图论精炼500题

忘了从哪转的了...

=============================以下是最小生成树+并查集======================================

【HDU】

1213   How Many Tables   

【基础并查集】

1272   小希的迷宫   

【基础并查集】

【注意】

可能存在多棵树的情况,当然出现这种情况要输出No

1325  Is It A Tree?   

【基础并查集】

【分析】

本题与上一题基本类似,代码主题都可以直接复制,但是需要注意的是有两个关键点:

1、结束条件是两个负数,不是两个-1!!!!!

2、题目给出的边的指向是有方向的,如下的这组测试数据:

1 2 3 2 0 0

这就不是一棵树,即需要记录一下每个点的入度,判断入度不能超过1

1856   More is better   

【基础并查集+哈希】

【方案】

题目说上限是10000000,开这么大的数组肯定是会爆内存的,因此对于每个boy的编号需要进行哈希处理

1102   Constructing Roads  

【基础最小生成树】

1232   畅通工程   

【基础并查集】

1233   还是畅通工程   基础最小生成树

1863   畅通工程   基础最小生成树

1875   畅通工程再续   基础最小生成树

1879   继续畅通工程   基础最小生树

3371     Connect the Cities    最小生成树

【注意】

这道题的数据对于裸的Kruskal来说可能数据略大,25000条边的稠密图

【两个方案】

1.考虑优化;

2.用Prim做(貌似从discuss的反馈来看,处理的不好的话也可能会超)

【对比】

Kruskal(mlogm)适合稀疏图,写起来比较简单,快排+并查集即可

Prim(n^2)适合稠密图,优化方案比如前向星存储,不过稠密图不能用堆优化

【bug】

限于HDU的评测环境,G++提交TLE,C++提交裸的Kruskal可以过

1301   Jungle Roads   基础最小生成树

1162   Eddy's picture   基础最小生成树

1198   Farm Irrigation   并查集

1598   find the most comfortable road 枚举+最小生成树★★

【方案】

1.Prim,二分枚举答案(也就是差值),最短路算法从起点开始走,判断是否可以走到终点

2.Kruskal,这里满足的贪心条件是如果最小边确定了,那么剩下的路径肯定是越小越好,故枚举最小边,在这一条边的基础上构造最小生成树,判断是否能把起终点都包含在一个集合内,更新最小差值

数据量在可以承受的范围之内

1811   Rank of Tetris   并查集+拓扑排序★★

【方案】

首先用并查集预处理,把相等的点全部缩成一个;然后在缩点之后的基础上进行拓扑排序,判断是否存在唯一的拓扑序列。

拓扑排序用入度栈来做,时间戳的方案还没想过。

3926   Hand in Hand   同构图(并查集)

【分析】

题意简单地说就是判断两张图的形式是否一致:

