Poj graph theory and network stream problems

Poj 2449 remmarguts 'date (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2449
Typical problem: K Short Circuit
Solution: Dijkstra + A * (REC), many methods
Related: http://acm.pku.edu.cn/JudgeOnline/showcontest? Contest_id = 1144
This question is also included in the search recommendation question

Poj 3013-big Christmas tree (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3013
Question: The simplest and most short circuit, but this question is too long. It requires better program speed and accuracy.
Solution: Dijkstra

Poj 3463-Sightseeing (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3463
Question: Number of Shortest Path and 1 greater than Shortest Path
Solution: You need to understand Dijkstra

Poj 3613-cow relays (difficult)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3613
Question: Obtain the shortest path of n sides.
Solution: Floyd + multiply, greedy

Poj 3621-Sightseeing cows (moderate)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3621
Question: finding a loop, happy value/maximum total path
Solution: parameter search + shortest short circuit (MS original Bellman TLE, only through spfa)

Poj 3635-Full tank? (Medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3635
Question: Transient Deformation
Solution: guangsearch
Related: http://hi.baidu.com/hnu_reason/blog/item/086e3dccfc8cb21600e9286b.html

Tree Generation
The basic spanning tree is not put.

Poj 1639-Picnic planning (difficult)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1639
Question: Minimum Spanning Tree with a limited vertex level
Solution: greedy + prim/Kruskal

Poj 1679-the unique MST (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1679
Determine whether the MST is unique
Solution: Prim is enough, but it is easy to make mistakes.

Poj 2728-desert King (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2728
Question: the so-called optimal Ratio Spanning Tree
Solution: parameter search + prim

Poj 3164-Command Network (hard)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3164
Question: minimum tree structure
Solution: The Liu Zhu algorithm is less likely to be obtained?

Poj 3522-slim span (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3522
Ask a spanning tree to minimize the difference between the smallest edge and the smallest edge.
Solution: Use Kruskal

Connectivity, degree, and Topology Problems
This type of problem involves techniques such as DFS and point reduction.

Poj 1236-network of schools (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1236
Question: How many sides can be added to a fully connected graph?
Solution: scale down, view degree

Poj 1659-frogs 'neighborhood (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1659
Question: Build a chart based on the degree Sequence
Solution: greedy. For detailed proof, see Havel theorem.

Poj 2553-the bottom of a graph (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2553
Poj 2186-popular cows (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2186
Point in degree 0

Poj 2762-going from u to V or from V to u? (Medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2762
Question: Determination of unidirectional Connected Graphs
Solution: shrink point + dp find the longest chain

Poj 2914-minimum cut (hard)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2914
Objective: undirected graph minimal cut
Solution: stoer-Wagner algorithm. network stream and enumeration are used to determine whether

Poj 2942-Knights of the Round Table (difficult)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2942
Question: Check whether the dual-China Unicom component (or block) contains an odd circle
Solution: Obtain the dual-connected components and then perform black and white dyeing to determine the bipartite graph.
Related: http://hi.baidu.com/zfy0701/blog/item/57ada7ed104ce9d2b31cb104.html

Poj 3177-redundant paths (moderate)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3177
Poj 3352-road construction (moderate)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3352
Question: How many sides can be added to a bidirectional connected graph?
Solution: scale down the Vertex Tree of different parts separated by the cut edge to see the inbound degree
We recommend that you compare the number of edges added to a directed graph to a strongly connected graph in the following figure: 1236.

Poj 3249-Test for job (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3249
Solution: BFS/DFS + dp

Poj 3592-instantaneous transference (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3592
Solution: scale down, longest path, few people do water questions, pay attention to details

Poj 3687-labeling bils (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3687
Solution: topological sorting

Poj 3694-Network (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3694
Solution: Dual-Connected Component + query set

2-SAT problems
It is not difficult to understand the meaning of this type of problem.

Poj 2723-Get Luffy out (moderate)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2723
Poj 2749-building roads (difficult)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2749
Solution: Binary + 2-Sat Determination

Poj 3207-Ikki's Story IV-panda's trick (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3207
Solution: simple 2-Sat, but other methods are faster

Poj 3648-wedding (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3648
Solution: it would be interesting to use 2-Sat, but the brute force search still takes 0 ms.

Poj 3678-Katu puzzle (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3678
Solution: simply verify the Image Based on the Union diagram.

