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

Source: Internet
Author: User

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

Related Article

Contact Us

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

  • Sales Support

    1 on 1 presale consultation

  • After-Sales Support

    24/7 Technical Support 6 Free Tickets per Quarter Faster Response

  • Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.