POJ 1459 网络流
网络流模板题，这份代码转自kuangbin神，觉得还是很经得起考验的！
首先是dinic：
/* 最大流模板 dinic算法 */ #include<stdio.h> #include<string.h> #include<algorithm> #include<iostream> using namespace std; const int INF=0x3f3f3f3f; const int MAXN=150;//点数的最大值 const int MAXM=20500;//边数的最大值 struct Node { int from,to,next; int cap; }edge[MAXM]; int tol; int dep[MAXN];//dep为点的层次 int head[MAXN]; int n; void init() { tol=0; memset(head,-1,sizeof(head)); } void addedge(int u,int v,int w)//第一条变下标必须为偶数 { edge[tol].from=u; edge[tol].to=v; edge[tol].cap=w; edge[tol].next=head[u]; head[u]=tol++; edge[tol].from=v; edge[tol].to=u; edge[tol].cap=0; edge[tol].next=head[v]; head[v]=tol++; } int BFS(int start,int end) { int que[MAXN]; int front,rear; front=rear=0; memset(dep,-1,sizeof(dep)); que[rear++]=start; dep[start]=0; while(front!=rear) { int u=que[front++]; if(front==MAXN)front=0; for(int i=head[u];i!=-1;i=edge[i].next) { int v=edge[i].to; if(edge[i].cap>0&&dep[v]==-1) { dep[v]=dep[u]+1; que[rear++]=v; if(rear>=MAXN)rear=0; if(v==end)return 1; } } } return 0; } int dinic(int start,int end) { int res=0; int top; int stack[MAXN];//stack为栈，存储当前增广路 int cur[MAXN];//存储当前点的后继 while(BFS(start,end)) { memcpy(cur,head,sizeof(head)); int u=start; top=0; while(1) { if(u==end) { int min=INF; int loc; for(int i=0;i<top;i++) if(min>edge[stack[i]].cap) { min=edge[stack[i]].cap; loc=i; } for(int i=0;i<top;i++) { edge[stack[i]].cap-=min; edge[stack[i]^1].cap+=min; } res+=min; top=loc; u=edge[stack[top]].from; } for(int i=cur[u];i!=-1;cur[u]=i=edge[i].next) if(edge[i].cap!=0&&dep[u]+1==dep[edge[i].to]) break; if(cur[u]!=-1) { stack[top++]=cur[u]; u=edge[cur[u]].to; } else { if(top==0)break; dep[u]=-1; u=edge[stack[--top]].from; } } } return res; } int main()//多源多汇点，在前面加个源点，后面加个汇点，转成单源单汇点 { //freopen("in.txt","r",stdin); //freopen("out.txt","w",stdout); int start,end; int np,nc,m; int u,v,z; while(scanf("%d%d%d%d",&n,&np,&nc,&m)!=EOF) { init(); while(m--) { while(getchar()!='('); scanf("%d,%d)%d",&u,&v,&z); u++;v++; addedge(u,v,z); } while(np--) { while(getchar()!='('); scanf("%d)%d",&u,&z); u++; addedge(0,u,z); } while(nc--) { while(getchar()!='('); scanf("%d)%d",&u,&z); u++; addedge(u,n+1,z); } start=0; end=n+1; int ans=dinic(start,end); printf("%d\n",ans); } return 0; }
然后还喜获isap模板，同样来自kuangbin神：
/* 最大流模板 sap */ #include<stdio.h> #include<string.h> #include<algorithm> #include<iostream> using namespace std; const int MAXN=150;//点数的最大值 const int MAXM=20500;//边数的最大值 const int INF=0x3f3f3f3f; struct Node { int from,to,next; int cap; }edge[MAXM]; int tol; int head[MAXN]; int dep[MAXN]; int gap[MAXN];//gap[x]=y :说明残留网络中dep[i]==x的个数为y int n; void init() { tol=0; memset(head,-1,sizeof(head)); } void addedge(int u,int v,int w) { edge[tol].from=u; edge[tol].to=v; edge[tol].cap=w; edge[tol].next=head[u]; head[u]=tol++; edge[tol].from=v; edge[tol].to=u; edge[tol].cap=0; edge[tol].next=head[v]; head[v]=tol++; } void BFS(int start,int end) { memset(dep,-1,sizeof(dep)); memset(gap,0,sizeof(gap)); gap[0]=1; int que[MAXN]; int front,rear; front=rear=0; dep[end]=0; que[rear++]=end; while(front!