每人最多只有两只手,所以能够形成的图块只有环和链两种,可以通过并查集来得到每组的点数,并在过程中判断某组是否成环并标记。最后对比一下两张图的数据即可。

3938   Portal     离线+并查集★★ 2489     Minimal Ratio Tree   dfs枚举组合情况+最小生成树★

第一次使用STL的优先队列代替自己定义的堆

4081            Qin Shi Huang's National Road System 最小生成树+DFS★★

4126            Genghis Khan the Conqueror         枚举+最小生成树+DFS(难)★★★★

1829&&poj2492    A Bug's Life                       基础种类并查集★

1558               Segment set                     计算几何+并查集★

3461               Code Lock                         并查集(有点难想到)★★

3367               Pseudoforest                    最大生成树★

2473               Junk-Mail Filter                并查集+设立虚父节点(马甲)★★

3172               Virtual Friends                 带权并查集★

3635               Dragon Balls                     带权并查集★

3047               Zjnu Stadium                   带权并查集★

3038               How Many Answers Are Wrong      种类并查集★★

2818               Building Block                  带权并查集★

3234               Exclusive-OR                    异或并查集(难)★★★

2121            Ice_cream’s world II           最小树形图(要输出根有点恶心)★★

4009            Transfer water                         最小树形图(模板题)★

3311              Dig The Wells                 斯坦纳树(状压DP)(模板题)★★

4085                Peach Blossom Spring             斯坦纳树(状压DP)(有可能是森林...)★★★

2586               How far away ?                     LCA★

2874               Connections between cities    LCA★

3486               Interviewe                        RMQ★

2888               Check Corners                  二维RMQ★

3183                A Magic Lamp                  RMQ(有点难想到,有点难联系到RMQ)★★

【POJ】

1258                                                 最经典的MST★

1789               Truck History                   最小生成树★

1287               Networking                     简单★

2349               Arctic Network                         简单★

1611               The Suspects                   并查集★

2377                                                 kruskal★

2524               Ubiquitous Religions              并查集★

2236               Wireless Network           并查集+计算几何★

2560                                                 Kruskal 并查集★

1861                                                 Kruskal ★

3625                                                 prim★

1679 -             The Unique MST(基础)                  判断MST是否唯一★

3522 -             Slim Span(基础)            求一颗生成树,让最大边最小边差值最小★

2485               Highways                         MST中的最长边★

2395                                                 最小生成树的最长边★

1751               Highways                         求出方案★

POJ-1182        食物链                            种类并查集★★

POJ 1456        Supermarket                    贪心+区间合并★

POJ-1703                                         种类并查集★

POJ-1988                                         种类并查集★

POJ-1733        Parity game                     种类并查集,先要离散化一下,不影响结果★

POJ-1417        True Liars(难)                  并查集+DP 种类并查集★★

POJ-2912        Rochambeau(难)                     baidu的题,很不错...是食物链的加强版.判断裁判比较难想.★★★

