P2604 [ZJOI2010]网络扩容 | 建平行边

标签：now P2604 int flow ZJOI2010 edge maxn 行边 dis

本来的思路是纯纯地打一个大暴力

在残余网络上跑spfa，每跑出一条增广路就是当前能扩容的最小花费

然后k<=10,只需要跑最多十次:)

正解是建平行边啦，容量为inf，费用为扩容费用，起到的效果是等价的~

#include<bits/stdc++.h>
using namespace std;
const int maxn=100010;
const int inf=INT_MAX;
bool vis[maxn];
int n,m,c,w,k,s,t,x,y,z,f,dis[maxn],pre[maxn],last[maxn],flow[maxn],maxflow,mincost;
//dis最小花费;pre每个点的前驱；last每个点的所连的前一条边；flow源点到此处的流量 
struct Edge{
    int to,next,flow,dis;//flow流量 dis花费 
}edge[maxn];
int head[maxn],num_edge; 
queue <int> q;

void add_edge(int from,int to,int flow,int dis)
{
    edge[++num_edge].next=head[from];
    edge[num_edge].to=to;
    edge[num_edge].flow=flow;
    edge[num_edge].dis=dis;
    head[from]=num_edge;
}

bool spfa(int s,int t)
{
    memset(dis,0x7f,sizeof(dis));
    memset(flow,0x7f,sizeof(flow));
    memset(vis,0,sizeof(vis));
    q.push(s); vis[s]=1; dis[s]=0; pre[t]=-1;
    
    while (!q.empty())
    {
        int now=q.front();
        q.pop();
        vis[now]=0;
        for (int i=head[now]; i!=-1; i=edge[i].next)
        {
            if (edge[i].flow>0 && dis[edge[i].to]>dis[now]+edge[i].dis)//正边 
            {
                dis[edge[i].to]=dis[now]+edge[i].dis;
                pre[edge[i].to]=now;
                last[edge[i].to]=i;
                flow[edge[i].to]=min(flow[now],edge[i].flow);//
                if (!vis[edge[i].to])
                {
                    vis[edge[i].to]=1;
                    q.push(edge[i].to);
                }
            }
        }
    }
    return pre[t]!=-1;
}

void MCMF()
{
    while (spfa(s,t))
    {
        int now=t;
        maxflow+=flow[t];
        mincost+=flow[t]*dis[t];
        while (now!=s)
        {//从源点一直回溯到汇点 
            edge[last[now]].flow-=flow[t];//flow和dis容易搞混 
            edge[last[now]^1].flow+=flow[t];
            now=pre[now];
        }
    }
}
int ix[maxn],iy[maxn],ic[maxn],iw[maxn];
int main()
{
    //freopen("lys.in","r",stdin);
    memset(head,-1,sizeof(head));num_edge=-1;//初始化 
    cin>>n>>m>>k;
    for (int i=1; i<=m; i++)
    {   cin>>x>>y>>c>>w;
        add_edge(x,y,c,0); add_edge(y,x,0,0);
        // u,v,flow,cost 
        //反边的流量为0，花费是相反数 
        ix[i]=x;iy[i]=y;ic[i]=c;iw[i]=w;
    }
    s=1,t=n;
    MCMF();
    cout<<maxflow<<" ";
    t=n+1;
    add_edge(n,t,k,0);
    add_edge(t,n,0,0);
    for(int i=1;i<=m;i++){
        add_edge(ix[i],iy[i],inf,iw[i]); add_edge(iy[i],ix[i],0,-iw[i]);
    }
    MCMF();
    cout<<mincost<<endl;
    return 0;
}

 

标签：now,P2604,int,flow,ZJOI2010,edge,maxn,行边,dis
From： https://www.cnblogs.com/liyishui2003/p/16814740.html