UVALive-5095 Transportation （最小费用流+拆边）

题目大意：有n个点，m条单向边。要运k单位货物从1到n，但是每条道路上都有一个参数ai，表示经这条路运送x个单位货物需要花费ai*x*x个单位的钱。求最小费用。

题目分析：拆边。例如：u到v的容量为5，则拆成容量均为1，单位费用分别为1,3,5,7,9的5条边。求流恰好能满足运输需求时的最小费用即可。

 

代码如下：

# include<iostream>
# include<cstdio>
# include<cmath>
# include<string>
# include<vector>
# include<list>
# include<set>
# include<map>
# include<queue>
# include<cstring>
# include<algorithm>
using namespace std;

# define LL long long
# define REP(i,s,n) for(int i=s;i<n;++i)
# define CL(a,b) memset(a,b,sizeof(a))
# define CLL(a,b,n) fill(a,a+n,b)

const double inf=1e30;
const int INF=1<<30;
const int N=5005;

int k;

struct Edge
{
    int fr,to,cap,fw,cost;
    Edge(int fr,int to,int cap,int fw,int cost){
        this->fr=fr;
        this->to=to;
        this->cap=cap;
        this->fw=fw;
        this->cost=cost;
    }
};
struct MCMF
{
    vector<Edge>edges;
    vector<int>G[N];
    int s,t,n;
    int inq[N];
    int p[N];
    int a[N];
    int d[N];

    void init(int n,int s,int t)
    {
        this->n=n;
        this->s=s,this->t=t;
        for(int i=0;i<n;++i) G[i].clear();
        edges.clear();
    }

    void addEdge(int u,int v,int cap,int cost)
    {
        edges.push_back(Edge(u,v,cap,0,cost));
        edges.push_back(Edge(v,u,0,0,-cost));
        int m=edges.size();
        G[u].push_back(m-2);
        G[v].push_back(m-1);
    }

    bool bellmanFord(int &flow,int &cost)
    {
        fill(d,d+n,INF);
        memset(inq,0,sizeof(inq));
        d[s]=0,inq[s]=1,p[s]=0,a[s]=INF;

        queue<int>q;
        q.push(s);
        while(!q.empty())
        {
            int x=q.front();
            q.pop();
            inq[x]=0;
            for(int i=0;i<G[x].size();++i){
                Edge &e=edges[G[x][i]];
                if(e.cap>e.fw&&d[e.to]>d[x]+e.cost){
                    d[e.to]=d[x]+e.cost;
                    p[e.to]=G[x][i];
                    a[e.to]=min(a[x],e.cap-e.fw);
                    if(!inq[e.to]){
                        inq[e.to]=1;
                        q.push(e.to);
                    }
                }
            }
        }
        if(d[t]==INF) return false;
        flow+=a[t];
        cost+=d[t]*a[t];
        for(int u=t;u!=s;u=edges[p[u]].fr){
            edges[p[u]].fw+=a[t];
            edges[p[u]^1].fw-=a[t];
        }
        return true;
    }

    void minCost(int &flow,int &cost)
    {
        flow=cost=0;
        while(bellmanFord(flow,cost))
            if(flow>=k) break;
    }
};
MCMF cf;

int n,m;

int main()
{
    while(~scanf("%d%d%d",&n,&m,&k))
    {
        cf.init(n+1,1,n);
        int a,b,c,d;
        while(m--)
        {
            scanf("%d%d%d%d",&a,&b,&c,&d);
            int cnt=1;
            while(d--)
            {
                cf.addEdge(a,b,1,cnt*c);
                cnt+=2;
            }
        }
        int flow,cost;
        cf.minCost(flow,cost);
        if(flow>=k) printf("%d\n",cost);
        else printf("-1\n");
    }
    return 0;
}