zoj Reactor Cooling

Reactor Cooling

无源汇上下界最大流问题。

1、流量平衡。

2、满足上下界

模板题。

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

const int MAXN = 200000 + 10;
const int INF = 1 << 30;
struct Edge{
   int from,to,cap,flow;
   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 d[MAXN],cur[MAXN];
int src,sink,N,M;
bool vst[MAXN];

int b[MAXN],du[MAXN];
int sum;

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

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

    while(!Q.empty()){
        int x = Q.front(); Q.pop();
        for(int i = 0;i < 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 < 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,sizeof(cur));
        flow += DFS(src,INF);
    }
    return flow;
}

void solve(){
   int flow = maxFlow();

   if(flow != sum){
      puts("NO");
      return;
   }

   puts("YES");
   for(int i = 0;i < M;++i){
      printf("%dn",edges[i<<1].flow + b[i]);
   }
}

int main()
{
//    freopen("Input.txt","r",stdin);

    int T;
    scanf("%d",&T);
    while(T--){
        scanf("%d%d",&N,&M);
        init();
        int u,v,c;
        memset(du,sizeof(du));
        for(int i = 0;i < M;++i){
            scanf("%d%d%d%d",&u,&v,&b[i],&c);
            addEdge(u,c - b[i]);
            du[u] -= b[i];
            du[v] += b[i];
        }
        sum = 0;
        for(int i = 1;i <= N;++i){
            if(du[i] > 0){
                addEdge(src,i,du[i]);
                sum += du[i];
            }
            else
                addEdge(i,-du[i]);
        }

        solve();
    }
    return 0;
}

（编辑：李大同）

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