Jungle Roads

问题描述


The Head Elder of the tropical（热带） island of Lagrishan has a problem. A burst（爆发） of foreign aid money was spent on extra roads between villages some years ago. But the jungle overtakes roads relentlessly（残酷地）, so the large road network is too expensive to maintain. The Council of Elders must choose to stop maintaining some roads. The map above on the left shows all the roads in use now and the cost in aacms per month to maintain them. Of course there needs to be some way to get between all the villages on maintained roads, even if the route is not as short as before. The Chief Elder would like to tell the Council of Elders what would be the smallest amount they could spend in aacms per month to maintain roads that would connect all the villages. The villages are labeled A through I in the maps above. The map on the right shows the roads that could be maintained most cheaply, for 216 aacms（推测是一种货币单位） per month. Your task is to write a program that will solve such problems.

输入要求

The input consists of one to 100 data sets, followed by a final line containing only 0. Each data set starts with a line containing only a number n, which is the number of villages, 1 < n < 27, and the villages are labeled with the first n letters of the alphabet, capitalized. Each data set is completed with n-1 lines that start with village labels in alphabetical order. There is no line for the last village. Each line for a village starts with the village label followed by a number, k, of roads from this village to villages with labels later in the alphabet. If k is greater than 0, the line continues with data for each of the k roads. The data for each road is the village label for the other end of the road followed by the monthly maintenance cost in aacms for the road. Maintenance costs will be positive integers less than 100. All data fields in the row are separated by single blanks. The road network will always allow travel between all the villages. The network will never have more than 75 roads. No village will havemore than 15 roads going to other villages (before or after in the alphabet). In the sample input below, the first data set goes with the map above.

输出要求

The output is one integer per line for each data set: the minimum cost in aacms per month to maintain a road system that connect all the villages. Caution: A brute force solution that examines every possible set of roads will not finish within the one minute time limit.

输入样本

9
A 2 B 12 I 25
B 3 C 10 H 40 I 8
C 2 D 18 G 55
D 1 E 44
E 2 F 60 G 38
F 0
G 1 H 35
H 1 I 35
3
A 2 B 10 C 40
B 1 C 20
0

输出样本

216
30

基本思路

情景抽象：最小生成树问题。
这题目问的就是从有多少个村庄，然后要维护这些村庄之间的道路，但是每个道路维护的成本不同，我们的任务是：算出维持连通所有村庄的道路所需最低成本。
套路：kruskal+并查集

实现代码

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#include <iostream>
#include <algorithm>

using namespace std;
const int maxsize=27;
int fa[maxsize];
int N,m,w,es;
char b,e;
struct edge
{
  int begin,end,weight;

  bool operator<(const edge &rhs)
  {
    return this->weight<rhs.weight;
  }
}edges[maxsize*(maxsize-1)];

void init()
{
  for(int i=0;i<maxsize;i++)
    fa[i]=i;
}

int find(int x)
{
  return (fa[x]==x)?x:(fa[x]=find(fa[x]));
}

bool Union(int u,int v)
{
  int uu=find(u);
  int vv=find(v);
  if(uu!=vv)
  {
    fa[uu]=vv;
    return true;
  }
  else
    return false;
}

int main()
{
  while(cin>>N&&N)
  {
    init();
    es=0;
    for(int i=0;i<N-1;i++)
    {

      cin>>b>>m;
      while(m--){
        cin>>e>>w;
        edges[es].begin=b-'A';
        edges[es].end=e-'A';
        edges[es++].weight=w;
      }
    }
    sort(edges,edges+es);
    int sum=0;
    for(int i=0;i<es;i++)
    {
      if(Union(edges[i].begin,edges[i].end))
        sum+=edges[i].weight;
    }
    cout<<sum<<endl;
  }

  return 0;

}