POJ 2728        Desert King(中等)                  最优比率生成树★★

POJ 1639        Picnic Planning(较难)             顶点度数有限制的最小生成树★★

POJ 3164        Command Network(难)                  最小树形图★★

poj3723                                             好题!!! ★★

poj3228                                             好好题!!! ★★

【ZOJ】

ZOJ-3261 逆向并查集 ★★

===============================以下是最短路系列====================================

【HDU】

1548            A strange lift                    基础最短路(或bfs)★

2544            最短路                           基础最短路★

3790             最短路径问题                         基础最短路★

2066              一个人的旅行                       基础最短路(多源多汇,可以建立超级源点和终点)★

2112            HDU Today                       基础最短路★

1874            畅通工程续                     基础最短路★

1217            Arbitrage                      货币交换 Floyd (或者 Bellman-Ford 判环)★

1245            Saving James Bond          计算几何+最短路★

1317            XYZZY                              Bellman-Ford判环,有负权★

1535            Invitation Cards            有向图的来回最短路,(反向建图)★

1546            Idiomatic Phrases Game       最短路★

2680            Choose the best route          最短路★

2923            Einbahnstrasse                         最短路★

3339            In Action                         最短路+背包★

2224            The shortest path            双调旅行商问题★★

2807            The Shortest Path            矩阵运算+最短路(floyd)★★

1595            find the longest of the shortest枚举+最短路(删掉任意一条边的最长最短路)★★

3986            Harry Potter and the Final Battle 枚举+最短路(删掉任意一条边的最长最短路)★★

1599            find the mincost route            floyd求最小环★

1839                Delay Constrained...                二分下限+最短路(带限制最短路)★★   

3631               Shortest Path                   Floyd插点法★★

4114                Disney's FastPass             最短路+二维状压DP(难)★★★

3832            Earth Hour                        三点连通(斯坦纳树)★

3873            Invade the Mars                       Dij变体(好题!,带限制最短路)★★★

4063               Aircraft                     几何构图+最短路★★★★

hdu4179          Difficult Routes               dis[][]开二维状态的最短路(带限制最短路)★★

1869               六度分离                        Floyd最短路★

1385            Minimum Transport Cost            最短路+输出路径(输出字典序最小路径,有点恶心)★★     

1224            free DIY Tour                   最短路+输出路径★

1142            A Walk Through the Forest  最短路+记忆搜索★★

1596            find the safest road               乘积最小的最短路★

1598            find the most comfortable road     二分速度差+最短路(带限制最短路)★★

2722            Here We Go(relians) Again      最短路★

2962            Trucking                          二分+最短路(带限制最短路)★★

1690            Bus System                      最短路★

2433            Travel                                删边+最短路之和(预处理桥边)★★★                        

2363            Cycling                              二分+最短路(带限制最短路)★★

2377            Bus Pass                   最短路(寻找一个点的最长最短路最小)★★

2833            WuKong                            最短路+记忆化搜索(求两条最短路的最多公共点)★★

1688            Sightseeing                       最短次短路条数★★

3191            How Many Paths Are There    次短路条数★★

2482            Transit search                   最短路★★★

3768               Shopping                  最短路+dfs(或最短路+状压DP)★★

3035            War                           平面图最小割(建图麻烦)★★

3870            Catch the Theves            平面图最小割(建图麻烦)★★

3860                Circuit Board                    平面图最小割(建图麻烦)★★

【POJ】

1062               昂贵的聘礼                     竟然可以和最短路联系起来★★

1094               Sorting It All Out              Floyd判环+拓扑排序★

1125                Stockbroker Grapevine            Floyd★

1135               Domino Effect                  最短路,比较有意思★★

1161               Walls                                 最短路(图太恶心了)★★

1502               MPI Maelstrom                        Floyd★

1511            Invitation Cards               来回最短路★

1556                The Doors                       计算几何+最短路★★

1724               ROADS                              带限制的最短路,dis[][]开二维来记录信息(或广搜)★★

1734               Sightseeing trip                floyd最小环路径★

1797               Heavy Transportation              二分枚举+最短路★

1847               Tram                                 简单最短路★

1860                Currency Exchange          货币兑换★

1949               Chores                              反向建边,求最长路★★

2139               Six Degrees of Cowvin Bacon  Floyd★

2240                Arbitrage                  货币兑换★

2253                Frogger                             二分+最短路★

2312               坦克大战                         spfa最短路本质变形-->广搜★

2387               Til the Cows Come Home                基础最短路★

2394                Checking an Alibi             最短路★

2449                Remmarguts' Date          A*求第K短路★★

2457               Part Acquisition               最短路 (输出路径)★★

2472               106 miles to Chicago               乘积最短路(log一下,乘变加)★★

2502                Subway

2570               Fiber Network floyd

3013               圣诞树

3037                Skiing

3072               Robot

3114               Countries in War             强联通+最短路

3160               Father Christmas flymouse    强联通+最长路

3255               Roadblock

3259               Wormholes                      (寻找负权回路)

3268               Silver Cow Part

3311               Hie with the Pie              floyd+状压

3328               Cliff Climbing

3439               Server Relocation

3463               Sightseeing                      次短路条数

3159       

3521                Geometric Map                        计算几何+最短路

3549                GSM phone                     计算几何+最短路

3594               Escort of Dr. Who How

3613               Cow Relays                     经过N条边的最短路 // floyd + 二分矩阵

3615               Cow Hurdles

3621               最优比率环

3635               full tank?

