最大流 && 最小费用最大流模板
模板从 这里 搬运，链接博客还有很多网络流题集题解参考。
最大流模板 ( 可处理重边 )
const int maxn = 1e6 + 10; const int INF = 0x3f3f3f3f; 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){} }; struct Dinic { int n,m,s,t; //结点数,边数(包括反向弧),源点与汇点编号 vector<Edge> edges; //边表 edges[e]和edges[e^1]互为反向弧 vector<int> G[maxn]; //邻接表,G[i][j]表示结点i的第j条边在e数组中的序号 bool vis[maxn]; //BFS使用,标记一个节点是否被遍历过 int d[maxn]; //d[i]表从起点s到i点的距离(层次) int cur[maxn]; //cur[i]表当前正访问i节点的第cur[i]条弧 void init(int n,int s,int t) { this->n=n,this->s=s,this->t=t; for(int i=0;i<=n;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) ); m = edges.size(); G[from].push_back(m-2); G[to].push_back(m-1); } bool BFS() { memset(vis,0,sizeof(vis)); queue<int> Q;//用来保存节点编号的 Q.push(s); d[s]=0; vis[s]=true; 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(!vis[e.to] && e.cap>e.flow) { vis[e.to]=true; d[e.to] = d[x]+1; Q.push(e.to); } } } return vis[t]; } //a表示从s到x目前为止所有弧的最小残量 //flow表示从x到t的最小残量 int DFS(int x,int a) { if(x==t || a==0)return a; int flow=0,f;//flow用来记录从x到t的最小残量 for(int& i=cur[x]; i<G[x].size(); i++) { Edge& e=edges[G[x][i]]; if(d[x]+1==d[e.to] && (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; } } if(!flow) d[x] = -1;///炸点优化 return flow; } int Maxflow() { int flow=0; while(BFS()) { memset(cur,0,sizeof(cur)); flow += DFS(s,INF); } return flow; } }DC;
#include<bits/stdc++.h> using namespace std; const int maxn = 1210; const int maxm = 240005;///边要是题目规定的两倍 const int INF = 0x3f3f3f3f; struct edge{ int to,cap,tot,rev; }; struct DINIC{ int n,m; edge w[maxm]; int fr[maxm]; int num[maxn],cur[maxn],first[maxn]; edge e[maxm]; void init(int n){ memset(cur,0,sizeof(cur)); this->n=n; m=0; } void AddEdge(int from,int to,int cap){ w[++m]=(edge){to,cap}; num[from]++,fr[m]=from; w[++m]=(edge){from,0}; num[to]++,fr[m]=to; } void prepare(){ first[1]=1; for(int i=2;i<=n;i++) first[i]=first[i-1]+num[i-1]; for(int i=1;i<n;i++) num[i]=first[i+1]-1; num[n]=m; for(int i=1;i<=m;i++){ e[first[fr[i]]+(cur[fr[i]]++)]=w[i]; if (!(i%2)){ e[first[fr[i]]+cur[fr[i]]-1].rev=first[w[i].to]+cur[w[i].to]-1; e[first[w[i].to]+cur[w[i].to]-1].rev=first[fr[i]]+cur[fr[i]]-1; } } } int q[maxn]; int dist[maxn]; int t; bool bfs(int s){ int l=1,r=1; q[1]=s; memset(dist,-1,(n+1)*4); dist[s]=0; while(l<=r){ int u=q[l++]; for(int i=first[u];i<=num[u];i++){ int v=e[i].to; if ((dist[v]!=-1) || (!e[i].cap)) continue; dist[v]=dist[u]+1; if (v==t) return true; q[++r]=v; } } return dist[t]!=-1; } int dfs(int u,int flow){ if (u==t) return flow; int ans=0; for(int& i=cur[u];i<=num[u];i++){ int v=e[i].to; if (!e[i].cap || dist[v]!=dist[u]+1) continue; int t=dfs(v,min(flow,e[i].cap)); if (t){ e[i].cap-=t; e[e[i].rev].tot+=t; flow-=t; ans+=t; if (!flow) return ans; } } return ans; } int MaxFlow(int s,int t){ int ans=0; this->t=t; while(bfs(s)){ do{ memcpy(cur,first,(n+1)*4); int flow; while(flow=dfs(s,INF)) ans+=flow; }while(bfs(s)); for(int i=1;i<=m;i++) e[i].cap+=e[i].tot,e[i].tot=0; } return ans; } }DC; int main(void) { int N, M, S, T; while(~scanf("%d %d %d %d", &N, &M, &S, &T)){ DC.init(N); while(M--){ int u, v, w; scanf("%d %d %d", &u, &v, &w); DC.AddEdge(u, v, w); } DC.prepare(); printf("%d", DC.MaxFlow(S, T)); } return 0; }
