HOJ 2543 Stone IV

传说中的凸费用流问题，对于一条有c1容量免费，超出容量部分增加的每单位流量费用为c2的边(u,v)，在原图中拆成两条边(u,v,c1,0),(u,v,INF,c2)。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <queue>
#define maxn 1010
#define maxm 200010
#define INF 0x3f3f3f3f
using namespace std;
typedef long long LL;
int N,M,C,P;
struct MCMF{
    int src,sink,e,n;
    int first[maxn];
    int cap[maxm],cost[maxm],v[maxm],next[maxm];
    bool flag;
    void init(){
        e = 0;
        memset(first,-1,sizeof(first));
    }

    void add_edge(int a,int b,int cc,int ww){
        //printf("add:%d to %d,cap = %d,cost = %d
",a,b,cc,ww);
        cap[e] = cc;cost[e] = ww;v[e] = b;
        next[e] = first[a];first[a] = e++;
        cap[e] = 0;cost[e] = -ww;v[e] = a;
        next[e] = first[b];first[b] = e++;
    }

    int d[maxn],pre[maxn],pos[maxn];
    bool vis[maxn];

    bool spfa(int s,int t){
        memset(pre,-1,sizeof(pre));
        memset(vis,0,sizeof(vis));
        queue<int> Q;
        for(int i = 0;i <= n;i++)   d[i] = INF;
        Q.push(s);pre[s] = s;d[s] = 0;vis[s] = 1;
        while(!Q.empty()){
            int u = Q.front();Q.pop();
            vis[u] = 0;
            for(int i = first[u];i != -1;i = next[i]){
                if(cap[i] > 0 && d[u] + cost[i] < d[v[i]]){
                    d[v[i]] = d[u] + cost[i];
                    pre[v[i]] = u;pos[v[i]] = i;
                    if(!vis[v[i]])  vis[v[i]] = 1,Q.push(v[i]);
                }
            }
        }
        return pre[t] != -1;
    }

    LL Mincost;
    int Maxflow;

    int MinCostFlow(int s,int t,int nn){
        Mincost = 0,Maxflow = 0,n = nn;
        while(spfa(s,t)){
            LL min_f = INF;
            for(int i = t;i != s;i = pre[i])
                if(cap[pos[i]] < min_f) min_f = cap[pos[i]];
            Mincost += d[t] * min_f;
            Maxflow += min_f;
            if(Mincost > C){
                Maxflow -= ceil((Mincost - C) * 1.0 / d[t]);
                break;
            }
            for(int i = t;i != s;i = pre[i]){
                cap[pos[i]] -= min_f;
                cap[pos[i]^1] += min_f;
            }
        }
        return Mincost;
    }
};


MCMF g;

int main(){
    int T;
    scanf("%d",&T);
    while(T--){
        scanf("%d%d%d%d",&N,&M,&C,&P);
        g.init();
        int src = N+1,sink = 2;
        g.add_edge(src,1,INF,P);
        for(int i = 1;i <= M;i++){
            int u,v,c1,c2;
            scanf("%d%d%d%d",&u,&v,&c1,&c2);
            u++;v++;
            g.add_edge(u,v,c1,0);
            g.add_edge(v,u,c1,0);
            g.add_edge(u,v,INF,c2);
            g.add_edge(v,u,INF,c2);
        }
        g.MinCostFlow(src,sink,src);
        printf("%d
",g.Maxflow);
    }
    return 0;
}