题录

OJ上的一些水题(可用来练手和增加自信)
(poj3299,poj2159,poj2739,poj1083,poj2262,poj1503,poj3006,poj2255,poj3094)
初期:

一.基本算法:
(1)枚举. (poj1753,poj2965)
(2)贪心(poj1328,poj2109,poj2586)
(3)递归和分治法.
(4)递推.
(5)构造法.(poj3295)
(6)模拟法.(poj1068,poj2632,poj1573,poj2993,poj2996)
二.图算法:
(1)图的深度优先遍历和广度优先遍历.
(2)最短路径算法(dijkstra,bellman-ford,floyd,heap+dijkstra)
(poj1860,poj3259,poj1062,poj2253,poj1125,poj2240)
(3)最小生成树算法(prim,kruskal)
(poj1789,poj2485,poj1258,poj3026)
(4)拓扑排序 (poj1094)
(5)二分图的最大匹配 (匈牙利算法) (poj3041,poj3020)
(6)最大流的增广路算法(KM算法). (poj1459,poj3436)
三.数据结构.
(1)串 (poj1035,poj3080,poj1936)
(2)排序(快排、归并排(与逆序数有关)、堆排) (poj2388,poj2299)
(3)简单并查集的应用.
(4)哈希表和二分查找等高效查找法(数的Hash,串的Hash)
(poj3349,poj3274,POJ2151,poj1840,poj2002,poj2503)
(5)哈夫曼树(poj3253)
(6)堆
(7)trie树(静态建树、动态建树) (poj2513)
四.简单搜索
(1)深度优先搜索 (poj2488,poj3083,poj3009,poj1321,poj2251)
(2)广度优先搜索(poj3278,poj1426,poj3126,poj3087.poj3414)
(3)简单搜索技巧和剪枝(poj2531,poj1416,poj2676,1129)
五.动态规划
(1)背包问题. (poj1837,poj1276)
(2)型如下表的简单DP(可参考lrj的书 page149):
1.E[j]=opt{D+w(i,j)} (poj3267,poj1836,poj1260,poj2533)
2.E[i,j]=opt{D[i-1,j]+xi,D[i,j-1]+yj,D[i-1][j-1]+zij} (最长公共子序列)

     (poj3176,poj1080,poj1159) 
   3.C[i,j]=w[i,j]+opt{C[i,k-1]+C[k,j]}.(最优二分检索树问题) 

六.数学
(1)组合数学:
1.加法原理和乘法原理.
2.排列组合.
3.递推关系.
(POJ3252,poj1850,poj1019,poj1942)
(2)数论.
1.素数与整除问题
2.进制位.
3.同余模运算.
(poj2635, poj3292,poj1845,poj2115)
(3)计算方法.
1.二分法求解单调函数相关知识.(poj3273,poj3258,poj1905,poj3122)
七.计算几何学.
(1)几何公式.
(2)叉积和点积的运用(如线段相交的判定,点到线段的距离等). (poj2031,poj1039)

 (3)多边型的简单算法(求面积)和相关判定(点在多边型内,多边型是否相交) 
     (poj1408,poj1584) 
 (4)凸包. (poj2187,poj1113)

中级:

一.基本算法:
(1)C++的标准模版库的应用. (poj3096,poj3007)
(2)较为复杂的模拟题的训练(poj3393,poj1472,poj3371,poj1027,poj2706)
二.图算法:
(1)差分约束系统的建立和求解. (poj1201,poj2983)
(2)最小费用最大流(poj2516,poj2195)
(3)双连通分量(poj2942)
(4)强连通分支及其缩点.(poj2186)
(5)图的割边和割点(poj3352)
(6)最小割模型、网络流规约(poj3308, )
三.数据结构.
(1)线段树. (poj2528,poj2828,poj2777,poj2886,poj2750)
(2)静态二叉检索树. (poj2482,poj2352)
(3)树状树组(poj1195,poj3321)
(4)RMQ. (poj3264,poj3368)
(5)并查集的高级应用. (poj1703,2492)
(6)KMP算法. (poj1961,poj2406)
四.搜索
(1)最优化剪枝和可行性剪枝
(2)搜索的技巧和优化 (poj3411,poj1724)
(3)记忆化搜索(poj3373,poj1691)
五.动态规划
(1)较为复杂的动态规划(如动态规划解特别的施行商问题等)
(poj1191,poj1054,poj3280,poj2029,poj2948,poj1925,poj3034)
(2)记录状态的动态规划. (POJ3254,poj2411,poj1185)
(3)树型动态规划(poj2057,poj1947,poj2486,poj3140)
六.数学
(1)组合数学:
1.容斥原理.
2.抽屉原理.
3.置换群与Polya定理(poj1286,poj2409,poj3270,poj1026).
4.递推关系和母函数.
(2)数学.
1.高斯消元法(poj2947,poj1487, poj2065,poj1166,poj1222)
2.概率问题. (poj3071,poj3440)
3.GCD、扩展的欧几里德(中国剩余定理) (poj3101)
(3)计算方法.
1.0/1分数规划. (poj2976)
2.三分法求解单峰(单谷)的极值.
3.矩阵法(poj3150,poj3422,poj3070)
4.迭代逼近(poj3301)
(4)随机化算法(poj3318,poj2454)
(5)杂题.
(poj1870,poj3296,poj3286,poj1095)
七.计算几何学.
(1)坐标离散化.
(2)扫描线算法(例如求矩形的面积和周长并,常和线段树或堆一起使用).
(poj1765,poj1177,poj1151,poj3277,poj2280,poj3004)
(3)多边形的内核(半平面交)(poj3130,poj3335)
(4)几何工具的综合应用.(poj1819,poj1066,poj2043,poj3227,poj2165,poj3429
)