=rear) { int u=que[front++]; if(front==MAXN)front=0; for(int i=head[u];i!=-1;i=edge[i].next) { int v=edge[i].to; if(edge[i].cap!=0||dep[v]!=-1)continue; que[rear++]=v; if(rear>=MAXN)rear=0; dep[v]=dep[u]+1; ++gap[dep[v]]; } } } int SAP(int start,int end) { int res=0; BFS(start,end); int cur[MAXN]; int S[MAXN]; int top=0; memcpy(cur,head,sizeof(head)); int u=start; int i; while(dep[start]<n) { if(u==end) { int temp=INF; int inser; for(i=0;i<top;i++) if(temp>edge[S[i]].cap) { temp=edge[S[i]].cap; inser=i; } for(i=0;i<top;i++) { edge[S[i]].cap-=temp; edge[S[i]^1].cap+=temp; } res+=temp; top=inser; u=edge[S[top]].from; } if(u!=end&&gap[dep[u]-1]==0)//出现断层，无增广路 break; for(i=cur[u];i!=-1;i=edge[i].next) if(edge[i].cap!=0&&dep[u]==dep[edge[i].to]+1) break; if(i!=-1) { cur[u]=i; S[top++]=i; u=edge[i].to; } else { int min=n; for(i=head[u];i!=-1;i=edge[i].next) { if(edge[i].cap==0)continue; if(min>dep[edge[i].to]) { min=dep[edge[i].to]; cur[u]=i; } } --gap[dep[u]]; dep[u]=min+1; ++gap[dep[u]]; if(u!=start)u=edge[S[--top]].from; } } return res; } int main()//多源多汇点，在前面加个源点，后面加个汇点，转成单源单汇点 { // freopen("in.txt","r",stdin); // freopen("out.txt","w",stdout); int start,end; int np,nc,m; int u,v,z; while(scanf("%d%d%d%d",&n,&np,&nc,&m)!=EOF) { init(); while(m--) { while(getchar()!='('); scanf("%d,%d)%d",&u,&v,&z); u++;v++; addedge(u,v,z); } while(np--) { while(getchar()!='('); scanf("%d)%d",&u,&z); u++; addedge(0,u,z); } while(nc--) { while(getchar()!='('); scanf("%d)%d",&u,&z); u++; addedge(u,n+1,z); } start=0; end=n+1; n+=2;//n一定是点的总数，这是使用SAP模板需要注意的 int ans=SAP(start,end); printf("%d\n",ans); } return 0; }
最小费用最大流
const int maxn=500; const int INF=0x3f3f3f3f; struct Edge { int from,to,cap,flow,cost; Edge(int u,int v,int c,int d,int p):from(u),to(v),cap(c),flow(d),cost(p) {} }; struct MCMF { int s,t,flow,cost; vector<Edge>edges; vector<int>G[maxn]; int inq[maxn]; int d[maxn]; int p[maxn]; int a[maxn]; void init() { for(int i=0;i<maxn;i++) G[i].clear(); edges.clear(); } void AddEdge(int from,int to,int cap,int cost) { edges.push_back((Edge){from,to,cap,0,cost}); edges.push_back((Edge){to,from,0,0,-cost}); int l=edges.size(); G[from].push_back(l-2); G[to].push_back(l-1); } bool BellmanFord(int s,int t) { for(int i=0;i<maxn;i++) d[i]=INF; memset(inq,0,sizeof(inq)); d[s]=0;inq[s]=1;p[s]=0;a[s]=INF; queue<int>Q; Q.push(s); while(!Q.empty()) { int u=Q.front(); Q.pop(); inq[u]=0; for(int i=0;i<G[u].size();i++) { Edge &e=edges[G[u][i]]; if(e.cap>e.flow&&d[e.to]>d[u]+e.cost) { d[e.to]=d[u]+e.cost; p[e.to]=G[u][i]; a[e.to]=min(a[u],e.cap-e.flow); if(!inq[e.to]) { Q.push(e.to); inq[e.to]=1; } } } } if(d[t]==INF)return false; flow+=a[t]; cost+=d[t]*a[t]; int u=t; while(u!=s) { edges[p[u]].flow+=a[t]; edges[p[u]^1].flow-=a[t]; u=edges[p[u]].from; } return true; } int Mincost(int s,int t) { flow=cost=0; while(BellmanFord(s,t)); return cost; } }solve;
