Krydom: 暁の水平线に胜利を刻むのです




Usaco93 Drainage Ditches [poj 1273]


IMG_1877   IMG_1875

♦♦♦♦♦♦   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.

输入文件中包含多个测试数据。每个测试数据的第1行为两个整数M和N,用空格隔开。0≤M≤200,2≤N≤200,其中M是排水沟的数目,N是这些排水沟形成的汇合结点数目。结点1为池塘,结点N为小河。接下来有M行,每行描述了一条排水沟,用三个整数来描述:Si,Ei和Ci,其中Si和Ei(1≤Si,Ei≤N)标明了这条排水沟的起点和终点,水流从Si流向Ei,Ci(0≤Ci≤10 000 000)表示通过这条排水沟的最大流水速度。

♦♦♦♦♦♦   Output   ♦♦♦♦♦♦

For each case, output a single integer, the maximum rate at which water may emptied from the pond.


♦♦♦♦♦♦   Sample Input   ♦♦♦♦♦♦

5 4

1 2 40

1 4 20

2 4 20

2 3 30

3 4 10

♦♦♦♦♦♦   Sample Output   ♦♦♦♦♦♦


♦♦♦♦♦♦   Hint   ♦♦♦♦♦♦


♦♦♦♦♦♦   题解  ♦♦♦♦♦♦

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Usaco93 Drainage Ditches [poj 1273]