[模版] 网络流最大流、费用流

反向边作用讨论：http://blog.csdn.net/qq_21110267/article/details/43540483

我理解的很有限，希望有研究过的人能给我评论指导。

代码：

By：Rujia Liu

数据结构和比较函数（用于排序）：

struct Edge {int from, to, cap, flow; };bool operator < (const Edge& a, const Edge& b) {return a.from < b.from || (a.from == b.from && a.to < b.to); }

最大流：

1.Dinic

struct Dinic {int n, m, s, t;vector<Edge> edges; // 边数的两倍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int d[maxn]; // 从起点到i的距离int cur[maxn]; // 当前弧指针void ClearAll(int n) {for(int i = 0; i < n; i++) G[i].clear();edges.clear();}void ClearFlow() {for(int i = 0; i < edges.size(); i++) edges[i].flow = 0; }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;Q.push(s);vis[s] = 1;d[s] = 0;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] = 1;d[e.to] = d[x] + 1;Q.push(e.to);}}}return vis[t];}int DFS(int x, int a) {if(x == t || 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[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;}}return flow;}int Maxflow(int s, int t) {this->s = s; this->t = t;int flow = 0;while(BFS()) {memset(cur, 0, sizeof(cur));flow += DFS(s, INF);}return flow;}vector<int> Mincut() { // call this after maxflowvector<int> ans;for(int i = 0; i < edges.size(); i++) {Edge& e = edges[i];if(vis[e.from] && !vis[e.to] && e.cap > 0) ans.push_back(i);}return ans;}void Reduce() {for(int i = 0; i < edges.size(); i++) edges[i].cap -= edges[i].flow;} };ISAP：

struct ISAP {int n, m, s, t;vector<Edge> edges;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int d[maxn]; // 从起点到i的距离int cur[maxn]; // 当前弧指针int p[maxn]; // 可增广路上的上一条弧int num[maxn]; // 距离标号计数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;Q.push(t);vis[t] = 1;d[t] = 0;while(!Q.empty()) {int x = Q.front(); Q.pop();for(int i = 0; i < G[x].size(); i++) {Edge& e = edges[G[x][i]^1];if(!vis[e.from] && e.cap > e.flow) {vis[e.from] = 1;d[e.from] = d[x] + 1;Q.push(e.from);}}}return vis[s];}void ClearAll(int n) {this->n = n;for(int i = 0; i < n; i++) G[i].clear();edges.clear();}void ClearFlow() {for(int i = 0; i < edges.size(); i++) edges[i].flow = 0; }int Augment() {int x = t, a = INF;while(x != s) {Edge& e = edges[p[x]];a = min(a, e.cap-e.flow);x = edges[p[x]].from;}x = t;while(x != s) {edges[p[x]].flow += a;edges[p[x]^1].flow -= a;x = edges[p[x]].from;}return a;}int Maxflow(int s, int t, int need) {this->s = s; this->t = t;int flow = 0;BFS();memset(num, 0, sizeof(num));for(int i = 0; i < n; i++) num[d[i]]++;int x = s;memset(cur, 0, sizeof(cur));while(d[s] < n) {if(x == t) {flow += Augment();if(flow >= need) return flow;x = s;}int ok = 0;for(int i = cur[x]; i < G[x].size(); i++) {Edge& e = edges[G[x][i]];if(e.cap > e.flow && d[x] == d[e.to] + 1) { // Advanceok = 1;p[e.to] = G[x][i];cur[x] = i; // 注意x = e.to;break;}}if(!ok) { // Retreatint m = n-1; // 初值注意for(int i = 0; i < G[x].size(); i++) {Edge& e = edges[G[x][i]];if(e.cap > e.flow) m = min(m, d[e.to]);}if(--num[d[x]] == 0) break;num[d[x] = m+1]++;cur[x] = 0; // 注意if(x != s) x = edges[p[x]].from;}}return flow;}vector<int> Mincut() { // call this after maxflowBFS();vector<int> ans;for(int i = 0; i < edges.size(); i++) {Edge& e = edges[i];if(!vis[e.from] && vis[e.to] && e.cap > 0) ans.push_back(i);}return ans;}void Reduce() {for(int i = 0; i < edges.size(); i++) edges[i].cap -= edges[i].flow;}void print() {printf("Graph:\n");for(int i = 0; i < edges.size(); i++)printf("%d->%d, %d, %d\n", edges[i].from, edges[i].to , edges[i].cap, edges[i].flow);} };
费用流：

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]; // Beintman-Fordint p[maxn]; // 上一条弧int a[maxn]; // 可改进量void init(int n) {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) {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);}bool BellmanFord(int s, int t, int& ans) {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] = 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] > 0) return false;ans += (int)d[t] * (int)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;}// 需要保证初始网络中没有负权圈int Mincost(int s, int t) {int cost = 0;while(BellmanFord(s, t, cost));return cost;} };
zkw费用流（By：HZWER）

bool spfa() {memset(mark,0,sizeof(mark));for(int i=0;i<=T;i++)d[i]=-1;int head=0,tail=1;q[0]=T;mark[T]=1;d[T]=0;while(head!=tail){int now=q[head];head++;if(head==605)head=0;for(int i=last[now];i;i=e[i].next)if(e[i^1].v&&d[now]+e[i^1].c>d[e[i].to]){d[e[i].to]=d[now]+e[i^1].c;if(!mark[e[i].to]){mark[e[i].to]=1;q[tail++]=e[i].to;if(tail==605)tail=0;}}mark[now]=0;}return d[0]!=-1; } int dfs(int x,int f) {mark[x]=1;if(x==T)return f;int w,used=0;for(int i=last[x];i;i=e[i].next)if(d[e[i].to]==d[x]-e[i].c&&e[i].v&&!mark[e[i].to]){w=f-used;w=dfs(e[i].to,min(w,e[i].v));ans+=w*e[i].c;e[i].v-=w;e[i^1].v+=w;used+=w;if(used==f)return f;}return used; } void zkw() {while(spfa()){mark[T]=1;while(mark[T]){memset(mark,0,sizeof(mark));dfs(0,inf);}} }

总结

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