高级:
一.基本算法要求:
(1)代码快速写成,精简但不失风格
(poj2525,poj1684,poj1421,poj1048,poj2050,poj3306)
(2)保证正确性和高效性. poj3434
二.图算法:
(1)度限制最小生成树和第K最短路. (poj1639)
(2)最短路,最小生成树,二分图,最大流问题的相关理论(主要是模型建立和求解)

     (poj3155, poj2112,poj1966,poj3281,poj1087,poj2289,poj3216,poj2446 
  (3)最优比率生成树. (poj2728) 
  (4)最小树形图(poj3164) 
  (5)次小生成树. 
  (6)无向图、有向图的最小环    

三.数据结构.
(1)trie图的建立和应用. (poj2778)
(2)LCA和RMQ问题(LCA(最近公共祖先问题) 有离线算法(并查集+dfs) 和 在线算法
(RMQ+dfs)).(poj1330)
(3)双端队列和它的应用(维护一个单调的队列,常常在动态规划中起到优化状态转移
的
目的). (poj2823)
(4)左偏树(可合并堆).
(5)后缀树(非常有用的数据结构,也是赛区考题的热点).
(poj3415,poj3294)
四.搜索
(1)较麻烦的搜索题目训练(poj1069,poj3322,poj1475,poj1924,poj2049,poj3426)

  (2)广搜的状态优化:利用M进制数存储状态、转化为串用hash表判重、按位压缩存储

状态、双向广搜、A算法. (poj1768,poj1184,poj1872,poj1324,poj2046,poj1482)
(3)深搜的优化:尽量用位运算、一定要加剪枝、函数参数尽可能少、层数不易过大
、可以考虑双向搜索或者是轮换搜索、IDA算法. (poj3131,poj2870,poj2286)
五.动态规划
(1)需要用数据结构优化的动态规划.
(poj2754,poj3378,poj3017)
(2)四边形不等式理论.
(3)较难的状态DP(poj3133)
六.数学
(1)组合数学.
1.MoBius反演(poj2888,poj2154)
2.偏序关系理论.
(2)博奕论.
1.极大极小过程(poj3317,poj1085)
2.Nim问题.
七.计算几何学.
(1)半平面求交(poj3384,poj2540)
(2)可视图的建立(poj2966)
(3)点集最小圆覆盖.
(4)对踵点(poj2079)
八.综合题.
(poj3109,poj1478,poj1462,poj2729,poj2048,poj3336,poj3315,poj2148,poj1263
)

POJ DP 练习：
列表一：经典题目题号：
容易：
1018, 1050, 1088, 1125, 1143, 1157, 1163, 1178, 1179, 1189, 1191,1208, 1276, 1322, 1414, 1456, 1458,
1609, 1644, 1664, 1690, 1699, 1740, 1742, 1887, 1926, 1936, 1952, 1953, 1958, 1959, 1962, 1975, 1989, 2018,
2029, 2039, 2063, 2081, 2082, 2181, 2184, 2192, 2231, 2279, 2329, 2336, 2346, 2353, 2355, 2356, 2385, 2392, 2424,
不易：
1019, 1037, 1080, 1112, 1141, 1170, 1192, 1239, 1655, 1695, 1707, 1733(区间减法加并查集),
1737, 1837, 1850, 1920(加强版汉罗塔), 1934(全部最长公共子序列), 1964(最大矩形面积，O(n*m)算法), 2138, 2151, 2161, 2178,
推荐：
1015, 1635, 1636(挺好的), 1671, 1682, 1692(优化), 1704, 1717, 1722, 1726, 1732, 1770,
1821, 1853, 1949, 2019, 2127, 2176, 2228, 2287, 2342, 2374, 2378, 2384, 2411