///这个是找到的别人的代码 ///我见过的最快的最大流代码了 ///但是我不知道原理，所以只能套一套这样子.... #include <bits/stdc++.h> const int MAXN = 1e6 + 10; const int INF = INT_MAX; struct Node { int v, f, index; Node(int v, int f, int index) : v(v), f(f), index(index) {} }; int n, m, s, t; std::vector<Node> edge[MAXN]; std::vector<int> list[MAXN], height, count, que, excess; typedef std::list<int> List; std::vector<List::iterator> iter; List dlist[MAXN]; int highest, highestActive; typedef std::vector<Node>::iterator Iterator; inline void init() { for(int i=0; i<=n; i++) edge[i].clear(); } inline void addEdge(const int u, const int v, const int f) { edge[u].push_back(Node(v, f, edge[v].size())); edge[v].push_back(Node(u, 0, edge[u].size() - 1)); } inline void globalRelabel(int n, int t) { height.assign(n, n); height[t] = 0; count.assign(n, 0); que.clear(); que.resize(n + 1); int qh = 0, qt = 0; for (que[qt++] = t; qh < qt;) { int u = que[qh++], h = height[u] + 1; for (Iterator p = edge[u].begin(); p != edge[u].end(); ++p) { if (height[p->v] == n && edge[p->v][p->index].f > 0) { count[height[p->v] = h]++; que[qt++] = p->v; } } } for (int i = 0; i <= n; i++) { list[i].clear(); dlist[i].clear(); } for (int u = 0; u < n; ++u) { if (height[u] < n) { iter[u] = dlist[height[u]].insert(dlist[height[u]].begin(), u); if (excess[u] > 0) list[height[u]].push_back(u); } } highest = (highestActive = height[que[qt - 1]]); } inline void push(int u, Node &e) { int v = e.v; int df = std::min(excess[u], e.f); e.f -= df; edge[v][e.index].f += df; excess[u] -= df; excess[v] += df; if (0 < excess[v] && excess[v] <= df) list[height[v]].push_back(v); } inline void discharge(int n, int u) { int nh = n; for (Iterator p = edge[u].begin(); p != edge[u].end(); ++p) { if (p->f > 0) { if (height[u] == height[p->v] + 1) { push(u, *p); if (excess[u] == 0) return; } else { nh = std::min(nh, height[p->v] + 1); } } } int h = height[u]; if (count[h] == 1) { for (int i = h; i <= highest; i++) { for (List::iterator it = dlist[i].begin(); it != dlist[i].end(); ++it) { count[height[*it]]--; height[*it] = n; } dlist[i].clear(); } highest = h - 1; } else { count[h]--; iter[u] = dlist[h].erase(iter[u]); height[u] = nh; if (nh == n) return; count[nh]++; iter[u] = dlist[nh].insert(dlist[nh].begin(), u); highest = std::max(highest, highestActive = nh); list[nh].push_back(u); } } inline int hlpp(int n, int s, int t) { if (s == t) return 0; highestActive = 0; highest = 0; height.assign(n, 0); height[s] = n; iter.resize(n); for (int i = 0; i < n; i++) if (i != s) iter[i] = dlist[height[i]].insert(dlist[height[i]].begin(), i); count.assign(n, 0); count[0] = n - 1; excess.assign(n, 