HDU 4411

费用流

建图见下面代码，

解释下这条加边addedge(2*v+1,2*v+2,k,0);

费用流第一遍跑肯定是跑含有v条负无穷的边。

如果以后跑反向边是对第一次跑n条负无穷的边的优化，如果没有优化就干脆不出动警力

#include<cstdio>
#include<cstring>
#include<queue>
#define N 300
#define inf -100000000
using namespace std;
typedef long long ll;
int n,cnt;
int head[N],pre[N],vis[N];
ll dis[N];
int map[110][110];
ll ans;
struct Edge{
    int u,v,c,next;
    ll w;
}edge[40010];

void init(){
    memset(head,-1,sizeof(head));
    memset(map,-1,sizeof(map));
    for(int i=0;i<n/2;i++)
        map[i][i]=0;
    cnt=0;
}
void addedge(int u,int v,int cap,int cost){
    edge[cnt].u=u;
    edge[cnt].v=v;
    edge[cnt].c=cap;
    edge[cnt].w=cost;
    edge[cnt].next=head[u];
    head[u]=cnt++;
    edge[cnt].u=v;
    edge[cnt].v=u;
    edge[cnt].c=0;
    edge[cnt].w=-cost;
    edge[cnt].next=head[v];
    head[v]=cnt++;
}
bool spfa(){
    int i,j;
    queue<int>q;
    q.push(0);
    for(i=1;i<=n;i++){
        dis[i]=-inf;
        vis[i]=0;
    }
    dis[0]=0,vis[0]=1;
    while(!q.empty()){
        int u=q.front();
        q.pop();
        vis[u]=0;
        for(i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].v;
            if(edge[i].c && dis[v] > dis[u]+edge[i].w){
                dis[v]=dis[u]+edge[i].w;
                pre[v]=i;
                if(!vis[v]){
                    vis[v]=1;
                    q.push(v);
                }
            }
        }
    }
    if(dis[n]==-inf)return 0;
    return 1;
}
void end(){
    int u,p,cap=-1;
    for(u=n;u;u=edge[p].u){
        p=pre[u];
        if(cap==-1 || cap>edge[p].c)
            cap=edge[p].c;
    }
    for(u=n;u;u=edge[p].u){
        p=pre[u];
        edge[p].c-=cap;
        edge[p^1].c+=cap;
        ans+=cap*edge[p].w;
    }
}
int main(){
    int v,e,k,i,j,p;
    int u,vv,w;
    while(scanf("%d %d %d",&v,&e,&k)){
        if(v==0 && e==0 && k==0)break;
        n=2*v+2;
        init();
        for(i=1;i<=e;i++){
            scanf("%d %d %d",&u,&vv,&w);
            if(map[u][vv]==-1 || map[u][vv]>w)
                map[u][vv]=map[vv][u]=w;
        }
        for(p=0;p<=v;p++)
            for(i=0;i<=v;i++){
                if(map[i][p]==-1)continue;
                for(j=0;j<=v;j++){
                    if(map[p][j]==-1)continue;
                    if(map[i][j]==-1 || map[i][j]>map[i][p]+map[p][j])
                        map[j][i]=map[i][j]=map[i][p]+map[p][j];
                }
            }
        addedge(0,2*v+1,k,0);
        addedge(2*v+1,2*v+2,k,0);
        for(i=1;i<=v;i++){
            addedge(2*v+1,i*2-1,-inf,map[0][i]);
            addedge(i*2,n,-inf,map[i][0]);
            addedge(2*i-1,2*i,1,inf);
            for(j=i+1;j<=v;j++)
                addedge(i*2,j*2-1,-inf,map[i][j]);
        }
        ans=0;
        while(spfa())
            end();
        printf("%lld\n",ans-v*inf);
    }
    return 0;
}