ACM第一阶段学习内容

一、知识目录

字符串处理 ................................................................. 3
1、KMP 算法 ............................................................ 3
2、扩展 KMP ............................................................ 6
3、Manacher 最长回文子串 ................................................ 7
4、AC 自动机 ........................................................... 8
5、后缀数组 ........................................................... 10
6、后缀自动机 ......................................................... 14
数学 ..................................................................... 15
1、素数 .............................................................. 15
2、素数筛选和合数分解 .................................................. 18
3、扩展欧几里得算法（求 ax+by=gcd 的解以及逆元素） ......................... 18
4、求逆元............................................................. 19
5、模线性方程组 ....................................................... 19
6、随机素数测试和大数分解(POJ 1811)..................................... 20
7、欧拉函数 ........................................................... 23
8、高斯消元（浮点数） .................................................. 24
9、FFT............................................................... 25
10、高斯消元法求方程组的解 .............................................. 28
11、 整数拆分 ......................................................... 33
12、求 A^B 的约数之和对 MOD 取模 ......................................... 35
13、莫比乌斯反演 ...................................................... 35
14、Baby-Step Giant-Step ............................................ 38
相关公式.............................................................. 38
数据结构.................................................................. 39
1、划分树............................................................. 39
2、RMQ............................................................... 41
3、树链剖分 ........................................................... 43
4、伸展树（splay tree） ............................................... 48
5、动态树............................................................. 53
6、主席树............................................................. 58
图论 ..................................................................... 68
1、最短路............................................................. 68
2、最小生成树 ......................................................... 72
3、次小生成树 ......................................................... 73
4、有向图的强连通分量 .................................................. 74
5、图的割点、桥和双连通分支的基本概念..................................... 77
6、割点与桥 ........................................................... 78
7、边双连通分支 ....................................................... 81
8、点双连通分支 ....................................................... 83
9、最小树形图 ......................................................... 86
10、二分图匹配 ........................................................ 88
11、生成树计数 ........................................................ 91
11、二分图多重匹配 ..................................................... 94
12、KM 算法（二分图最大权匹配）.......................................... 95
13、最大流............................................................ 96
14、最小费用最大流 ....................................................102
15、2-SAT...........................................................103
16、曼哈顿最小生成树 ..................................................107
17、一般图匹配带花树 ..................................................110
18、LCA.............................................................113
计算几何.................................................................119
1、基本函数 ..........................................................119
2、凸包 .............................................................123
3、平面最近点对（HDU 1007） ...........................................124
4、旋转卡壳 ..........................................................126 

5、半平面交 ..........................................................131 
6、三点求圆心坐标（三角形外心） .........................................135 
动态规划.................................................................136 
1、最长上升子序列 O(nlogn) ............................................136 
其他 ....................................................................136 
1、高精度............................................................136 
2、完全高精度 ........................................................138 
3、strtok 和 sscanf 结合输入 ..........................................143 
4、解决爆栈，手动加栈 .................................................143 
5、STL..............................................................144 
6、输入输出外挂 ......................................................145 
7、莫队算法 ..........................................................146

二、参考资料
Summer 2017 Code Training 1

模板：上海大学ACM模板-第3-24页

【字符串-参考资料】
1、 从头到尾彻底理解KMP
http://www.cnblogs.com/zhangtianq/p/5839909.html
2、最长回文子串
http://blog.csdn.net/kangroger/article/details/37742639
3、AC自动机最详细的讲解，让你一次学会AC自动机
http://blog.csdn.net/creatorx/article/details/71100840
4、后缀数组
http://www.cnblogs.com/shanchuan04/p/5324009.html
http://blog.csdn.net/fp_hzq/article/details/8990932
5、后缀自动机
https://www.zhihu.com/question/34039162

文件：2017CT1资料_SAM后缀自动机-陈立杰讲稿、2017CT1-柔性字符串匹配、2017CT1-algorithms on strings字符串算法大全。

【数学-参考资料】
1、素数有关算法
http://blog.csdn.net/snow_me/article/details/52588819
2、扩展欧几里德算法
http://blog.csdn.net/zhjchengfeng5/article/details/7786595
3、逆元
http://blog.csdn.net/acdreamers/article/details/8220787
4、Miller_rabin算法
http://blog.csdn.net/maxichu/article/details/45458569
5、欧拉函数
http://blog.csdn.net/sentimental_dog/article/details/52002608
6、模线性方程组
http://blog.csdn.net/qq_21120027/article/details/51340218