3660               传递闭包

3662               Telephone Lines

============================以下是差分约束系列============================

【HDU】

1384               Intervals

1529               Cashier Employment

1531               King

1534               Schedule Problem

3440               House Man

3592               World Exhibition

3666               THE MATRIX PROBLEM

【POJ】

1201

1275

1364

1716

2949

2983

3159

3169

3687

============================以下是二分匹配系列============================

普通匹配,多重匹配

【HDU】

1068                Girls and Boys

1150                Machine Schedule

1151                Air Raid

1179                Ollivanders: Makers of Fine Wands since 382 BC.

1281                棋盘游戏

1498                50 years, 50 colors

1507                Uncle Tom's Inherited Land*

1528                Card Game Cheater

1845                Jimmy’s Assignment

2063                过山车

2119                Matrix

2444                The Accomodation of Students

2768                Cat vs. Dog

3081                Marriage Match II

3360                National Treasures

1045                也可搜索

1350                最小路径覆盖

3118                类似二分匹配

3729

2389

1054

2819                完全匹配

1668               二分+多重匹配

3605                多重匹配

3861                强连通+二分匹配

2236                无题II

hdu3468

hdu4185 奇偶匹配

【POJ】

1087                A Plug for UNIX

1274               The Perfect Stall

1469                COURSES

1486               Sorting Slides                  二分图的必须边

1548                Robots

1698                Alice's Chance

1719                Shooting Contest

1904               King's Quest                    求二分图所有可能的匹配边

2060               Taxi Cab Scheme             最小路径覆盖

2112               Optimal Milking             二分+多重匹配

2226               Muddy Fields                  行列的覆盖

2239               Selecting Courses

2289               Jamie's Contact Groups           二分+多重匹配

2446               Chessboard

2536               Gopher II

2584                T-Shirt Gumbo

2594               Treasure Exploration               可相交最小路径覆盖

2672                Hotkeys

2724               Purifying Machine

3020               Antenna Placement

3041               Asteroids                         简单行列匹配

3189                Steady Cow Assignment                 二分+多重匹配

3207               Ikki's Story IV - Panda's Trick

3216               Repairing Company

3343               Against Mammoths

3692               Kindergarten

2771                                                  最大独立集

============================以下是KM算法系列============================

【HDU】

2255                奔小康赚大钱

1533                Going Home

1853                Cyclic Tour

3488                Tour

3435                A new Graph Game

2426                Interesting Housing Problem

2853                Assignment

3718                Similarity

3722                Card Game

3395                Special Fish

2282                Chocolate

2813                One fihgt one

2448                Mining Station on the Sea

3315                My Brute

3523                Image copy detection

【POJ】

2195               Going Home                    最小权值匹配

2400               Supervisor, Supervisee           输出所有最小权匹配

2516               Minimum Cost                        最小权值匹配或最小费用流

3565                Ants

3686               The Windy's                    最小权值匹配

       

============================以下是最大团&稳定婚姻系列============================

【HDU】

1530                Maximum Clique

1435                Stable Match

3585                maximum shortest distance 二分+最大团

1522                Marriage is Stable

1914                The Stable Marriage Problem

【POJ】

1129                四色定理 着色问题

1419                最大独立集

2989                极大团

3487               The Stable Marriage Problem 稳定婚姻

============================以下是强双联通系列============================

【HDU】

强连通:

1269              迷宫城堡                       判断是否是一个强连通

2767                Proving Equivalences            至少加几条边让整个图变成强连通

3836               Equivalent Sets              至少加几条边让整个图变成强连通

1827             Summer Holiday            传递的最小费用

3072            Intelligence System               传递的最小费用

3861                The King’s Problem              强连通+二分匹配

3639                Hawk-and-Chicken                 强连通缩点 + 树形dp(累加子节点的总权值)

3594               Cactus                              仙人掌图

双连通:

2242                考研路茫茫――空调教室  双联通缩点+树形DP

2460                Network                           边双连通

3849                By Recognizing These Guys, We Find Social Networks Useful  双连通求桥

3896                Greatest TC                    双连通

4005               The war                          边双连通

LCA:

2586                How far away ?

2874                Connections between cities

3078                Network                         LCA+排序

3830                Checkers                         二分+LCA

【POJ】

强连通:

1236                Network of Schools

2553               The Bottom of a Graph                  好题! 找出度为0的集合

2186            Popular Cows                         好题! 找出度为0的,其他分量都指向它的集合

2375                Cow Ski Area                   强连通

2762            Going from u to v or from v to u?  缩点+拓扑排序

3160             Father Christmas flymouse  强连通+最短路

3180               The Cow Prom                        判断有几个环, 分量中元素大于1的个数

3114                Countries in War            强连通+最短路

3592                Instantaneous Transference          强连通分量+最长路

1904                King's Quest                   强连通+并查集

                        

双连通:

3694               Network                         边双连通 (同hdu2460)

3177               Redundant Paths                  构造边双连通

3352               Road Construction                构造边双连通

2942               Knights of the Round Table     (点双连通经典题)

1515               Street Directions             (无向图改有向图)

1438               One-way Traffic             (混合图改有向图)

LCA:

1330                Nearest Common Ancestors

1470                Closest Common Ancestors

1986                Distance Queries

3417                Network

3728                The merchant                         LCA+并查集,更新询问

2763                Housewife Wind                      LCA+树状数组

============================以下是2-SAT系列============================

【HDU】

3062               Party

1824               Let's go home

3622               Bomb Game

3715               Go Deeper

1815               Building roads

2723               Get Luffy Out

1816               Get Luffy Out *

1814               Peaceful Commission

4115               Eliminate the Conflict

【POJ】

2296               Map Labeler

2723               Get Luffy Out

2749              Building roads

3207              Ikki's Story IV - Panda's Trick

3648               Wedding

3678               Katu Puzzle

3683              Priest John's Busiest Day

3905               Perfect Election

============================以下是欧拉回路系列============================

【HDU】

1878                欧拉回路  判断

3018                Ant Trip 一笔画问题

1116

2894                兹鼓欧拉回路

1956

3472                混合欧拉

【POJ】

2513                                                欧拉路

1041              John's trip                      欧拉回路

1386               Play on Words                        单词接龙

2230                Watchcow                      欧拉回路

2513               Colored Sticks                无向图欧拉路

2337               Catenyms                       欧拉路径

1392               Ouroboros Snake           兹鼓欧拉回路

1780              code

1637                                                混合欧拉

【zoj】

1992

============================以下是拓扑排序系列============================

【HDU】

1285                确定比赛名次

2094                产生冠军

2647                Reward

3342                Legal or Not

1811                Rank of Tetris                 拓扑+并查集

3231                                                 三维拓扑

【POJ】

1094               Sorting It All Out            Floyd+拓扑

2367               Genealogical tree

3660               Cow Contest

3687               Labeling Balls                  神奇的拓扑

1128                Frame Stacking              DFS版拓扑

1270                Following Orders           拓扑+回溯

1420                Spreadsheet                   模拟拓扑

2762                Going from u to v or from v to u?  强连通+拓扑

3553                Task schedule

============================以下是竞赛图系列============================

竞赛图下的哈密顿问题

Strange Country II   ZOJ-3332

Task Sequences       POJ-1776

The book SGU-122

Tour Route       POJ-3780

Tour Route       HDOJ-3414

============================以下是网络流系列============================

【HDU】

1532                Drainage Ditches(基础)           [最大流]

3549                Flow Problem(基础)                [最大流]

3572                Task Schedule                  [最大流]任务分配,判断满流

2732                Leapin' Lizards(难)           [最大流]

3338                Kakuro Extension             [最大流][数和]神奇最大流行进列出

2883                kebab                                [最大流]判断满流

3605                Escape                              [最大流](多重匹配

3081                Marriage Match II            [二分最大流]+并查集

3277                Marriage Match III           [二分最大流]同上,多了拆点

3416                Marriage Match IV          [最大流]最短路+最大流

2485                Destroying the bus stations    [最大流]最短路+最大流

3468                Treasure Hunting             [最大流](二分匹配)+最短路

3551                Hard Problem                  [最大流]

3998                Sequence(难)                   [DP+最大流]最长上升子序列

3917                Road constructions         [最大权闭包]

3879                Base Station                     [最大权闭包]

3061                Battle                                [最大权闭包]

3996                Gold Mine                        [最大权闭包]

3472                HS BDC                             [混合欧拉]

hdu4183 来回走不重复点的网络流.

-------------------------

1533                Going Home(基础)          [费用流]

3488                Tour                          [费用流]圈

3435                A new Graph Game         [费用流]圈

1853                Cyclic Tour                        [费用流]圈

2686                Matrix                               [费用流]

3376                Matrix Again                    [费用流]

3667                Transportation                 [费用流]拆边

3315                My Brute                  [费用流](可用KM)

3395                Special Fish                      [费用流](可用KM匹配)

2448                Mining Station on the Sea      [费用流](可用最短路+KM匹配)

4067                Random Maze(难)                   [费用流]

3947                River Problem(难)           [费用流]神奇费用流,流量不等式建图

3046                Pleasant sheep and big big wolf [最小割]

1565                方格取数(1)                     [最小割]

1569                方格取数(2)                     [最小割]