列表二：完整DP题目列表
1015 Jury Compromise
1029 False coin
1036 Gangsters
1037 A decorative fence
1038 Bugs Integrated, Inc.
1042 Gone Fishing
1050 To the Max
1062 昂贵的聘礼
1074 Parallel Expectations
1080 Human Gene Functions
1088 滑雪
1093 Formatting Text
1112 Team Them Up!
1141 Brackets Sequence
1143 Number Game
1157 LITTLE SHOP OF FLOWERS
1159 Palindrome
1160 Post Office
1163 The Triangle
1170 Shopping Offers
1178 Camelot
1179 Polygon
1180 Batch Scheduling
1185 炮兵阵地
1187 陨石的秘密
1189 钉子和小球
1191 棋盘分割
1192 最优连通子集
1208 The Blocks Problem
1239 Increasing Sequences
1240 Pre-Post-erous!
1276 Cash Machine
1293 Duty Free Shop
1322 Chocolate
1323 Game Prediction
1338 Ugly Numbers
1390 Blocks
1414 Life Line
1432 Decoding Morse Sequences
1456 Supermarket
1458 Common Subsequence
1475 Pushing Boxes
1485 Fast Food
1505 Copying Books
1513 Scheduling Lectures
1579 Function Run Fun
1609 Tiling Up Blocks
1631 Bridging signals 2分+DP NLOGN
1633 Gladiators
1635 Subway tree systems
1636 Prison rearrangement
1644 To Bet or Not To Bet
1649 Market Place
1651 Multiplication Puzzle
1655 Balancing Act
1661 Help Jimmy
1664 放苹果
1671 Rhyme Schemes
1682 Clans on the Three Gorges
1690 (Your)((Term)((Project)))
1691 Painting A Board
1692 Crossed Matchings
1695 Magazine Delivery
1699 Best Sequence
1704 Georgia and Bob
1707 Sum of powers
1712 Flying Stars
1714 The Cave
1717 Dominoes
1718 River Crossing
1722 SUBTRACT
1726 Tango Tango Insurrection
1732 Phone numbers
1733 Parity game
1737 Connected Graph
1740 A New Stone Game
1742 Coins P
1745 Divisibility
1770 Special Experiment
1771 Elevator Stopping Plan
1776 Task Sequences
1821 Fence
1837 Balance
1848 Tree
1850 Code
1853 Cat
1874 Trade on Verweggistan
1887 Testing the CATCHER
1889 Package Pricing
1920 Towers of Hanoi
1926 Pollution
1934 Trip
1936 All in All
1937 Balanced Food
1946 Cow Cycling
1947 Rebuilding Roads
1949 Chores
1952 BUY LOW, BUY LOWER
1953 World Cup Noise
1958 Strange Towers of Hanoi
1959 Darts
1962 Corporative Network
1964 City Game
1975 Median Weight Bead
1989 The Cow Lineup
2018 Best Cow Fences
2019 Cornfields
2029 Get Many Persimmon Trees
2033 Alphacode
2039 To and Fro
2047 Concert Hall Scheduling
2063 Investment
2081 Recaman’s Sequence
2082 Terrible Sets
2084 Game of Connections
2127 Greatest Common Increasing Subsequence
2138 Travel Games
2151 Check the difficulty of problems
2152 Fire
2161 Chandelier
2176 Folding
2178 Heroes Of Might And Magic
2181 Jumping Cows
2184 Cow Exhibition
2192 Zipper
2193 Lenny’s Lucky Lotto Lists
2228 Naptime
2231 Moo Volume
2279 Mr. Young’s Picture Permutations
2287 Tian Ji – The Horse Racing
2288 Islands and Bridges
2292 Optimal Keypad
2329 Nearest number - 2
2336 Ferry Loading II
2342 Anniversary party
2346 Lucky tickets
2353 Ministry
2355 Railway tickets
2356 Find a multiple
2374 Fence Obstacle Course
2378 Tree Cutting
2384 Harder Sokoban Problem
2385 Apple Catching
2386 Lake Counting
2392 Space Elevator
2397 Spiderman
2411 Mondriaan’s Dream
2414 Phylogenetic Trees Inherited
2424 Flo’s Restaurant
2430 Lazy Cows
2915 Zuma
3017 Cut the Sequence
3028 Shoot-out
3124 The Bookcase
3133 Manhattan Wiring
3345 Bribing FIPA
3375 Network Connection
3420 Quad Tiling ?

概率期望：
https://ac.nowcoder.com/acm/contest/697/A
https://ac.nowcoder.com/acm/contest/697/B