Poj 3683-priest John's busiest day (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3683
Solution: Compatibility diagram between N ^ 2 enumeration points, solving 2-Sat

Maximum Flow Problems
There are many variants, and the understanding of the maximum flow theorem of the minimum cut is the key

Poj 1149-pigs (difficult)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1149
Absolutely classic architecture questions

Poj 1273-drainage ditches (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1273
Maximum inbound door

Poj 1459-Power Network (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1459
Basic Diagram

Poj 1637-Sightseeing Tour (crazy)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1637
Question: Check whether the Euler's trace of a hybrid graph exists.
Solution: undirected edges, arbitrary orientation, diagram, detailed introduction to the Black Book p324

Poj 1815-friendship (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1815
Question: Minimum Cut
Solution: Split points into edge Cutting
Related: http://hi.baidu.com/zfy0701/blog/item/a521f230b06dea9fa9018e0e.html

Poj 1966-cable TV network (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1966
Question: How many points are removed to make the graph not connected?
Solution: Determine any Source Vertex, enumerate the sink vertex to obtain the vertex cut set (convert to the Edge Cut), and find the smallest vertex cut

Poj 2112-optimal milking (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2112
Binary enumeration, maximum stream

Poj 2391-ombrophobic bovines (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2391
Question: Floyd, split point, binary Enumeration
Related: http://hi.baidu.com/zfy0701/blog/item/3e0006c4f73f0eaf8226acff.html

Poj 2396-budget (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2396
Question: a feasible upstream/downstream stream with a source sink
Solution: Use the matrix-Network Flow Model to map and then split the edge
Related: http://hi.baidu.com/zfy0701/blog/item/6449d82a64e15e3e5343c1ba.html
, The Application of the minimal cut model in the competition

Poj 2455-secret milking machine (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2455
Binary enumeration. In general, you need to write an update operation on the edge capacity instead of re-composing all the elements each time.

Poj 2699-the maximum number of strong kings (difficult)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2699
Solution: enumerative users + maximum stream (thanks to the prompt for creating the xpcnq_71 dashboard)

Poj 2987-firing (difficult)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2987
Question: Maximum permission Closure
Solution: enlarge edge weight first. The first question is "Total"-"maximum flow", and the second question is "minimum cut ".
Related: http://wywcgs.spaces.live.com/blog/cns! 4d861a02a3382142! 1109. Entry? & _ C02_owner = 1
Profit (medium)
Http://www.vijos.cn/Problem_Show.asp? Id = 1352
Special situations of the max weight closure Graph
This is also the type of zoj 2071-technology trader.
Http://acm.zju.edu.cn/show_problem.php? PID = 1, 2071

Poj 3084-panic room (medium, good question)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3084
Question: omitted
Solution: Modeling Based on the Minimum Cut

Poj 3155-hard life (challenging)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3155
Question: maximum density subgraph
Solution: parameter search + max weight closure diagram, A. V. Goldberg paper (NB solution)
The application of the minimal cut model in the informatics Competition

Poj 3189-Steady cow assignment (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3189
Question: finding the smallest interval to complete matching
Solution: This question fully demonstrates the strength of SAP, which is purely violent. A better way is to continually Delete edges and add edges to continue the network flow process during the enumeration interval.

Poj 3204-Ikki's story I-road reconstruction (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3204
Zoj 2532-Internship (basic)
Http://acm.zju.edu.cn/show_problem.php? PID = 1, 2532
Determine whether an edge is in a cut.
Solution ))

Poj 3308-paratroopers (difficult)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3308
Poj 2125-destroying the graph (hard)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2125
Question: Least vertex weight coverage

Poj 3469-dual core CPU (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3469
Question: Minimum Cut

Poj 3498-March of the Penguins (moderate)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3498
Question: network stream that meets the point Capacity Limit
Solution: Split points convert the point capacity to the edge capacity, and enumerate the points

Zoj 2587-unique attack (difficult)
Http://acm.zju.edu.cn/show_problem.php? PID = 1, 2587
Determine whether the minimum cut is unique
Solution: understand the nature of the DFS Minimum Cut Algorithm.

Spoj 839-optimal marks (hard)
Http://www.spoj.pl/problems/OPTM/
Question: omitted
Solution: Very classic. For details, see Amber's training team paper. Calculate the minimum cut based on each digit of the number.

Sgu 326-Perspective (medium)
Http://acm.sgu.ru/problem.php? C0 & proble m = 326
Classic Graph

Cost Flow Problems
The solutions that can be obtained by km are not placed here. In addition, unless a special graph is used, the continuous augmented Path Algorithm is enough.

