[Go] Summary and summary of some graph theory and network stream beginners

Shortest PathThere are not many types of such problems, with less deformation

 

Poj 2449 remmarguts 'date (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2449 meaning: Classic problem: K short circuit solution: Dijkstra + A * (REC), a lot of related methods: 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: the number of paths with the shortest path and 1 greater than the Shortest Path

 

Poj 3613-cow relays (hard) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3613 question: Find the shortest path of n sides: Floyd + multiply, greedy

 

Poj 3621-Sightseeing cows (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3621 meaning: Find a loop, happy value/total path maximum solution: parameter search + the most short circuit (MS original Bellman TLE, only through spfa)
Poj 3635-Full tank? (Medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3635 question: the most short circuit deformation solution: wide search related: http://hi.baidu.com/hnu_reason/blog/item/086e3dccfc8cb21600e9286b.html

Tree GenerationThe basic spanning tree is not put.

 

Poj 1639-Picnic planning (hard) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1639 question: greedy + prim/Kruskal

 

Poj 1679-the unique MST (basic) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1679 question: Determine whether the MST is the only solution: prim.

 

Poj 2728-desert King (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2728 question: optimal rate generation tree solution: parameter search + prim

 

Poj 3164-Command Network (hard) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3164 question: minimum tree structure solution: Liu Zhu algorithm. Is this less likely?

 

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

 

Connectivity, degree, and Topology ProblemsThis 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: according to the degree Sequence Structure Graph solution: greedy. For details, 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 question: point with a degree of 0 in the point chart of the strongly connected component

 

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: Contraction + dp find the longest chain

 

Poj 2914-minimum cut (hard) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2914 question: undirected graph least cut solution: stoer-Wagner algorithm, which is determined by network flow addition Enumeration

Poj 2942-Knights of the Round Table (hard) http://acm.pku.edu.cn/JudgeOnline/problem? Double Unicom component (or block) contains odd ring solution: Find the double connected component after the black and white dyeing for Bipartite Graph determination related: http://hi.baidu.com/zfy0701/blog/item/57ada7ed104ce9d2b31cb104.html

 

Poj 3177-redundant paths (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3177

Poj 3352-road construction (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3352 question: how many edges can be added to a bidirectional connected graph solution: We recommend that you compare the split edges with different scaled points in the tree, how many edges are added to a directed graph into a strongly connected graph?

 

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: shrink point, longest path, few people do water questions, pay attention to details

 

Poj 3687-labeling Bols (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 problemsIt is not difficult to understand the meaning of this type of problem.

 

Poj 2723-Get Luffy out (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2723 poj 2749-building roads (hard) 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 will be interesting to use 2-Sat, but the brute force search is still 0 ms

 

Poj 3678-Katu puzzle (basic) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3678 Solution

 

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 ProblemsThere are many variants, and the understanding of the maximum flow theorem of the minimum cut is the key

 

Poj 1149-pig (hard) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1149 an absolute classical composition question

 

Poj 1273-drainage ditches (basic) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 1273 maximum incoming 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: find out if there is a solution for the Euler's trace of a hybrid graph: No directed edge, no directed graph, and create a diagram.

 

Poj 1815-friendship (medium) http://acm.pku.edu.cn/JudgeOnline/problem? The smallest point cut solution: Split point into edge cut 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 unconnected solution: Determine any source point, calculate the vertex cut set for the enumerated sink point (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? 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? A feasible stream solution with a source sink: Use a matrix-Network Flow Model diagram, and then split edge-related: http://hi.baidu.com/zfy0701/blog/item/6449d82a64e15e3e5343c1ba.html, the minimum cut model in the competition application

 

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

 

Poj 2699-the maximum number of strong kings (hard) 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 (hard) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2987 meaning: Maximum right closure solution: first side right amplification, the first question total-maximum flow, the second question to find the 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 max weight closure graph Special Case zoj 2071-technology trader is also of this type, lazy did not do 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: 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 + maximum weight closure graph,. v. goldberg's paper (Nb-solution) on 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 minimum range to complete the matching solution: This 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 = 2532 question: determine whether an edge is a side solution in a certain cut: DFS seeking and splitting on both sides, or brute-force enumeration (you need to write an operation to cancel an extended path (but the data is weak, ))

 

Poj 3308-paratroopers (hard) 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 Overwrite
Poj 3469-dual core CPU (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3469 question: Minimum Cut

 

Poj 3498-March of the Penguins (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3498 question: network flow solution that satisfies the point Capacity Limit: Split points to convert the point capacity to the edge capacity, and enumerate the points

 

Zoj 2587-unique attack (hard) http://acm.zju.edu.cn/show_problem.php? PID = 2587 question: Determine whether the minimum cut is the only solution: understand the nature of the DFS Minimum Cut Algorithm.
Spoj 839-optimal marks (difficult) http://www.spoj.pl/problems/OPTM/ meaning: Very classic Oh, see Amber training team paper, according to each digit of the number to find the minimum cut

 

Sgu 326-Perspective (medium) http://acm.sgu.ru/problem.php? Contest = 0 & problem = 326 Classic Graph

The cost flow problem can be solved by km. In addition, unless it is a special graph, it is enough to use the continuous augmented path algorithm.

 

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

 

Poj 3422-Kaka's matrix travels (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3422 question: solution: Split

 

Poj 3680-intervals (hard) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3680 meaning: omitted, this is still a classic solution: discuss is more detailed

 

Spoj 371-boxes (simple) http://www.spoj.pl/problems/BOXES/

 

Sgu 185-two shortest (medium) http://acm.sgu.ru/problem.php? Contest = 0 & problem = 185 question: find two solutions to the shortest path that you don't want to pay: The cost flow, or the Shortest Path + the maximum flow.

 

Matching ProblemIt 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? The necessary edge solution of the Bipartite Graph: need to 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: all possible matching edge solutions for a bipartite graph: although the matching algorithm is not used in the end, the idea of matching must be understood to 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 Overwrite

 

Poj 2594-treasure accounting (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2594 question: intersection of the minimum path overwrite solution: first pass the closure
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: row and column overwrite solution: least point set overwrite = maximum match

 

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 (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2400 question: Output all least weight matching solutions: km, then backtracking, perspiration, the two input matrices are reversed.

 

Poj 2516-minimum cost (medium) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 2516 question: least weight match or least cost flow solution: Split point + km algorithm (only correct), cost flow (MS error may also pass)

 

Poj 3686-The Windy's (hard) http://acm.pku.edu.cn/JudgeOnline/problem? Id = 3686 question: minimum weight matching solution: Split points. Even if you 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/

 

Sgu 206. Roads (hard) http://acm.sgu.ru/problem.php? Contest = 0 & problem = 206 solution: classic question. You can also use spoj 412 to optimize the question.

 

NP problemsIt 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: a very large number of groups solution: get started with the crazy TLE, and then find the paper: 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 = 1492 question: the greatest solution of the graph: search. If the speed is required, refer to the corresponding paper.

 

Other

 

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 question: 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