BZOJ 1834: [ZJOI2010]network 网络扩容 最小费用流_最大流_残量网络

对于第一问，跑一遍最大流即可.

对于第二问，在残量网络上的两点间建立边 <u,v>，容量为无限大，费用为扩充费用.

跑一遍最小费用流即可.

Code:

#include <vector>
#include <cstdio>
#include <queue>
#include <algorithm>
#include <cstring>
#define setIO(s) freopen(s".in","r",stdin)
#define inf 100000000
#define maxn 100000
#define ll long long
using namespace std;
struct Edges{
    int u,v,c,w;
}EDGE[maxn];
int n,m,k,s,t;
struct Edge{
    int from,to,cap,cost;
    Edge(int u,int v,int c,int f) : from(u),to(v),cap(c),cost(f){}
};
vector<int>G[maxn];
vector<Edge>edges;
void addedge(int u,int v,int c,int f){
    edges.push_back(Edge(u,v,c,f));
    edges.push_back(Edge(v,u,0,-f));
    int o = edges.size();
    G[u].push_back(o - 2);
    G[v].push_back(o - 1);
}
namespace Dinic{
    int d[maxn],vis[maxn];
    queue<int>Q;
    int BFS(){
        memset(vis,0,sizeof(vis));
        vis[s] = 1,d[s] = 0; Q.push(s);
        while(!Q.empty()){
            int u = Q.front(); Q.pop();
            int sz = G[u].size();
            for(int i=0;i<sz;++i) {
                Edge r = edges[G[u][i]];
                if(!vis[r.to] && r.cap > 0) {
                    d[r.to] = d[u] + 1;
                    vis[r.to] = 1;
                    Q.push(r.to);
                }
            }
        }
        return vis[t];
    }
    int current[maxn];
    int DFS(int x,int cur){
        if(x==t) return cur;
        int flow=0,f;
        int sz = G[x].size();
        for(int i=current[x];i<sz;++i) {
            int u = G[x][i];
            Edge r = edges[u];
            if(d[r.to] == d[x] + 1 && r.cap > 0){
                f = DFS(r.to,min(cur,r.cap));
                if(f > 0) {
                    flow += f;
                    cur -= f;
                    edges[u].cap -= f;
                    edges[u^1].cap += f;
                }
            }
            if(cur==0) break;
        }
        return flow;
    }
    int maxflow(){
        int flow=0;
        while(BFS()){
            memset(current,0,sizeof(current));
            flow += DFS(s,inf);
        }
        return flow;
    }
};
namespace MCMF{
    queue<int>Q;
    int d[maxn],inq[maxn];
    int flow2[maxn],a[maxn];
    long long ans;
    int SPFA(){
        for(int i=0;i<maxn;++i) d[i] = flow2[i] = inf;
        memset(inq,0,sizeof(inq));
        inq[s] = 1; d[s] = 0;
        Q.push(s);
        while(!Q.empty()){
            int u=Q.front();Q.pop(); inq[u] = 0;
            int sz = G[u].size();
            for(int i=0;i<sz;++i) {
                Edge r = edges[G[u][i]];
                if(r.cap > 0 && d[r.to] > d[u] + r.cost) {
                    d[r.to] = d[u] + r.cost;
                    a[r.to] = G[u][i];
                    flow2[r.to] = min(flow2[u],r.cap);
                    if(!inq[r.to]) {
                        inq[r.to] = 1;
                        Q.push(r.to);
                    }
                }
            }
        }
        if(flow2[t] == inf) return 0;
        int f = flow2[t];
        edges[a[t]].cap -= f, edges[a[t] ^ 1].cap += f;
        int u = edges[a[t]].from;
        while(u != s){
            edges[a[u]].cap -= f;
            edges[a[u]^1].cap += f;
            u = edges[a[u]].from;
        }
        ans += (ll)(d[t] * f);
        return 1;
    }
    long long  getcost(){
        while(SPFA());
        return ans;
    }
};
int main(){
    //setIO("input");
    scanf("%d%d%d",&n,&m,&k);
    s = 1, t = n;
    for(int i = 1;i <= m; ++i)  scanf("%d%d%d%d",&EDGE[i].u,&EDGE[i].v,&EDGE[i].c,&EDGE[i].w);
    for(int i = 1;i <= m; ++i)
        addedge(EDGE[i].u,EDGE[i].v,EDGE[i].c,0);
    printf("%d ",Dinic::maxflow());
    for(int i = 1;i <= m; ++i)
        addedge(EDGE[i].u,EDGE[i].v,inf,EDGE[i].w);
    s = 0 , t = n + 1;
    addedge(s,1,k,0);
    addedge(n,n+1,k,0);
    printf("%lld",MCMF::getcost());
    return 0;
}