Poj 2175-evacuation plan (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2175
Question: Determine whether a given solution is the optimal solution.
Solution: Construct a stream based on the given plan, and then consume only one negative circle

Poj 3422-Kaka's matrix travels (moderate)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3422
Question: omitted
Solution: Split points

Poj 3680-intervals (difficult)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3680
Question: omitted. This question is still quite classic.
Solution: details in discuss

Spoj 371-boxes (simple)
Http://www.spoj.pl/problems/BOXES/
Question: omitted
Solution: billing flow, but it seems better than Network Flow

Sgu 185-two shortest (medium)
Http://acm.sgu.ru/problem.php? C0 & proble m = 185
Question: find two shortest paths
Solution: Charge flow, which can also be the shortest path + the largest stream.

Matching Problem
It is important to correctly understand the KM algorithm.

Here I would like to say a few more words: the most correct solution to the least weight match is to use a large number-the current edge weight, instead of directly performing Edge Weight inversion (this can only process completely bipartite graphs with equal left and right vertices, that is, K (n, n)

The above may be a bit of a problem.

Poj 1486-sorting slides (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1486
Question: required edges of a Bipartite Graph
Solution: To really understand the maximum matching algorithm, see the http://hi.baidu.com/kevin0602/blog/item/1d5be63b5bec9bec14cecb44.html

Poj 1904-King's Quest (medium, good question)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1904
Question: Find all possible matching edges in a bipartite graph.
Solution: although the matching algorithm is not used in the end, you need to understand the idea of matching and convert it into a strongly connected component.

Poj 2060-Taxi Cab Scheme (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2060
Question: Minimum path coverage

Poj 2594-treasure accounting (moderate)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2594
The minimum path that can be intersection is overwritten.
Solution: first pass the closure to convert

Poj 3041-Asteroids (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3041
Poj 2226-muddy fields (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2226
Question: Coverage of rows and columns
Solution: least point set coverage = maximum matching

Poj 2195-Going Home (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2195
Question: Minimum Weight Matching
Solution: Km Algorithm

Poj 2400-supervisor, supervisee (moderate)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2400
Question: output all minimum weight matching
Solution: km, then trace back, sweat, and the two input matrices are reversed.

Poj 2516-minimum cost (moderate)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2516
Question: minimum weight matching or minimum charge flow
Solution: Split point + km algorithm (only the correct one can pass) and Charge flow (the cost flow may pass through the wrong ms)

Poj 3686-The Windy's (hard)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3686
Question: Minimum Weight Matching
Solution: Split the points, and use the KM algorithm to access the water. The data is actually very weak (50*50*2500)-> 16 Ms
Related: http://hi.baidu.com/kevin0602/blog/item/2829dc01d7143b087bec2c97.html

Spoj 412-K-path cover (difficult)
Https://www.spoj.pl/problems/COVER/
Question: omitted
Solution: a perfect match
Related: http://hi.baidu.com/roba/blog/item/c842fdfac10d24dcb48f31d7.html

Sgu 206. Roads (difficult)
Http://acm.sgu.ru/problem.php? C0 & proble m = 206
Solution: Typical questions. You can also use spoj 412 to optimize the questions.

NP problems
It is generally implemented by searching or DP.

Poj 1419-graph coloring (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1419
Question: Graph Coloring
Solution: search. Unfortunately, the data on the question is too weak.

Poj 2989-all friends (hard)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2989
Question: The number of large groups
Solution: I started to get mad at tle. Later I found my thesis: finding all cliques of an undirected graph (Coen bron & joep kerboscht)

Zoj 1492-maximum clique (basic)
Http://acm.zju.edu.cn/show_problem.php? PID = 1, 1492
Question: the largest group of pictures
Solution: search. If the speed is required, refer to the corresponding paper.

Others
Not big class

Poj 1470-closest common ancestors (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1470
Question: LCA
Solution: Tarjan or rmq. The input is disgusting.

Poj 1985-cow Marathon (basic)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1985
The longest path on the tree
Solution: DP

Poj 1986-distance queries (medium)
Http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1986
Question: LCA
Solution: Tarjan or rmq

Hoj 11192-Justice leleague (interesting Graph Theory)
Http://acm.hnu.cn: 8080/online /? Action = problem & type = show & id = 11192 & courseid = 99

Hoj 11277-new island (interesting Graph Theory)
Http://acm.hnu.cn: 8080/online /? Action = problem & type = show & id = 11277> courseid = 109

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