sgu Flow construction

Flow construction

题目:

给出N个节点M条水管，要求在满足上下界的情况下。满足起点最小的流量。

算法：

这是最小流？？？？不知道。只知道用求解上下界最大流的方法就过了。

做这题收获了很多东西。知道了同一点的flow是真实的流量值，虽然以前在书上或论文中看到过，不过印象不深，但是经过这题深刻的懂了。就是这题输出的时候有点麻烦。。。要记录每次的路径，然后用我刚才说的那个，同一个点的flow是真实的流量值!!!!

#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <cstdio>
#include <cstring>
using namespace std;

const int INF = 1 << 28;
const int MAXN = 200 + 10;
///////////////////////////////////////

//上下界最小流

struct Edge{
    int from,to,cap,flow,cost;
    Edge(){};
    Edge(int _from,int _to,int _cap,int _flow)
        :from(_from),to(_to),cap(_cap),flow(_flow){};
};
vector<Edge> edges;
vector<int> G[MAXN];
int cur[MAXN],d[MAXN];
bool vst[MAXN];
int N,M,src,sink;

////////////////////////////////

//上下界网络流
int sum;
int in[MAXN],id[MAXN*MAXN],low[MAXN*MAXN];

void init(){
    src = N + 2; sink = src + 1;
    for(int i = 0;i <= sink;++i)
        G[i].clear();
    edges.clear();
}

void addEdge(int from,int to,int cap){
    edges.push_back(Edge(from,to,cap,0));
    edges.push_back(Edge(to,from,0,0));
    int sz = edges.size();
    G[from].push_back(sz - 2);
    G[to].push_back(sz - 1);
}

bool BFS(){
    memset(vst,0,sizeof(vst));
    queue<int> Q;
    vst[src] = 1;
    d[src] = 0;
    Q.push(src);

    while(!Q.empty()){
        int x = Q.front(); Q.pop();
        for(int i = 0;i < (int)G[x].size();++i){
            Edge& e = edges[G[x][i]];
            if(!vst[e.to] && e.cap > e.flow){
                vst[e.to] = 1;
                d[e.to] = d[x] + 1;
                Q.push(e.to);
            }
        }
    }

    return vst[sink];
}

int DFS(int x,int a){
    if(x == sink||a == 0)
        return a;

    int flow = 0,f;
    for(int& i = cur[x];i < (int)G[x].size();++i){
        Edge& e = edges[G[x][i]];
        if(d[e.to] == d[x] + 1&&(f = DFS(e.to,min(a,e.cap - e.flow))) > 0){
            e.flow += f;
            edges[G[x][i]^1].flow -= f;
            flow += f;
            a -= f;
            if(a == 0) break;
        }
    }
    return flow;
}

int maxFlow(){
   int flow = 0;
   while(BFS()){
       memset(cur,0,sizeof(cur));
       flow += DFS(src,INF);
   }
   return flow;
}

void solve(){
   for(int i = 1;i <= N;++i){
       if(in[i] > 0){
          sum += in[i];
          addEdge(src,i,in[i]);
       } else {
          addEdge(i,sink,-in[i]);
       }
   }

   sum -= maxFlow();
   addEdge(N,1,INF);   //是图变成无源无汇
   int flow = maxFlow();

   if(flow != sum){
       puts("Impossible");
       return;
   }

   int sz = edges.size();    //N --> 1 的容量
   printf("%d\n",edges[sz - 2].flow);  //反向弧的流量，即为正向真实流的流量!!!
   for(int i = 0;i < M;++i){
      if(low[i] > 0)
         printf("%d%c",low[i],i == M - 1 ? '\n':' ');
      else
         printf("%d%c",edges[id[i]].flow,i == M - 1 ? '\n':' ');
   }

}

int main()
{
    while(scanf("%d%d",&N,&M) == 2){
        init();
        int x,y,c,d;
        sum = 0;
        memset(in,0,sizeof(in));

        for(int i = 0; i < M;++i){
            scanf("%d%d%d%d",&x,&y,&c,&d);
            if(d == 0){              //流量没限制
               id[i] = edges.size();
               addEdge(x,y,c);

            } else {
               //sum += c;
               in[x] -= c;
               in[y] += c;
               low[i] = c;
              // addEdge(src,y,c);
               //id[i] = edges.size();   //反向弧的流量，即为正向真实流的流量!!!
               //addEdge(x,sink,c);
            }
        }

        solve();
    }
    return 0;
}