Summer 2017 Code Training 2

模板：上海大学ACM模板-第25-42页

【数学-参考资料（续）】
1、高斯消元法
http://blog.csdn.net/duanxian0621/article/details/7408887

2、FFT（快速傅氏变换）
http://www.gatevin.moe/acm/fft%E7%AE%97%E6%B3%95%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0/

3、莫比乌斯反演
http://blog.csdn.net/acdreamers/article/details/8542292

4、离散对数（Baby Step Giant Step）
http://blog.csdn.net/acdreamers/article/details/8579511

【数据结构-参考资料】
1、划分树
http://blog.csdn.net/shiqi_614/article/details/8041390

2、主席树
http://blog.csdn.net/sprintfwater/article/details/9162041

3、区间最值查询（RMQ）
http://blog.csdn.net/liang5630/article/details/7917702
http://blog.csdn.net/metalseed/article/details/7953260

Summer 2017 Code Training 3
模板：上海大学ACM模板-第43-74页

【数据结构-参考资料（续）】
1、树链剖分原理
http://blog.csdn.net/acdreamers/article/details/10591443

2、树状数组
http://blog.csdn.net/ljd4305/article/details/10101535

3、线段树
http://www.cnblogs.com/TenosDoIt/p/3453089.html

4、Splay Tree（伸展树）
http://blog.csdn.net/niuox/article/details/8018280

5、动态树
http://blog.csdn.net/d891320478/article/details/9181385

6、主席树
http://blog.csdn.net/sprintfwater/article/details/9162041

【图论-参考资料】
1、最短路：Dijkstra算法
http://www.cnblogs.com/skywang12345/p/3711512.html

2、最短路：Bellman-Ford算法
http://blog.csdn.net/niushuai666/article/details/6791765

3、最短路：SPFA算法
http://www.layz.net/LAOJ/suanfa/s9-4.html

4、最小生成树：Kruskal算法
http://blog.csdn.net/luomingjun12315/article/details/47700237

5、最小生成树：Prim算法
http://blog.csdn.net/yeruby/article/details/38615045

6、次小生成树
http://yzmduncan.iteye.com/blog/1018358

Summer 2017 Code Training 4
模板：上海大学ACM模板-第74-96页

【图论-参考资料（续）】
1、有向图的强连通分量：Tarjan算法
http://www.cnblogs.com/uncle-lu/p/5876729.html

2、有向图的强连通分量：Kosaraju算法
http://www.cnblogs.com/nullzx/p/6437926.html

3、最小树形图
http://www.cnblogs.com/Ash-ly/p/5536796.html

4、二分图
http://dsqiu.iteye.com/blog/1689505
http://www.renfei.org/blog/bipartite-matching.html

5、二分图最大匹配：匈牙利算法
http://blog.csdn.net/dark_scope/article/details/8880547
http://www.cnblogs.com/pony1993/archive/2012/07/25/2607738.html

6、二分图最大匹配：Hopcroft-Karp算法
http://blog.csdn.net/wall_f/article/details/8248373

7、生成树计数：Matrix-Tree定理
http://blog.csdn.net/longshuai0821/article/details/7764267

8、二分图多重匹配问题
http://blog.csdn.net/u014427196/article/details/48319639

9、二分图最大权匹配：Kuhn-Munkres算法
http://www.cnblogs.com/kuangbin/archive/2012/08/19/2646535.html

Summer 2017 Code Training 5
模板：上海大学ACM模板-第97-121页

【图论-参考资料（续）】
1、最大流问题
http://blog.csdn.net/yiqingnian28/article/details/23388633
http://www.cnblogs.com/kuangbin/archive/2011/07/26/2117636.html

2、最小费用最大流
http://blog.csdn.net/stillxjy/article/details/52047189

3、2-SAT
http://blog.csdn.net/jarjingx/article/details/8521690

4、曼哈顿距离最小生成树
http://blog.csdn.net/acm_cxlove/article/details/8890003

5、莫队算法
http://blog.csdn.net/hzj1054689699/article/details/51866615

6、一般图匹配问题：带花树
http://blog.csdn.net/u014261987/article/details/41350003
http://blog.csdn.net/jackyguo1992/article/details/11271497

