【转】poj1639+最小k度限制生成树

没看懂。。。留着慢慢研究。。。。

 

Description

The Contortion Brothers are a famous set of circus clowns, known worldwide for their incredible ability to cram an unlimited number of themselves into even the smallest vehicle. During the off-season, the brothers like to get together for an Annual Contortionists Meeting at a local park. However, the brothers are not only tight with regard to cramped quarters, but with money as well, so they try to find the way to get everyone to the party which minimizes the number of miles put on everyone's cars (thus saving gas, wear and tear, etc.). To this end they are willing to cram themselves into as few cars as necessary to minimize the total number of miles put on all their cars together. This often results in many brothers driving to one brother's house, leaving all but one car there and piling into the remaining one. There is a constraint at the park, however: the parking lot at the picnic site can only hold a limited number of cars, so that must be factored into the overall miserly calculation. Also, due to an entrance fee to the park, once any brother's car arrives at the park it is there to stay; he will not drop off his passengers and then leave to pick up other brothers. Now for your average circus clan, solving this problem is a challenge, so it is left to you to write a program to solve their milage minimization problem.

Input

Input will consist of one problem instance. The first line will contain a single integer n indicating the number of highway connections between brothers or between brothers and the park. The next n lines will contain one connection per line, of the form name1 name2 dist, where name1 and name2 are either the names of two brothers or the word Park and a brother's name (in either order), and dist is the integer distance between them. These roads will all be 2-way roads, and dist will always be positive.The maximum number of brothers will be 20 and the maximumlength of any name will be 10 characters.Following these n lines will be one final line containing an integer s which specifies the number of cars which can fit in the parking lot of the picnic site. You may assume that there is a path from every brother's house to the park and that a solution exists for each problem instance.

Output

Output should consist of one line of the form Total miles driven: xxx where xxx is the total number of miles driven by all the brothers' cars.

Sample Input

10
Alphonzo Bernardo 32
Alphonzo Park 57
Alphonzo Eduardo 43
Bernardo Park 19
Bernardo Clemenzi 82
Clemenzi Park 65
Clemenzi Herb 90
Clemenzi Eduardo 109
Park Herb 24
Herb Eduardo 79
3

Sample Output

Total miles driven: 183

Source

East Central North America 2000

 

 

 

黑书上的例题，所以题意就不啰嗦了，具体模型是求一个无向图的最小生成树，其中有一个点的度有限制（假设为 k）。

 

要求最小 k 度生成树，我们可以按照下面的步骤来做：

设有度限制的点为 V0 ，V0称为根节点

1，把所有与 V0 相连的边删去，图会分成多个子图（假设为 m 个，显然的，如果 m > k，那么问题无解），让他们分别求最小生成树；然后用最小的代价将 m 个最小生成树和 V0 连起来，那我们就得到了一棵关于 V0 的最小 m 度生成树。

2，在 m 度生成树中找一个点和 V0 相连（设这条边的权值为 a），会生成一个环，为了满足最小生成树的要求，我们必须删掉一条边（设这条边的权值为 b），以使总权值尽量小，那么就要求 a 尽量的小，b 尽量的大。

完成一次 2 的操作后得到的是 m+1 度最小生成树，以此类推，直到得到最小 k 度生成树。

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PS：这道题并不是要求 k 度的最小生成树，而是要求根节点的度在不超过 k 值的情况下，该图的最小生成树。也就是说，不一定要求到 k 度生成树，只要图的总权值不能继续减小我们就可以停下来了。

转载于:https://www.cnblogs.com/mt522/p/5289938.html