网络流二·最大流最小割定理 HihoCoder - 1378

网络流二·最大流最小割定理

 HihoCoder - 1378

 

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3 const int maxv = 1010;
  4 const int maxe = 20010;
  5 const int inf = 0x3f3f3f3f;
  6 struct Edge{
  7     int u, v, nex;
  8     int cap, flow;
  9     Edge(int u=0, int v=0, int nex=0, int cap=0, int flow=0):
 10         u(u), v(v), nex(nex), cap(cap), flow(flow){}
 11 }e[maxe<<1];
 12 int head[maxv];
 13 int cnt;
 14 void init(){
 15     memset(head, -1, sizeof(head));
 16     cnt = 0;
 17 }
 18 
 19 void add(int u, int v, int cap){
 20     e[cnt] = Edge(u, v, head[u], cap, 0);
 21     head[u] = cnt++;
 22     e[cnt] = Edge(v, u, head[v], 0, 0);
 23     head[v] = cnt++;
 24 }
 25 
 26 int d[maxv], num[maxv], cur[maxv], p[maxv];
 27 int vis[maxv];
 28 int S, T;
 29 int N;
 30 
 31 void bfs(){
 32     memset(d, -1, sizeof(d));
 33     memset(vis, 0, sizeof(vis));
 34     queue<int> q;
 35     q.push(T);
 36     vis[T] = 1;
 37     d[T] = 0;
 38     while(!q.empty()){
 39         int u = q.front();
 40         q.pop();
 41         for(int i = head[u]; ~i; i = e[i].nex){
 42             int id = i&(-2);  //正边
 43             int v = e[id].u;
 44             if(!vis[v] && e[id].cap > e[id].flow){
 45                 vis[v] = 1;
 46                 d[v] = d[u] + 1;
 47                 q.push(v);
 48             }
 49         }
 50     }
 51 }
 52 
 53 int augment(){
 54     int u = T;
 55     int a = inf;
 56     while(u!=S){
 57         int id = p[u];
 58         a = min(a, e[id].cap - e[id].flow);
 59         u = e[id].u;
 60     }
 61     u = T;
 62     while(u!=S){
 63         int id = p[u];
 64         e[id].flow += a;
 65         e[id^1].flow -= a;
 66         u = e[id].u;
 67     }
 68     return a;
 69 }
 70 
 71 int ISAP(){
 72     bfs();
 73     int flow = 0;
 74     memset(num, 0, sizeof(num));
 75     for(int i = 0; i < N; i++){
 76         cur [i] = head[i];
 77         if(~d[i]) num[d[i]]++;
 78     }
 79     int u = S;
 80     while(d[S] < N){
 81         if(u == T){
 82             flow += augment();
 83             u = S;
 84         }
 85         int ok = 0;
 86         for(int i = cur[u]; ~i; i = e[i].nex){
 87             int v = e[i].v;
 88             if(d[u] == d[v]+1 && e[i].cap > e[i].flow){
 89                 p[v] = i;
 90                 ok = 1;
 91                 cur[u] = i;
 92                 u = v;
 93                 break;
 94             }
 95         }
 96         if(!ok){
 97             int m = N-1;
 98             for(int i = head[u]; ~i; i = e[i].nex){
 99                 if(e[i].cap > e[i].flow && ~d[e[i].v]) m = min(m, d[e[i].v]);
100             }
101             if(--num[d[u]] == 0) break;
102             num[d[u]=m+1]++;
103             cur[u] = head[u];
104             if(u != S) u = e[p[u]].u;
105         }
106     }
107     return flow;
108 }
109 vector<int> V;
110 void dfs(int u){
111     for(int i = head[u]; ~i; i = e[i].nex){
112         int v = e[i].v;
113         if(!vis[v]&&e[i].flow < e[i].cap){
114             V.push_back(v);
115             vis[v] = 1;
116             dfs(v);
117         }
118     }
119 }
120 int main(){
121     init();
122     int n, m;
123     scanf("%d %d", &n, &m);
124     int u, v, cap;
125     for(int i = 0; i < m; i++){
126         scanf("%d %d %d", &u, &v, &cap);
127         u--;v--;
128         add(u, v, cap);
129     }
130     S = 0;
131     T = n-1;
132     N = n;
133     int ans = ISAP();
134     V.push_back(S);
135     memset(vis, 0, sizeof(vis));
136     vis[S] = 1;
137     dfs(S);
138     printf("%d %d\n%d",ans, V.size(), V[0]+1);
139     for(int i = 1; i < V.size(); i++){
140         printf(" %d", V[i]+1);
141     }
142     puts("");
143 }

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转载于:https://www.cnblogs.com/yijiull/p/7630978.html