poj1459 - Power Network

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题目大意：总共有n个节点，其中有发电站np个、用户nc个和调度器n-np-nc个三种节点，每个发电站有一个最大发电量，每个用户有个最大接受电量，现在有m条有向边，边有一个最大的流量代表，最多可以流出这么多电，现在从发电站发电到用户，问最多可以发多少电
解题思路：将发电站看成源点，用户看成汇点，这样求最大流就可以了，不过因为有多个源点和汇点，所以加一个超级源点指向所有的发电站，流量为无限大，加一个超级汇点让所有的用户指向他，流量也为无限大，这样，从超级源点到超级汇点求最大流即可。

 

题目比较简单，总结了几种最大流的算法

 

/*EdmondsKarpMemory 320KTime 1282MS和没过没什么区别*/#include <iostream>#include <queue>using namespace std;#define min(a,b) (a<b?a:b)#define MAXV 105#define MAXINT INT_MAXtypedef struct{int flow;//流量int capacity;//最大容量值}maps;maps map[MAXV][MAXV];int vertime;//顶点总数int nedges;//边的总数int power_stations;//发电站总数int consumers;//消费者总数int maxflow;//最大流int sp,fp;//标记源点与汇点int parent[MAXV];//用于bfs寻找路径int bfs(int start,int end){int a[MAXV],i,v;queue <int>q;memset(a,0,sizeof(a));memset(parent,-1,sizeof(parent));q.push(start);a[start]=MAXINT;while(!q.empty()){v=q.front();q.pop();for(i=1;i<=vertime;i++){if(!a[i] && map[v][i].capacity>map[v][i].flow){q.push(i);parent[i]=v;a[i]=min(a[v],map[v][i].capacity-map[v][i].flow);}}if(v==end) break;}return a[end];}void EdmondsKarp(){int i,tmp;maxflow=0;while(tmp=bfs(sp,fp)){for(i=fp;i!=sp;i=parent[i]){map[i][parent[i]].flow-=tmp;//更新反向流map[parent[i]][i].flow+=tmp;//更新正向流}maxflow+=tmp;}}int main(){int i;int x,y,z;char ch;while(scanf("%d%d%d%d", &vertime, &power_stations,&consumers,&nedges)!= EOF){//Initmemset(map,0,sizeof(map));//Read Graghfor(i=1;i<=nedges;i++){//设置读图从1开始cin>>ch>>x>>ch>>y>>ch>>z;map[x+1][y+1].capacity=z;}//Build Gragh//建立超级源点指向所有的发电站sp=vertime+1;fp=vertime+2;vertime+=2;for (i=1; i<=power_stations; i++){cin>>ch>>x>>ch>>y;map[sp][x+1].capacity=y;}//建立超级汇点，使所有消费者指向它for (i=1; i<=consumers; i++){cin>>ch>>x>>ch>>y;map[x+1][fp].capacity=y;}EdmondsKarp();printf("%d\n",maxflow);}return 0;}

 

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/*dinicMemory 320KTime  563MS*/#include <iostream>#include <queue>using namespace std;#define min(a,b) (a<b?a:b)#define MAXV 105#define MAXINT INT_MAXtypedef struct{int flow;//流量int capacity;//最大容量值}maps;maps map[MAXV][MAXV];int dis[MAXV];//用于dinic分层int vertime;//顶点总数int nedges;//边的总数int power_stations;//发电站总数int consumers;//消费者总数int maxflow;//最大流int sp,fp;//标记源点与汇点bool bfs(){int v,i;queue <int>q;memset(dis,0,sizeof(dis));q.push(sp);dis[sp]=1;while(!q.empty()){v=q.front();q.pop();for(i=1;i<=vertime;i++)if(!dis[i] && map[v][i].capacity>map[v][i].flow){q.push(i);dis[i]=dis[v]+1;}if(v==fp) return 1;}return 0;}int dfs(int cur,int cp){if(cur==fp) return cp;int tmp=cp,t;for(int i=1;i<=vertime;i++)if(dis[i]==dis[cur]+1 && tmp && map[cur][i].capacity>map[cur][i].flow){t=dfs(i,min(map[cur][i].capacity-map[cur][i].flow,tmp));map[cur][i].flow+=t;map[i][cur].flow-=t;tmp-=t;}return cp-tmp;}void dinic(){maxflow=0;while(bfs()) maxflow+=dfs(sp,MAXINT);}int main(){int i;int x,y,z;char ch;while(scanf("%d%d%d%d", &vertime, &power_stations,&consumers,&nedges)!= EOF){//Initmemset(map,0,sizeof(map));//Read Graghfor(i=1;i<=nedges;i++){//设置读图从1开始cin>>ch>>x>>ch>>y>>ch>>z;map[x+1][y+1].capacity=z;}//Build Gragh//建立超级源点指向所有的发电站sp=vertime+1;fp=vertime+2;vertime+=2;for (i=1; i<=power_stations; i++){cin>>ch>>x>>ch>>y;map[sp][x+1].capacity=y;}//建立超级汇点，使所有消费者指向它for (i=1; i<=consumers; i++){cin>>ch>>x>>ch>>y;map[x+1][fp].capacity=y;}dinic();printf("%d\n",maxflow);}return 0;}

 

