网络流二·最大流最小割定理（Dinic模板+dfs/bfs找S集合模板）

Posted 2021-02-22 wsy107316

网络流二·最大流最小割定理

 

 AC_Code:

  1 #include <bits/stdc++.h>
  2 #include <ctime>
  3 #include <algorithm>
  4 #include <random>
  5 using namespace std;
  6 typedef long long ll;
  7 typedef unsigned long long ull;
  8 const int maxn = 2e4+10;
  9 const int inf = 0x3f3f3f3f;
 10 #define gok ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
 11 #define pii pair<int,int>
 12 #define fi first
 13 #define se second
 14 #define pb push_back
 15 #define rep(i,first,second) for(int i=first;i<=second;i++)
 16 #define dep(i,first,second) for(int i=first;i>=second;i--)
 17 #define erep(i,u) for(int i=head[u];~i;i=e[i].nxt)
 18 
 19 struct node{int to,nxt,c;}e[maxn<<1];
 20 int head[maxn<<1],tot,dep[maxn];
 21 bool vis[maxn];
 22 int n,m,cnt;
 23 
 24 void add(int u,int v,int w){
 25     e[tot].to=v;
 26     e[tot].c=w;
 27     e[tot].nxt=head[u];
 28     head[u]=tot++;
 29 }
 30 void addedge(int u,int v,int w){add(u,v,w),add(v,u,0);}
 31 bool bfs(int st,int ed){
 32     memset(dep,-1,sizeof(dep));
 33     queue<int>que;
 34     while( !que.empty()) que.pop();
 35     que.push(st);
 36     dep[st]=0;
 37     int u;
 38     while( !que.empty()){
 39         u=que.front();que.pop();
 40         erep(i,u){
 41             int v=e[i].to;
 42             if( dep[v]==-1 && e[i].c>0 ){
 43                 dep[v]=dep[u]+1;
 44                 que.push(v);
 45                 if( v==ed ) return true;
 46             }
 47 
 48         }
 49     }
 50     return dep[ed]!=-1;
 51 }
 52 int dfs(int st,int ed,int flow){
 53     if( st==ed || flow==0 ) return flow;
 54     int curr=0;
 55     erep(i,st){
 56         int v=e[i].to;
 57         int val=e[i].c;
 58         if( dep[st]+1==dep[v] && val>0 ){
 59             int d=dfs(v,ed,min(val,flow));
 60             if( d>0 ){
 61                 e[i].c-=d;e[i^1].c+=d;
 62                 curr+=d;flow-=d;
 63                 if( flow==0 ) break;
 64             }
 65         }
 66     }
 67     if( curr==0 ) dep[st]=inf;
 68     return curr;
 69 }
 70 
 71 int Dinic(int st,int ed){
 72     int flow=0;
 73     while( bfs(st,ed) ){
 74         flow+=dfs(st,ed,inf);
 75     }
 76     return flow;
 77 }
 78 /*
 79 void new_bfs(int st){               //bfs找S
 80     memset(vis,0,sizeof(vis));
 81     dep[st]=0;
 82     vis[st]=1;
 83     queue<int>que;
 84     while( !que.empty()) que.pop();
 85     que.push(st);
 86     while( !que.empty()){
 87         int u=que.front();que.pop();
 88         erep(i,u){
 89             int v=e[i].to;
 90             int val=e[i].c;
 91             if( !vis[v] && val>0){
 92                 vis[v]=1;
 93                 dep[v]=dep[u]+1;
 94                 que.push(v);
 95             }
 96         }
 97     }
 98 }
 99 */
100 void new_dfs(int u){                //dfs找S
101     vis[u]=1;
102     erep(i,u){
103         int v=e[i].to;
104         int val=e[i].c;
105         if( !vis[v] && val>0 ){
106             new_dfs(v);
107         }
108     }
109 }
110 
111 int main()
112 {
113     memset(head,-1,sizeof(head));
114     tot=0;
115     scanf("%d%d",&n,&m);
116     rep(i,1,m){
117         int u,v,cap;
118         scanf("%d%d%d",&u,&v,&cap);
119         addedge(u,v,cap);
120     }
121     int flow=Dinic(1,n);
122     new_dfs(1);
123 
124     printf("%d ",flow);
125     rep(i,1,n){
126         if( vis[i] ) cnt++;
127     }
128     printf("%d
",cnt);
129     rep(i,1,n){
130         if( vis[i] ) printf("%d ",i);
131     }
132     printf("
");
133     return 0;
134 }