7、LCA（最近公共祖先）
http://blog.csdn.net/liangzhaoyang1/article/details/52549822
http://www.cnblogs.com/wuminye/p/3527176.html
http://blog.csdn.net/Janis_z/article/details/52937631?locationNum=6&fps=1

【计算几何-参考资料】
8、计算几何
http://www.cnblogs.com/kuangbin/category/410309.html
文件：HIT-ACM计算几何模板

Summer 2017 Code Training 6
模板：上海大学ACM模板-第122-152页

【计算几何-参考资料】
1、计算几何
http://www.cnblogs.com/kuangbin/category/410309.html
HIT-ACM计算几何模板

【其他-参考资料】
2、动态规划
http://blog.csdn.net/baidu_28312631/article/details/47418773
http://blog.csdn.net/scythe666/article/details/50921628

3、莫队算法
http://blog.csdn.net/hnshhslsh/article/details/50582926

三、题解链接

Summer 2017 Code Training 1 

A - Cow Patterns
来源：POJ – 3167
知识点：扩展KMP等
http://www.cnblogs.com/zjh10/articles/2105716.html
http://blog.csdn.net/tmeteorj/article/details/8693366
http://www.cppblog.com/zxb/archive/2010/10/06/128782.aspx?opt=admin

B - Best Sequence
来源：POJ – 1699
知识点：扩展KMP+DFS等
http://blog.csdn.net/zzzz40/article/details/39186109

C – Palindrome
来源：POJ – 3974
知识点：Manacher算法等
http://blog.csdn.net/u010885899/article/details/45366633
http://blog.csdn.net/geniusluzh/article/details/8639759

D - Keywords Search
来源：HDU – 2222
知识点：AC自动机等
http://blog.csdn.net/hnust_xiehonghao/article/details/9130539

E - Longest Common Substring
来源：HDU – 1403
知识点：后缀数组DA算法（倍增算法）等
http://blog.csdn.net/xinag578/article/details/50164599

F - Power Strings
来源：POJ – 2406
知识点：后缀数组DC3算法等
http://blog.csdn.net/libin56842/article/details/46310425

G – String
来源：CodeForces - 123D
知识点：后缀自动机（SAM）等
http://blog.csdn.net/dyx404514/article/details/8713542
http://www.hankcs.com/program/algorithm/codeforces-123d-string.html

H - Prime Distance
来源：POJ – 2689
知识点：大区间素数筛选等
http://www.cnblogs.com/kuangbin/archive/2013/05/20/3089840.html

I - The Factor
来源：HDU – 5428
知识点：素数筛选合数分解等
http://www.bubuko.com/infodetail-1079772.html
http://www.cnblogs.com/Apro/p/4784808.html

J - A/B
来源：HDU - 1576
知识点：扩展欧几里得算法等
http://blog.csdn.net/ljd4305/article/details/26057385
http://blog.csdn.net/lyc1635566ty/article/details/50611246

K - X问题
来源：HDU - 1573
知识点：解一元线性同余方程组、中国剩余定理等
http://www.cnblogs.com/zhangmingcheng/p/4238407.html
http://blog.csdn.net/a601025382s/article/details/10296577

L - Prime Test
来源：POJ – 1811
知识点：大素数判断和素因子分解等
http://www.cnblogs.com/kuangbin/archive/2012/08/19/2646404.html

M - Farey Sequence
来源：POJ – 2478
知识点：欧拉函数等
http://blog.csdn.net/aaaaacmer/article/details/47272037

Summer 2017 Code Training 2 

A - Kind of a Blur
来源：HDU - 3359
知识点：高斯消元法等
http://blog.csdn.net/qwb492859377/article/details/47013321

B - A * B Problem Plus
来源：HDU – 1402
知识点：FFT、大整数乘法等
http://blog.csdn.net/sdj222555/article/details/9786527

C - 3-idiots
来源：HDU – 4609
知识点：FFT计数等
http://blog.csdn.net/qq_33184171/article/details/54427994

D - Painter's Problem
来源：POJ – 1681
知识点：高斯消元法（一类开关问题，对2取模的01方程组）等
http://www.cnblogs.com/kuangbin/archive/2012/08/31/2665913.html

E - Widget Factory
来源：POJ – 2947
知识点：高斯消元法（解同余方程组）等
http://www.cnblogs.com/gj-Acit/p/3903085.html