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/*sapMemory 328KTime  454MS*/#include <iostream>#include <queue>using namespace std;#define MAXV 110#define INF 1<<29#define min(a,b) (a>b?b:a)int n,c[MAXV][MAXV],r[MAXV][MAXV],source,sink;int dis[MAXV],maxflow;void bfs(){int v,i;queue <int>q;memset(dis,0,sizeof(dis));q.push(sink);while(!q.empty()){v=q.front();q.pop();for(i=0;i<=sink;i++){if(!dis[i] && c[i][v]>0){dis[i] = dis[v] +1;q.push(i);}}}}void sap(){int top=source,pre[MAXV],i,j,low[MAXV];bfs();//分层memset(low,0,sizeof(low));//保存路径的最小流量while(dis[source]<n){low[source]=INF;for(i=0;i<=sink;i++){//找到一条允许弧if(r[top][i]>0 && dis[top]==dis[i] +1) break;}if(i<=sink){//找到了low[i]=min(r[top][i],low[top]);//更新最小流量pre[i]=top;top=i;//记录增广路径if(top==sink){//找到一条增广路径更新残量maxflow += low[sink];j = top;while(j != source){i=pre[j];r[i][j]-=low[sink];r[j][i]+=low[sink];j=i;}top=source;//再从头找一条增广路径memset(low,0,sizeof(low));}}else{//找不到这样一条允许弧更新距离数组int mindis=INF;for(j=0;j <=sink;j++){if(r[top][j]>0 && mindis>dis[j] +1)mindis=dis[j] +1;}dis[top]=mindis;if(top!=source) top=pre[top];}}}int main(){int i,nedges,power_stations,consumers;int x,y,z;char ch;while(scanf("%d%d%d%d", &n, &power_stations,&consumers,&nedges)!= EOF){//Initmemset(r,0,sizeof(r));memset(c,0,sizeof(c));source=0;sink=n+1;n+=2;maxflow=0;//Read Graghfor(i=1;i<=nedges;i++){//设置读图从1开始cin>>ch>>x>>ch>>y>>ch>>z;c[x+1][y+1]=r[x+1][y+1]=z;}//Build Gragh//建立超级源点指向所有的发电站for (i=1;i<=power_stations;i++){cin>>ch>>x>>ch>>y;c[source][x+1]=r[source][x+1]=y;}//建立超级汇点，使所有消费者指向它for (i=1;i<=consumers;i++){cin>>ch>>x>>ch>>y;c[x+1][sink]=r[x+1][sink]=y;}sap();printf("%d\n",maxflow);}return 0;}

 

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/*sap+分层+gap优化Memory 328KTime  438MS*/#include <iostream>#include <queue>using namespace std;#define MAXV 110#define INF 1<<29#define min(a,b) (a>b?b:a)int n,c[MAXV][MAXV],r[MAXV][MAXV],source,sink;int dis[MAXV],maxflow,gap[MAXV];void bfs(){int v,i;queue <int>q;memset(dis,0,sizeof(dis));memset(gap,0,sizeof(gap));gap[0]++;q.push(sink);while(!q.empty()){v=q.front();q.pop();for(i=0;i<=sink;i++){if(!dis[i] && c[i][v]>0){dis[i] = dis[v] +1;gap[dis[i]]++;q.push(i);}}}}void sap(){int top=source,pre[MAXV],i,j,low[MAXV];bfs();//分层memset(low,0,sizeof(low));//保存路径的最小流量while(dis[source]<n){low[source]=INF;for(i=0;i<=sink;i++){//找到一条允许弧if(r[top][i]>0 && dis[top]==dis[i]+1 && dis[i]>=0) break;}if(i<=sink){//找到了low[i]=min(r[top][i],low[top]);//更新最小流量pre[i]=top;top=i;//记录增广路径if(top==sink){//找到一条增广路径更新残量maxflow += low[sink];j = top;while(j != source){i=pre[j];r[i][j]-=low[sink];r[j][i]+=low[sink];j=i;}top=source;//再从头找一条增广路径memset(low,0,sizeof(low));}}else{//找不到这样一条允许弧更新距离数组int mindis=INF;for(j=0;j <=sink;j++){if(r[top][j]>0 && mindis>dis[j] +1 && dis[j]>=0)mindis=dis[j] +1;}gap[dis[top]]--;if (gap[dis[top]] ==0) break;gap[mindis]++;dis[top]=mindis;if(top!=source) top=pre[top];}}}int main(){int i,nedges,power_stations,consumers;int x,y,z;char ch;while(scanf("%d%d%d%d", &n, &power_stations,&consumers,&nedges)!= EOF){//Initmemset(r,0,sizeof(r));memset(c,0,sizeof(c));source=0;sink=n+1;n+=2;maxflow=0;//Read Graghfor(i=1;i<=nedges;i++){//设置读图从1开始cin>>ch>>x>>ch>>y>>ch>>z;c[x+1][y+1]=r[x+1][y+1]=z;}//Build Gragh//建立超级源点指向所有的发电站for (i=1;i<=power_stations;i++){cin>>ch>>x>>ch>>y;c[source][x+1]=r[source][x+1]=y;}//建立超级汇点，使所有消费者指向它for (i=1;i<=consumers;i++){cin>>ch>>x>>ch>>y;c[x+1][sink]=r[x+1][sink]=y;}sap();printf("%d\n",maxflow);}return 0;}