0); excess[s] = INF; excess[t] = -INF; for (int i = 0; i < (int)edge[s].size(); i++) push(s, edge[s][i]); globalRelabel(n, t); for (int u /*, res = n*/; highestActive >= 0;) { if (list[highestActive].empty()) { highestActive--; continue; } u = list[highestActive].back(); list[highestActive].pop_back(); discharge(n, u); // if (--res == 0) globalRelabel(res = n, t); } return excess[t] + INF; } int main() { while(~scanf("%d %d %d %d", &n, &m, &s, &t)){ init(); for (int i = 0, u, v, f; i < m; i++) { scanf("%d %d %d", &u, &v, &f); addEdge(u, v, f); } printf("%d", hlpp(n + 1, s, t));///点是1~n范围的话，貌似要 n+1 } return 0; }
最小费用最大流模板
点都是 0~N-1
struct Edge { int from,to,cap,flow,cost; Edge(){} Edge(int f,int t,int c,int fl,int co):from(f),to(t),cap(c),flow(fl),cost(co){} }; struct MCMF { int n,m,s,t; vector<Edge> edges; vector<int> G[maxn]; bool inq[maxn]; //是否在队列 int d[maxn]; //Bellman_ford单源最短路径 int p[maxn]; //p[i]表从s到i的最小费用路径上的最后一条弧编号 int a[maxn]; //a[i]表示从s到i的最小残量 //初始化 void init(int n,int s,int t) { this->n=n, this->s=s, this->t=t; edges.clear(); for(int i=0;i<n;++i) G[i].clear(); } //添加一条有向边 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)); m=edges.size(); G[from].push_back(m-2); G[to].push_back(m-1); } //求一次增广路 bool BellmanFord(int &flow, int &cost) { for(int i=0;i<n;++i) d[i]=INF; memset(inq,0,sizeof(inq)); d[s]=0, a[s]=INF, inq[s]=true, p[s]=0; queue<int> Q; Q.push(s); while(!Q.empty()) { int u=Q.front(); Q.pop(); inq[u]=false; 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]=true; } } } } if(d[t]==INF) return false; flow +=a[t]; cost +=a[t]*d[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; } //求出最小费用最大流 int Min_cost() { int flow=0,cost=0; while(BellmanFord(flow,cost)); return cost; } }MM;
struct Edge { int from,to,cap,flow,cost; Edge(int u,int v,int ca,int f,int co):from(u),to(v),cap(ca),flow(f),cost(co){}; }; struct MCMF { int n,m,s,t; vector<Edge> edges; vector<int> G[maxn]; int inq[maxn];//是否在队列中 int d[maxn];//距离 int p[maxn];//上一条弧 int a[maxn];//可改进量 void init(int n)//初始化 { this->n=n; for(int i=0;i<=n;i++) G[i].clear(); edges.clear(); } void AddEdge(int from,int to,int cap,int cost)//加边 { edges.push_back(Edge(from,to,cap,0,cost)); edges.push_back(Edge(to,from,0,0,-cost)); int m=edges.size(); G[from].push_back(m-2); G[to].push_back(m-1); } bool SPFA(int s,int t,int &flow,int &cost)//寻找最小费用的增广路，使用引用同时修改原flow,cost { for(int i=0;i<n;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]--; 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)//满足可增广且可变短 { 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]) { inq[e.to]++; Q.push(e.to); } } } } if(d[t]==INF) return false;//汇点不可达则退出 flow+=a[t]; cost+=d[t]*a[t]; int u=t; while(u!=s)//更新正向边和反向边 { edges[p[u]].flow+=a[t]; edges[p[u]^1].flow-=a[t]; u=edges[p[u]].from; } return true; } int MincotMaxflow(int s,int t) { int flow=0,cost=0; while(SPFA(s,t,flow,cost)); return cost; } }MM;
网络流的知识可以参考《挑战程序设计竞赛Ⅱ》 or 以下链接
