A}{queue}\) |
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\(\textcolor{#52C41A}{vector}\) |
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| \(\textcolor{#9D3DCF}{bitset}\) |
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搜索
常见搜索
| \(\textcolor{#3498DB}{bfs}\) |
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\(\textcolor{#3498DB}{dfs}\) |
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\(\textcolor{#3498DB}{A^*}\) |
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| \(\textcolor{#3498DB}{IDA^*}\) |
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\(\textcolor{#3498DB}{DLX}\) |
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\(\textcolor{#3498DB}{记忆化搜索}\) |
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| \(\textcolor{#3498DB}{剪枝}\) |
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\(\textcolor{#3498DB}{随机化搜索}\) |
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特殊搜索
| \(\textcolor{#3498DB}{模拟退火}\) |
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\(\textcolor{#3498DB}{遗传算法}\) |
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\(\textcolor{#3498DB}{爬山算法}\) |
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字符串
KMP
| \(\textcolor{#3498DB}{KMP}\) |
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\(\textcolor{#3498DB}{exKMP}\) |
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AC自动机
| \(\textcolor{#3498DB}{AC自动机}\) |
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\(\textcolor{#3498DB}{Fail树}\) |
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后缀系列
| \(\textcolor{#9D3DCF}{后缀数组（倍增）}\) |
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\(\textcolor{#9D3DCF}{后缀数组（DC3）}\) |
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\(\textcolor{#9D3DCF}{后缀自动机}\) |
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| \(\textcolor{#9D3DCF}{后缀树}\) |
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\(\textcolor{#9D3DCF}{后缀平衡树}\) |
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\(\textcolor{#9D3DCF}{后缀仙人掌}\) |
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字符串Hash
| \(\textcolor{#52C41A}{字符串Hash}\) |
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Trie树
| \(\textcolor{#3498DB}{Trie树}\) |
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\(\textcolor{#9D3DCF}{可持久化Trie树}\) |
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manacher
| \(\textcolor{#3498DB}{manacher}\) |
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回文自动机
| \(\textcolor{#9D3DCF}{回文自动机}\) |
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最小表示法
| \(\textcolor{#3498DB}{最小表示法}\) |
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几何（大题）
| \(\textcolor{#9D3DCF}{基础知识（喵）}\) |
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\(\textcolor{#9D3DCF}{向量}\) |
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\(\textcolor{#9D3DCF}{凸包}\) |
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| \(\textcolor{#9D3DCF}{旋转卡壳}\) |
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\(\textcolor{#9D3DCF}{半平面交}\) |
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\(\textcolor{#9D3DCF}{随机增量}\) |
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| \(\textcolor{#9D3DCF}{Pick定理}\) |
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\(\textcolor{#9D3DCF}{梯形划分\&三角形划分}\) |
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\(\textcolor{#9D3DCF}{扫描线}\) |
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数论（大爹）
基础知识
| \(\textcolor{#FFC116}{\%理论}\) |
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\(\textcolor{#FFC116}{积性函数}\) |
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\(\textcolor{#FFC116}{高中数学知识}\) |
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素数
| \(\textcolor{#52C41A}{暴力判素数}\) |
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\(\textcolor{#9D3DCF}{Miller-Rabbin素数检测}\) |
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\(\textcolor{#52C41A}{埃拉托色尼筛}\) |
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| \(\textcolor{#52C41A}{欧拉筛（线性筛）}\) |
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\(\textcolor{#52C41A}{分解质因数}\) |
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欧拉函数
| \(\textcolor{#3498DB}{sqrt(n)求单个值的欧拉函数}\) |
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\(\textcolor{#3498DB}{线性筛欧拉函数}\) |
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\(\textcolor{#3498DB}{欧拉定理}\) |
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幂
| \(\textcolor{#52C41A}{快速幂}\) |
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\(\textcolor{#52C41A}{慢速幂}\) |
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gcd
| \(\textcolor{#52C41A}{辗转相除法}\) |
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\(\textcolor{#3498DB}{扩展欧几里得（exgcd）}\) |
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中国剩余定理（CRT）
| \(\textcolor{#3498DB}{互质版}\) |
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\(\textcolor{#9D3DCF}{不互质版}\) |
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矩阵
| \(\textcolor{#3498DB}{矩阵快速幂}\) |
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\(\textcolor{#9D3DCF}{矩阵求逆}\) |
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行列式
| \(\textcolor{#9D3DCF}{行列式}\) |
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莫比乌斯反演
| \(\textcolor{#9D3DCF}{莫比乌斯反演}\) |
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\(\textcolor{#9D3DCF}{莫比乌斯函数}\) |
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狄利克雷卷积
| \(\textcolor{#9D3DCF}{狄利克雷卷积}\) |
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容斥原理
| \(\textcolor{#52C41A}{抽屉原理（鸽巢原理）}\) |
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\(\textcolor{#3498DB}{Ramsey原理}\) |
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费马小定理
| \(\textcolor{#3498DB}{费马小定理}\) |
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逆元
| \(\textcolor{#3498DB}{线性求逆元}\) |
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\(\textcolor{#3498DB}{exgcd求逆元}\) |
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\(\textcolor{#3498DB}{费马小定理求逆元}\) |
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高斯消元
| \(\textcolor{#3498DB}{高斯消元}\) |
