UVA1486 Transportation 费用流 拆边。

 

#include <iostream>
#include <cstdio>
#include <cmath>
#include <queue>
#include <cstring>
using namespace std;
const int maxm = 50000*4;
const int maxn = 110;
struct node
{
    int v,cost,flow,next;//v表示指向的下一个顶点，a表示系数，flow表示可以过的流量
}edge[maxm];
int head[maxn],dis[maxn],pre[maxn],cur[maxn],vis[maxn],aug[maxn];
int s,t,v,n,m,k,id,flow;
void add_edge(int u,int v,int flow,int cost){
    edge[id].v = v;edge[id].cost = cost;edge[id].flow = flow;edge[id].next = head[u];head[u] = id++;
    edge[id].v = u;edge[id].cost = -cost;edge[id].flow = 0;edge[id].next = head[v];head[v] = id++;
}
int min(int x,int y){
    return x < y ? x : y;
}
void init(){
    s = 0,t = n+1;
    memset(head,-1,sizeof(head));id = 0;
    int u,v,a,flow;

    while( m-- ){
        scanf("%d%d%d%d",&u,&v,&a,&flow);
        for(int i = 1; i <= flow; i++)//因为边很少，所以可以拆边
        add_edge(u,v,1,i*i*a - a*(i-1)*(i-1));//每增加一条边，费用增加
    }
    //源点流出的流量为k，汇点流入的流量为k
    add_edge(0,1,k,0);
    add_edge(n,n+1,k,0);
}
int spfa(){
    memset(dis,-1,sizeof(dis));
    memset(vis,0,sizeof(vis));
    memset(aug,-1,sizeof(aug));
    queue<int>que;
    aug[s] = (1<<30) -1;
    dis[s] = 0;vis[s] = 1;pre[s] = s;
    que.push(s);
    while( !que.empty()){
        int u = que.front();
        que.pop();
        vis[u] = 0;
        for(int id = head[u]; id != -1; id = edge[id].next)
        {
            int v = edge[id].v;
            if( edge[id].flow > 0)
            {
                int MIN = min(aug[u],edge[id].flow);
                if(dis[v] == -1 || dis[v] > dis[u] + edge[id].cost)
                {
                    dis[v] = dis[u] + edge[id].cost;
                    pre[v] = u;cur[v] = id;
                    aug[v] = MIN;
                    // cout << v << " " << aug[v] << endl;
                    if(!vis[v] ){
                        vis[v] = 1;
                        que.push(v);
                    }
                }
            }
        }
    }
    if( dis[t] == -1 )return 0;
    return 1;
}
int get_max(){

    int mincost = 0;
    while(spfa() ){
          mincost += dis[t];
        k -= aug[t];
        int now = t;
        while( now != s){
            edge[cur[now]].flow -= aug[t];
            edge[cur[now]^1].flow += aug[t];
            now = pre[now];
        }
    }
    if(k > 0)return -1;
    return mincost;
}
int main(){
   // freopen("in.txt","r",stdin);
    while(~scanf("%d%d%d",&n,&m,&k)){
        init();
        printf("%d\n",get_max());
    }
    return 0;
}