F - Partition
来源：HDU – 4651
知识点：整数拆分等
http://www.cnblogs.com/zhsl/archive/2013/08/07/3242268.html

G - Integer Partition
来源：HDU – 4658
知识点：整数划分、生成函数等
http://blog.csdn.net/a601025382s/article/details/10299367

H - Sumdiv
来源：POJ – 1845
知识点：求A^B的约数之和对MOD取模等
http://www.cnblogs.com/kuangbin/archive/2012/08/10/2631225.html

I - GCD
来源：HDU – 1695
知识点：莫比乌斯反演等
http://blog.csdn.net/lixuepeng_001/article/details/50577932

J - Discrete Logging
来源：POJ – 2417
知识点：离散对数（Baby Step Giant Step）等
http://www.cnblogs.com/kuangbin/archive/2013/08/24/3278852.html

K - K-th Number
来源：POJ – 2104
知识点：经典划分树、主席树等
http://blog.csdn.net/pure_lady/article/details/46806833
http://www.cnblogs.com/oyking/p/3230296.html

L - Sliding Window
来源：POJ – 2823
知识点：单调队列、线段树、一维RMQ等
http://blog.csdn.net/u013351484/article/details/45112271

M – Cornfields
来源：POJ – 2019
知识点：二维RMQ等
http://www.cnblogs.com/kuangbin/p/3227420.html

Summer 2017 Code Training 3

A - Aragorn's Story
来源： HDU – 3966
知识点：树链剖分+树状数组等
http://www.cnblogs.com/kuangbin/archive/2013/08/14/3258736.html

B - Query on a tree
来源： SPOJ – QTREE
知识点：树链剖分+线段树等
http://blog.csdn.net/niuox/article/details/8145842

C - SuperMemo
来源：POJ – 3580
知识点：Splay Tree（伸展树）等
http://blog.csdn.net/jasonzhu8/article/details/5747811

D - Query on The Trees
来源：HDU – 4010
知识点：动态树等
http://www.cnblogs.com/kuangbin/archive/2013/09/04/3300251.html

E - D-query
来源：SPOJ - DQUERY
知识点：主席树-区间不同数的个数 等
http://blog.csdn.net/aozil_yang/article/details/65448883

F - K-th Number
来源：POJ – 2104
知识点：主席树-静态区间第k大 等
http://www.cnblogs.com/kuangbin/archive/2013/09/05/3302731.html

G - Count on a tree
来源：SPOJ – COT
知识点：LCA+主席树等
http://blog.csdn.net/acm_cxlove/article/details/8564167
http://www.cnblogs.com/arbitrary/archive/2013/10/09/3360104.html

H - Dynamic Rankings
来源： ZOJ - 2112
知识点：树状数组+主席树-动态第k大等
http://www.cnblogs.com/kuangbin/p/3308118.html

I - MPI Maelstrom
来源：POJ – 1502
知识点：Dijkstra算法等
http://blog.csdn.net/u013446688/article/details/42708487

J - Invitation Cards
来源：POJ – 1511
知识点：优先队列优化的Dijkstra算法等
http://www.cnblogs.com/kuangbin/p/3140958.html

K - Currency Exchange
来源：POJ – 1860
知识点：Bellman-Ford算法等
http://www.cnblogs.com/kuangbin/archive/2012/08/17/2644807.html

L - Wormholes
来源：POJ - 3259
知识点：SPFA等
http://blog.csdn.net/murmured/article/details/18669909

M - Highways
来源：POJ – 2485
知识点：最小生成树等
http://blog.csdn.net/mikasa3/article/details/51559191
http://blog.csdn.net/fanesemyk/article/details/51137466?locationNum=1&fps=1

N - Design Tutorial: Inverse the Problem
来源：CodeForces - 472D
知识点：最小生成树等
http://blog.csdn.net/u010660276/article/details/39901287

O - Qin Shi Huang's National Road System
来源：HDU - 4081
知识点：次小生成树等
http://blog.csdn.net/shuangde800/article/details/7982106

Summer 2017 Code Training 4

A - Popular Cows
来源：POJ – 2186
知识点：Tarjan算法等
http://www.dontcry-tat.com/2017/04/26/poj-2186-popular-cows/

B - 迷宫城堡
来源：HDU – 1269
知识点：Kosaraju算法等
http://blog.csdn.net/qq7366020/article/details/12943345

