poj1258 Agri-Net（Prime || Kruskal）

题目链接

http://poj.org/problem?id=1258

题意

有n个农场，现在要在n个农场之间铺设光纤使得n个农场连接起来，求铺设光纤的最短距离。

思路

最小生成树问题，使用Prime算法或者Kruskal算法解决。

代码

Prime算法：

 #include <algorithm>
 #include <iostream>
 #include <cstring>
 #include <cstdio>
 using namespace std;

 const int INF = 0x7fffffff;
 const int N =  + ;
 int map[N][N];
 int dist[N];
 int n;

 void prime()
 {
     int min_edge, min_node;
     for (int i = ; i < n; i++)
         dist[i] = INF;
     int ans = ;
     int now = ;
     for (int i = ; i < n - ; i++)
     {
         dist[now] = -;
         min_edge = INF;
         for (int j = ; j < n; j++)
         {
             if (j != now && dist[j] >= )
             {
                 if (map[now][j]>)
                     dist[j] = min(dist[j], map[now][j]);
                 if (dist[j] < min_edge)
                 {
                     min_edge = dist[j];    //min_edge存储与当前结点相连的最短的边
                     min_node = j;
                 }
             }
         }
         ans += min_edge;
         now = min_node;
     }
     printf("%d\n", ans);
 }

 int main()
 {
     //freopen("poj1258.txt", "r", stdin);
     while (scanf("%d", &n) == )
     {
         memset(map, , sizeof(map));    //注意初始化
         for (int i = ; i < n; i++)
             for (int j = ; j < n; j++)
                 cin >> map[i][j];
         prime();
     }
     return ;
 }

Kruskal算法：

 #include <algorithm>
 #include <iostream>
 #include <cstring>
 #include <cstdio>
 #include <vector>
 using namespace std;

 struct Edge
 {
     int a, b, dist;

     Edge() {}
     Edge(int a, int b, int d) :a(a), b(b), dist(d) {}
 };

 bool cmp(Edge e1, Edge e2)
 {
     return e1.dist < e2.dist;
 }

 const int N =  + ;
 vector<Edge> v;
 int p[N];
 int map[N][N];
 int n;

 int find_root(int x)
 {
     if (p[x] == -)
         return x;
     else return find_root(p[x]);
 }

 void kruskal()
 {
     memset(p, -, sizeof(p));
     sort(v.begin(), v.end(), cmp);    //将边按边长从短到长排序
     int ans = ;
     for (int i = ; i < v.size(); i++)
     {
         int ra = find_root(v[i].a);
         int rb = find_root(v[i].b);
         if (ra != rb)
         {
             ans += v[i].dist;
             p[ra] = rb;
         }
     }
     printf("%d\n", ans);
 }

 int main()
 {
     //freopen("poj1258.txt", "r", stdin);
     while (scanf("%d", &n) == )
     {
         v.clear();    //注意初始化
         for (int i = ; i < n; i++)
             for (int j = ; j < n; j++)
                 cin >> map[i][j];
         for (int i = ; i < n; i++)
             for (int j = ; j < n; j++)
                 if (i < j) v.push_back(Edge(i, j, map[i][j]));
         kruskal();
     }
     return ;
 }