HDU1532 最大流 Ford-Fulkerson(邻接矩阵/邻接表) Dinic(邻接矩阵/邻接表)

最新推荐文章于 2019-02-17 23:29:46 发布

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最新推荐文章于 2019-02-17 23:29:46 发布 · 8.8k 阅读

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本文提供了Ford-Fulkerson算法的邻接矩阵版本（BFS和DFS）以及Dinic算法的邻接矩阵和邻接表模板，用于解决最大流问题。每个模板包括详细代码，适合初学者进行练习。题目描述了一个农田排水系统，目标是计算从池塘到河流的最大排水速率。

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Drainage Ditches

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 1507 Accepted Submission(s): 701

Problem Description

Every time it rains on Farmer John's fields, a pond forms over Bessie's favorite clover patch. This means that the clover is covered by water for awhile and takes quite a long time to regrow. Thus, Farmer John has built a set of drainage ditches so that Bessie's clover patch is never covered in water. Instead, the water is drained to a nearby stream. Being an ace engineer, Farmer John has also installed regulators at the beginning of each ditch, so he can control at what rate water flows into that ditch.
Farmer John knows not only how many gallons of water each ditch can transport per minute but also the exact layout of the ditches, which feed out of the pond and into each other and stream in a potentially complex network.
Given all this information, determine the maximum rate at which water can be transported out of the pond and into the stream. For any given ditch, water flows in only one direction, but there might be a way that water can flow in a circle.

Input

The input includes several cases. For each case, the first line contains two space-separated integers, N (0 <= N <= 200) and M (2 <= M <= 200). N is the number of ditches that Farmer John has dug. M is the number of intersections points for those ditches. Intersection 1 is the pond. Intersection point M is the stream. Each of the following N lines contains three integers, Si, Ei, and Ci. Si and Ei (1 <= Si, Ei <= M) designate the intersections between which this ditch flows. Water will flow through this ditch from Si to Ei. Ci (0 <= Ci <= 10,000,000) is the maximum rate at which water will flow through the ditch.