最大ストリームアルゴリズム

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プリフロー推進アルゴリズム(push-relable),時間複雑度O(V^2 E)

  
    
1 // The push-relable algorithm code due to CLRS chapter 26
2 #include < iostream >
3 #include < list >
4 using namespace std;
5 const int N = 100 ;
6 int n; // vertex number
7 int e[N]; // residual flow of the vertex
8 int h[N]; // height of the vertex
9 int c[N][N]; // capacity of the edge
10 int f[N][N]; // flow of the edge
11 list < int > ev; // excess flow vertex
12 list < int > edge[N]; // edge link list
13 bool flag[N]; // lable whether the vertex is in the flow list
14
15 inline void Push( int u, int v) // push flow from edge (u, v)
16 {
17 int df = min(e[u], c[u][v] - f[u][v]);
18 f[u][v] += df;
19 f[v][u] = - f[u][v];
20 e[u] -= df;
21 e[v] += df;
22 }
23
24 void Relable( int u) // re-lable heght of vertex u
25 {
26 h[u] = n * 2 - 1 ;
27 for (list < int > ::iterator iter = edge[u].begin(); iter != edge[u].end(); iter ++ )
28 {
29 if (c[u][ * iter] > f[u][ * iter] && h[ * iter] < h[u])
30 h[u] = h[ * iter];
31 }
32 h[u] ++ ;
33 }
34
35 void Discharge( int u) // discharge the residual flow of vertex u
36 {
37 list < int > ::iterator iter = edge[u].begin();
38 while (e[u] > 0 )
39 {
40 if (iter == edge[u].end())
41 {
42 Relable(u);
43 iter = edge[u].begin();
44 }
45 if (h[u] == h[ * iter] + 1 && c[u][ * iter] > f[u][ * iter])
46 {
47 Push(u, * iter);
48 if (e[ * iter] > 0 && ! flag[ * iter])
49 ev.push_back( * iter);
50 }
51 ++ iter;
52 }
53 }
54
55 void Init_PreFlow()
56 {
57 ev.clear();
58 h[ 0 ] = n;
59 e[ 0 ] = 0 ;
60 memset(flag, 0 , sizeof (flag));
61 memset(f, 0 , sizeof (f));
62 flag[ 0 ] = flag[n - 1 ] = true ;
63 for ( int u = 1 ; u < n; u ++ )
64 {
65 f[ 0 ][u] = c[ 0 ][u];
66 f[u][ 0 ] = - f[ 0 ][u];
67 e[u] = c[ 0 ][u];
68 if (e[u] > 0 && ! flag[u])
69 {
70 ev.push_back(u);
71 flag[u] = true ;
72 }
73 }
74
75 // construct link list
76 for ( int u = 0 ; u < n; u ++ )
77 for ( int v = u + 1 ; v < n; v ++ )
78 {
79 if (c[u][v] > 0 || c[v][u] > 0 )
80 {
81 edge[u].push_back(v);
82 edge[v].push_back(u);
83 }
84 }
85 }
86
87 int Push_Relable()
88 {
89 Init_PreFlow();
90 while ( ! ev.empty())
91 {
92 int u = ev.front();
93 Discharge(u);
94 ev.pop_front();
95 flag[u] = false ;
96 }
97 return e[n - 1 ];
98 }
99
100 int main()
101 {
102 int m, u, v, w;
103 while (scanf( " %d%d " , & m, & n) != EOF)
104 {
105 memset(c, 0 , sizeof (c));
106 for ( int i = 0 ; i < m; i ++ )
107 {
108 scanf( " %d%d%d " , & u, & v, & w);
109 c[u][v] = w;
110 }
111 printf( " Max Flow is %d
" , Push_Relable());
112 }
113 return 0 ;
114 }