Record 3.23 - Negative ring

Seek common method negative ring based SPFA:
① number of statistics for each point into the team, if the team a point n times, then there is a negative ring.
② side of the current shortest path statistics for each point contained, if the number of edges in the shortest path comprises a point greater than equal to n, then there is a negative ring.

The second method is usually used.

 1 bool spfa()
 2 {
 3     memset(dist, 0, sizeof dist);
 4     memset(cnt, 0, sizeof cnt);
 5     memset(st, 0, sizeof st);
 6 
 7     int hh = 0, tt = 0;
 8     for (int i = 1; i <= n; i ++ )
 9     {
10         q[tt ++ ] = i;
11         st[i] = true;
12     }
13 
14     while (hh != tt)
15     {
16         int t = q[hh ++ ];
17         if (hh == N) hh = 0;
18         st[t] = false;
19 
20         for (int i = h[t]; ~i; i = ne[i])
21         {
22             int j = e[i];
23             if (dist[j] > dist[t] + w[i])
24             {
25                 dist[j] = dist[t] + w[i];
26                 cnt[j] = cnt[t] + 1;
27                 if (cnt[j] >= n) return true;
28                 if (!st[j])
29                 {
30                     q[tt ++ ] = j;
31                     if (tt == N) tt = 0;
32                     st[j] = true;
33                 }
34             }
35         }
36     }
37 
38     return false;
39 }

\frac{\sum_{i = 1}^{n}f_{i}}{\sum_{i = 1}^{n}t_{i}} > Mid