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线性基
| \(\textcolor{#3498DB}{线性基}\) |
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排列组合
| \(\textcolor{#52C41A}{杨辉三角}\) |
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\(\textcolor{#9D3DCF}{Lucas定理}\) |
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\(\textcolor{#9D3DCF}{exLucas定理}\) |
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BSGS
| \(\textcolor{#9D3DCF}{BSGS}\) |
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\(\textcolor{#9D3DCF}{exBSGS}\) |
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数列
| \(\textcolor{#52C41A}{斐波那契数列}\) |
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\(\textcolor{#52C41A}{卡特兰数}\) |
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\(\textcolor{#3498DB}{斯特林数}\) |
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| \(\textcolor{#3498DB}{贝尔数}\) |
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\(\textcolor{#52C41A}{等差、等比数列}\) |
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Pólya定理
| \(\textcolor{#9D3DCF}{Pólya定理}\) |
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置换群
| \(\textcolor{#9D3DCF}{置换群}\) |
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原根
| \(\textcolor{#9D3DCF}{原根}\) |
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快速傅里叶变换（FFT）
| \(\textcolor{#9D3DCF}{快速傅里叶变换（FFT）}\) |
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\(\textcolor{#9D3DCF}{快速数论变换（NTT）}\) |
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\(\textcolor{#9D3DCF}{快速沃尔什变换（FWT）}\) |
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拉格朗日
| \(\textcolor{#9D3DCF}{拉格朗日乘子法}\) |
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\(\textcolor{#9D3DCF}{拉格朗日插值}\) |
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\(\textcolor{#9D3DCF}{拉格朗日四平方和定理}\) |
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线性规划
| \(\textcolor{#9D3DCF}{线性规划}\) |
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单纯性
| \(\textcolor{#9D3DCF}{单纯性}\) |
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辛普森积分
| \(\textcolor{#9D3DCF}{辛普森积分}\) |
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概率和期望
| \(\textcolor{#3498DB}{概率和期望}\) |
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动态规划（DP）
经典dp
| \(\textcolor{#52C41A}{简单dp}\) |
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\(\textcolor{#52C41A}{背包dp}\) |
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\(\textcolor{#52C41A}{区间dp}\) |
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特殊dp
| \(\textcolor{#52C41A}{普通状压}\) |
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\(\textcolor{#9D3DCF}{斯坦纳树}\) |
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\(\textcolor{#9D3DCF}{插头dp}\) |
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| \(\textcolor{#3498DB}{数位dp}\) |
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\(\textcolor{#3498DB}{树形dp}\) |
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\(\textcolor{#3498DB}{环形dp}\) |
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| \(\textcolor{#3498DB}{环+外向树上的dp}\) |
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\(\textcolor{#3498DB}{期望dp}\) |
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\(\textcolor{#3498DB}{记忆化dp}\) |
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| \(\textcolor{#3498DB}{DAG上的dp}\) |
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\(\textcolor{#3498DB}{多维dp}\) |
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\(\textcolor{#3498DB}{dp套dp}\) |
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dp优化
| \(\textcolor{#9D3DCF}{斜率优化}\) |
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\(\textcolor{#3498DB}{四边形不等式优化}\) |
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\(\textcolor{#3498DB}{数据结构优化dp}\) |
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| \(\textcolor{#3498DB}{改变状态优化dp}\) |
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\(\textcolor{#3498DB}{寻址dp}\) |
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其他算法及思想
思想
| \(\textcolor{#52C41A}{二分}\) |
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\(\textcolor{#52C41A}{三分}\) |
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\(\textcolor{#9D3DCF}{整体二分}\) |
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| \(\textcolor{#3498DB}{倍增}\) |
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\(\textcolor{#52C41A}{贪心}\) |
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\(\textcolor{#52C41A}{枚举}\) |
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| \(\textcolor{#52C41A}{分治}\) |
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\(\textcolor{#52C41A}{离散化}\) |
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\(\textcolor{#52C41A}{分块}\) |
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排序
| \(\textcolor{#52C41A}{快排}\) |
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\(\textcolor{#52C41A}{归并排序}\) |
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\(\textcolor{#52C41A}{桶排}\) |
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| \(\textcolor{#52C41A}{基数排序}\) |
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\(\textcolor{#52C41A}{计数排序}\) |
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\(\textcolor{#52C41A}{插入排序}\) |
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| \(\textcolor{#52C41A}{选择排序}\) |
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\(\textcolor{#52C41A}{冒泡排序}\) |
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前缀和
| \(\textcolor{#52C41A}{前缀和}\) |
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高精度
| \(\textcolor{#52C41A}{高精度}\) |
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递推、递归
| \(\textcolor{#52C41A}{递推、递归}\) |
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\(\textcolor{#3498DB}{矩阵加速递推}\) |
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位运算
| \(\textcolor{#52C41A}{位运算}\) |
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莫队
| \(\textcolor{#9D3DCF}{莫队及进阶莫队}\) |
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\(\textcolor{#9D3DCF}{树上莫队}\) |
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卡常
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