hdu Crazy Circuits

                                Crazy Circuits

 

题目：

   给出一个电路板，从+极出发到负极。现在给你电路板上的最小电流限制，要你在电流平衡的时候求得从正极出发的最小电流。

 

算法：

   很裸的有源汇最小流。安有源汇最大流做法后，先求出最大流。然后，通过添加 t-->s 容量INF，是其变成一个无源汇最小流问题，这样在跑一次最大流就是结果了。虽然没有严格证明是否正确，但是我用到现在，还没发现有错误的算法。

做题时in[]忘记清空了。找了半个小时！！！

 

/*   //!!!!!!!!!!!!!!   一定要注意清空初始化问题！！！！！！！！   */#include <iostream>#include <algorithm>#include <vector>#include <queue>#include <map>#include <cstdio>#include <cmath>#include <cstring>using namespace std;const int INF = 1 << 25;const int MAXN = 100 + 10;///////////////////////////////////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 src,sink,ss,tt;////////////////////////////////////////////int N,M;int low[MAXN+MAXN],in[MAXN];void init(){   ss = N + 2; tt = ss + 1;   src = tt + 1; sink = src + 1;   for(int i = 0;i <= sink;++i)      G[i].clear();   edges.clear();}void getId(char *str1,char *str2,int& x,int& y){    if(str1[0] == '+'){        x = ss;    } else if(str1[0] == '-'){        x = tt;    } else {        sscanf(str1,"%d",&x);    }    if(str2[0] == '+'){        y = ss;    } else if(str2[0] == '-'){        y = tt;    } else {        sscanf(str2,"%d",&y);    }}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;   Q.push(src);   vst[src] = 1;   d[src] = 0;   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;}int main(){    while(scanf("%d%d",&N,&M),(N||M)){        init();      //!!!!!!!!!!!!!        int x,y;        char str1[10],str2[10];        memset(in,0,sizeof(in));    //!!!!!!!!!!!!!!!!!!        for(int i = 0;i < M;++i){            scanf("%s%s%d",str1,str2,&low[i]);            //printf("%s %s\n",str1,str2);            getId(str1,str2,x,y);            //printf("%d --> %d\n",x,y);            addEdge(x,y,INF - low[i]);   //有下界,没有上界            in[x] -= low[i];            in[y] += low[i];        }        if(N == 0){            printf("%d\n",*max_element(low,low + M));            continue;        }        int sum = 0;        for(int i = 1;i <= tt;++i){            if(in[i] > 0){                sum += in[i];                addEdge(src,i,in[i]);            } else {                addEdge(i,sink,-in[i]);            }        }        sum -= maxFlow();        addEdge(tt,ss,INF);      //转换成无源汇网络流        int flow = maxFlow();        if(sum != flow){            puts("impossible");        } else {            int sz = edges.size();            printf("%d\n",edges[sz - 2].flow);        }    }    return 0;}