hdu 1599 无向图最小环

裸的无向图最小环，我们可以在Floyd的过程中求得。

具体思想是：枚举环中的编号最大的顶点k，然后枚举和k相关联的两个顶点i和j（i和j都小于k），则该环的长度为：dist[i][j] + g[j][k] + g[k][i]，循环到k的时候，dist[i][j]表示的是i到j的经过的顶点编号小于k的最短路，所以正确性很显然，由于i、j、k都不相同，所以环上至少是3个点。

 1 #include <iostream>

 2 #include <cstring>

 3 #include <cstdio>

 4 using namespace std;

 5 

 6 const int INF = 999999;

 7 const int N = 101;

 8 int dist[N][N];

 9 int g[N][N];

10 int n, m, ans;

11 

12 void floyd()

13 {

14     for ( int i = 1; i <= n; i++ )

15     {

16         for ( int j = 1; j <= n; j++ )

17         {

18             dist[i][j] = g[i][j];

19         }

20         dist[i][i] = g[i][i] = 0;

21     }

22     ans = INF;

23     for ( int k = 1; k <= n; k++ )

24     {

25         for ( int i = 1; i < k; i++ )

26         {

27             for ( int j = i + 1; j < k; j++ )

28             {

29                 int tmp = dist[i][j] + g[i][k] + g[k][j];

30                 if ( tmp < ans ) ans = tmp;

31             }

32         }

33         for ( int i = 1; i <= n; i++ )

34         {

35             for ( int j = 1; j <= n; j++ )

36             {

37                 int tmp = dist[i][k] + dist[k][j];

38                 if ( tmp < dist[i][j] )

39                 {

40                     dist[i][j] = tmp;

41                 }

42             }

43         }

44     }

45 }

46 

47 int main ()

48 {

49     while ( scanf("%d%d", &n, &m) != EOF )

50     {

51         for ( int i = 1; i <= n; i++ )

52         {

53             for ( int j = 1; j <= n; j++ )

54             {

55                 g[i][j] = INF;

56             }

57         }

58         while ( m-- )

59         {

60             int a, b, c;

61             scanf("%d%d%d", &a, &b, &c);

62             if ( c < g[a][b] )

63             {

64                 g[a][b] = g[b][a] = c;

65             }

66         }

67         floyd();

68         if ( ans == INF )

69         {

70             printf("It's impossible.\n");

71         }

72         else

73         {

74             printf("%d\n", ans);

75         }

76     }

77     return 0;

78 }