HDU 3879 base station (maximum weighted closed subgraph)

The classic example seems to be able to be converted to maxflow (N, N + M). At present, we can barely understand the practice of maxflow (n + M, N + M.

 

Question: Input n vertices and m edges in an undirected graph. The vertex weight is negative, the edge weight is positive, and the weight of the output largest weight closed subgraph.

(Largest weighted closed subgraph: the successor of each point in the graph must also be shown in the figure)

 

Architecture strategy: View edges as points (some questions have no right, and the modeling is slightly different ),

Connect Three edges (S, N + I, W) to the original edge e [I] (U, V, W), (N + I, U, INF ), (N + I, V, INF ).

Connect one edge (v, T, P [v]) to the original vertex v.

That is, the positive weight point is connected to the source point, and the negative weight point is connected to the sink point.

Sum-maxflow is the answer.

Obviously, the SAP graph has n + m + 2 and (n + M * 3) * 2.

For more information about the derivation, see the previous documents or other websites.

#include <cstdio>#include <cstring>#include <iostream>#include <cmath>#include <algorithm>#include <vector>#include <string>#include <set>#include <queue>using namespace std;#define ll long long#define MP make_pair#define mxn 56000#define mxe (51000*4*2)#define inf 1e9#define eps 1e-8struct SAP{    int dis[mxn],pre[mxn],gap[mxn],arc[mxn];    int f[mxe],cap[mxe];    int head[mxn],nxt[mxe],vv[mxe],e;    void init(){e=0;memset(head,-1,sizeof(head));}    void add(int u,int v,int c){        vv[e]=v,cap[e]=c,nxt[e]=head[u],head[u]=e++;        vv[e]=u,cap[e]=0,nxt[e]=head[v],head[v]=e++;    }    ll max_flow(int s,int t,int n){        int q[mxn],j,mindis;        ll ans=0;        int ht=0,tl=1,u,v;        int low;        bool found,vis[mxn];        memset(dis,0,sizeof(dis));        memset(gap,0,sizeof(gap));        memset(vis,0,sizeof(vis));        memset(arc,-1,sizeof(arc));        memset(f,0,sizeof(f));        q[0]=t;vis[t]=true;dis[t]=0;gap[0]=1;        while(ht<tl){            u=q[ht++];            for(int i=head[u];i!=-1;i=nxt[i]){                v = vv[i];                if(!vis[v]){                    vis[v]=true;                    dis[v]=dis[u]+1;                    q[tl++]=v;                    gap[dis[v]]++;                    arc[v]=head[v];                }            }        }        u=s;low=inf;pre[s]=s;        while(dis[s]<n){            found=false;            for(int &i=arc[u];i!=-1;i=nxt[i]){                if(dis[vv[i]]==dis[u]-1 && cap[i]>f[i]){                    found=true;v=vv[i];                    low=min(low,cap[i]-f[i]);                    pre[v]=u;u=v;                    if(u==t){                        while(u!=s){                            u=pre[u];                            f[arc[u]]+=low;                            f[arc[u]^1]-=low;                        }                        ans+=low;low=inf;                    }                    break;                }            }            if(found) continue;            mindis=n;            for(int i=head[u];i!=-1;i=nxt[i]){                if(mindis>dis[vv[i]] && cap[i]>f[i]){                    mindis=dis[vv[j=i]];                    arc[u]=i;                }            }            if(--gap[dis[u]]==0) return ans;            dis[u]=mindis+1;            gap[dis[u]]++;            u=pre[u];        }        return ans;    }}sap;int p[5050];int main(){int n,m;while(~scanf("%d%d",&n,&m)){for(int i=1;i<=n;++i) scanf("%d",p+i);ll sum = 0;sap.init();        for(int i=1;i<=m;++i){int a,b,c;scanf("%d%d%d",&a,&b,&c);sap.add(n+m+1,n+i,c);sap.add(n+i,a,inf);sap.add(n+i,b,inf);sum+=c;        }        for(int i=1;i<=n;++i)sap.add(i,n+m+2,p[i]);ll mf = sap.max_flow(n+m+1,n+m+2,n+m+2);printf("%I64d\n",sum-mf);    }    return 0;}

 

HDU 3879 base station (maximum weighted closed subgraph)