C - Critical Links
来源：UVA – 796
知识点：无向图求桥等
http://www.cnblogs.com/chenchengxun/p/4718717.html

D - Electricity
来源：POJ – 2117
知识点：无向图求割点
http://blog.csdn.net/liwen_7/article/details/7919220

E - Redundant Paths
来源：POJ – 3177
知识点：无向图的双连通问题等
http://mojijs.com/2014/11/165169/index.html

F - Knights of the Round Table
来源：POJ – 2942
知识点：点的双连通分量等
http://www.cnblogs.com/wangfang20/p/3201502.html

G - Command Network
来源：POJ – 3164
知识点：最小树形图等
http://blog.csdn.net/shuangde800/article/details/8039359

H - The Perfect Stall
来源：POJ – 1274
知识点：二分图最大匹配：匈牙利算法
http://blog.csdn.net/u013487051/article/details/37656979

I - Asteroids
来源：POJ – 3041
知识点：二分图最大匹配：匈牙利算法
http://blog.csdn.net/yeruby/article/details/39315713

J - COURSES
来源：POJ – 1469
知识点：二分图最大匹配：Hopcroft-Karp算法
http://blog.csdn.net/u011466175/article/details/23709885

K - Lightning
来源：HDU – 4305
知识点：生成树计数：Matrix-Tree定理
http://blog.csdn.net/julyana_lin/article/details/8067024

L - Highways
来源：SPOJ – HIGH
知识点：生成树计数
http://blog.csdn.net/gatevin/article/details/48051879

M - Alice's Chance
来源：POJ – 1698
知识点：二分图多重匹配
http://blog.csdn.net/l123012013048/article/details/47295503

N - 奔小康赚大钱
来源：HDU – 2255
知识点：二分图最大权匹配、KM算法等
http://blog.csdn.net/sr_19930829/article/details/40650359

Summer 2017 Code Training 6

A - Card
来源：HDU - 4350
知识点：模拟等
http://blog.csdn.net/wconvey/article/details/7848235

B - A Round Peg in a Ground Hole
来源：POJ - 1584
知识点：判断凸多边形、判断点在多边形内、判断圆在多边形内等
http://www.cnblogs.com/liuxin13/p/4799667.html

C - Cupid's Arrow
来源：HDU - 1756
知识点：判断点在多边形内外等
http://blog.csdn.net/lttree/article/details/24301607

D - Shape of HDU
来源：HDU - 2108
知识点：判断凸多边形等
http://blog.csdn.net/lttree/article/details/24241987

E - Wall
来源：HDU - 1348
知识点：求凸包周长等
http://blog.csdn.net/W1413882708/article/details/52191385

F - Quoit Design
来源：HDU - 1007
知识点：查找平面最近点对等
http://blog.csdn.net/sun1956/article/details/8294048

G - Beauty Contest
来源：POJ - 2187
知识点：求解平面最远点对等
http://blog.csdn.net/crazy_ac/article/details/10082403

H - Triangle
来源：ZOJ - 2419
知识点：求解平面点集最大三角形等
http://blog.csdn.net/zxy_snow/article/details/6595123

I - The widest road
来源：HDU - 2823
知识点：求解两凸包最小距离等
http://blog.csdn.net/clover_hxy/article/details/54022026

J - Art Gallery
来源：ZOJ- 1369
知识点：半平面交等
http://blog.csdn.net/l04205613/article/details/6626844

K - Kindergarten Electiond
来源：ZOJ-3715
知识点：枚举、贪心等
http://blog.csdn.net/zy691357966/article/details/44853449

L - Attack on Titans
来源：ZOJ-3747
知识点：递推等
http://blog.csdn.net/summer__show_/article/details/70243332

M - Alignment
来源：HDU - 1950
知识点：最长上升子序列等
http://www.cnblogs.com/blueprintf/p/5773393.html
http://blog.csdn.net/wall_f/article/details/8295812

N - Game of Connections
来源：HDU - 1134
知识点：卡特兰数等
http://blog.csdn.net/u013509299/article/details/19758565

O - Group
来源：HDU 4638
知识点：莫队算法、离线线段树等
http://blog.csdn.net/xlzhang223/article/details/51439180

P - Count on a tree II
来源：SPOJ - COT2
知识点：树上的莫队算法、树上区间查询等
http://blog.csdn.net/htt_h/article/details/47729479