最大流(push-relable)算法
预流推进算法(push-relable)，时间复杂度O(V^2E)
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\n", Push_Relable());
112 }
113 return 0;
114 }
