最大流增广路(KM算法) HDOJ 1853 Cyclic Tour

转载

mob60475702c725 2015-07-20 19:52:00

 1 /*
 2     KM： 相比HDOJ_1533，多了重边的处理，还有完美匹配的判定方法
 3 */
 4 #include <cstdio>
 5 #include <cmath>
 6 #include <algorithm>
 7 #include <cstring>
 8 using namespace std;
 9 
10 const int MAXN = 1e2 + 10;
11 const int INF = 0x3f3f3f3f;
12 int x[MAXN], y[MAXN];
13 int w[MAXN][MAXN];
14 int visx[MAXN], visy[MAXN];
15 int ly[MAXN];
16 int n, m, d;
17 
18 bool DFS(int u) {
19     visx[u] = true;
20     for (int i=1; i<=n; ++i)   {
21         if (!visy[i] && x[u] + y[i] == w[u][i]) {
22             visy[i] = true;
23             if (ly[i] == -1 || DFS (ly[i])) {
24                 ly[i] = u;  return true;
25             }
26         }
27         else if (x[u] + y[i] > w[u][i]) d = min (d, x[u] + y[i] - w[u][i]);
28     }
29     return false;
30 }
31 
32 int KM(void)    {
33     for (int i=1; i<=n; ++i)   {
34         x[i] = -INF;
35         for (int j=1; j<=n; ++j)   {
36             x[i] = max (x[i], w[i][j]);            
37         }
38     }
39 
40     memset (ly, -1, sizeof (ly));
41     memset (y, 0, sizeof (y));
42     for (int i=1; i<=n; ++i)    {
43         while (true)    {
44             memset (visx, false, sizeof (visx));
45             memset (visy, false, sizeof (visy));
46             d = INF;
47             if (DFS (i))    break;
48             for (int i=1; i<=n; ++i)   {
49                 if (visx[i])    x[i] -= d;
50             }
51             for (int j=1; j<=n; ++j)   {
52                 if (visy[j])    y[j] += d;
53             }
54         }
55     }
56 
57     for (int i=1; i<=n; ++i)    {
58         if (ly[i] == -1 || w[ly[i]][i] == -INF) return -1;
59     }
60 
61     int res = 0;
62     for (int i=1; i<=n; ++i)   {
63         res += x[i] + y[i];
64     }
65 
66     return -res;
67 }
68 
69 int main(void)  {       //HDOJ 1853 Cyclic Tour
70     //freopen ("HDOJ_1853.in", "r", stdin);
71 
72     while (scanf ("%d%d", &n, &m) == 2) {
73         if (!n && !m)   break;
74         for (int i=1; i<=n; ++i)    {
75             for (int j=1; j<=n; ++j)    w[i][j] = -INF;
76         }
77         for (int i=1; i<=m; ++i)    {
78             int u, v, c;    scanf ("%d%d%d", &u, &v, &c);
79             if (-c > w[u][v])   w[u][v] = -c;
80         }
81         printf ("%d\n", KM ());
82     }
83 
84     return 0;
85 }