3820                Golden Eggs                     [最小割]方格加强

3491                Thieves                             [最小割]最小点割集

3657                Game                                [最小割]最大点权独立集

3313                Key Vertex                        [最小割]

3251                Being a Hero                    [最小割] 

3157                Crazy Circuits                   [上下流]

3002                King of Destruction         [全局最小割]

3691                Nubulsa Expo                   [全局最小割]

【POJ】

1087                A Plug for UNIX              [最大流](可用二分匹配)

1274                The Perfect Stall              [最大流](可用二分匹配)

1325                Machine Schedule           [最大流](可用二分匹配)

1698                Alice's Chance                  [最大流](可用二分匹配)

2239                Selecting Courses            [最大流](可用二分匹配)

2446                Chessboard                      [最大流](可用二分匹配) 好题啊

2536                Gopher II                  [最大流](可用二分匹配)

2771                Guardian of Decency               [最大流]二分匹配最大独立集

3041               Asteroids                         [最大流](简单二分匹配)

2584               T-Shirt Gumbo                         [最大流](多重匹配)

3189               Steady Cow Assignment(中等)       [二分最大流](多重匹配)

1149               PIGS                                [最大流] 绝对经典的构图题

1273               Drainage Ditches           [最大流](基础)

1459               Power Network(基础)             [最大流]

3281               Dining                              [最大流]

2112               Optimal Milking(基础)                  [二分最大流]

2289               Jamie's Contact Groups          [二分最大流]

2391               Ombrophobic Bovines(中等)         [二分最大流]

2455               Secret Milking Machine(基础)       [二分最大流]

3228               Gold Transportation               [二分最大流](并查集)

2699               The Maximum Number of Strong Kings(较难)  [枚举人数 + 最大流]

3498                March of the Penguins(中等)        [最大流]枚举汇点,满足点容量限制的网络流

2987               Firing(较难)                    [最大权闭包]

1637               Sightseeing tour(Crazy)         [混合欧拉]

2135               Farm Tour                       [费用流] (来回最短路)

2175                Evacuation Plan(中等)           [费用流] 消圈

2195                Going Home                     [费用流]

2516               Minimum Cost                        [费用流]

3422               Kaka's Matrix Travels(中等)          [费用流]拆点

3680               Intervals(较难)               [费用流]经典,费用流+离散化

3686                The Windy's                     [费用流](KM匹配)

3762                The Bonus Salary!            [费用流]

1815               Friendship(中等)           [最小割]最小点割集

1966              Cable TV Network(中等)       [最小割]最小点割集

2125               Destroying The Graph(难)     [最小割]最小点权覆盖

3084               Panic Room(中等,好题)     [最小割]边连通度

3204               Ikki's Story I - Road Reconstruction(基础) [最小割]求关键边

3308               Paratroopers(较难)                 [最小割]乘积取对数,最小点权覆盖

3436                ACM Computer Factory           [最小割]收集流,残留搜集找边

3469               Dual Core CPU(中等)             [最小割]收集流

3921                Destroying the bus stations    [最小割]点连通

2396               Budget(中等)                          [有源汇的上下界可行流]

3155               Hard Life(很挑战一题)                  [最大密度子图]

2914                Minimum Cut                  [无向图最小割]

============================以下是dancing links系列============================

1001                Easy Finding                     POJ-3740

1002                Power Stations                         HDOJ-3663

1003                Treasure Map                   ZOJ-3209

1004                Lamp                                 HDOJ-2828

1005                whosyourdaddy                       HDOJ-3498

1006                Bomberman - Just Search!      HDOJ-3529

1007                Square Destroyer             POJ-1084

1008                Matrix                               HDOJ-2119

1009                Divisibility                        HDOJ-3335

1010                Radar                                HDOJ-2295

1011                Fire station                       HDOJ-3656

1012                Repair Depots                  HDOJ-3156

1013                Dominoes                         HDOJ-2518

1014                Street Fighter                   HDOJ-3957

1015                Sudoku Killer                    HDOJ-1426

1016                Sudoku                             POJ-2676

1017                Sudoku                             POJ-3074

1018                Sudoku                             POJ-3076

1019                Su-Su-Sudoku                  HDOJ-2780

1020                Sudoku                             HDOJ-3111

1021                Sudoku                             HDOJ-3909

1022                Squiggly Sudoku                      HDOJ-4069

1023                Triangle War II                  ZOJ-3038

1024                A Puzzling Problem         HDOJ-1603

1025                Maximum Clique                     HDOJ-1530

hust1017                                          精确覆盖。

fzu1686,nuaa1507                                  重复覆盖。

hit2199,2882,2959                                 精确覆盖(数独)。

SPOJ1771                                          精确覆盖(N皇后问题)。

poj3435

原文地址:https://www.cnblogs.com/jcf94/p/4079903.html