[模版] 网络流最大流、费用流

来源：互联网发布：阿里云服务器免费体验编辑：程序博客网时间：2024/04/30 03:19

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 maxflow    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;  }};

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) { // Advance          ok = 1;          p[e.to] = G[x][i];          cur[x] = i; // 注意          x = e.to;          break;        }      }      if(!ok) { // Retreat        int 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 maxflow    BFS();    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-Ford  int 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);}    }}

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