网络流之最大流-我的模板

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以HDU 3549这道模板题来分别给出我的EK,DINIC,SAP算法，原题连接：http://acm.hdu.edu.cn/showproblem.php?pid=3549

一般地，求解最大流问题存在EK,DINIC,SAP三种算法。EK算法是基于BFS寻找增广路的，SAP算法是利用距离标号，DINIC算法是利用分层网络来寻找增广路。具体原理和一些基本概念我这里就不再赘述了。相关书籍已经写得非常清楚了。我是参考《ACM-ICPC程序设计系列-图论及其应用》的第5章的网络流。

下面给出我的三种算法的模板，都通过了HDU3549的测试。

EK算法

#include<cstdio>#include<cstring>#include<cmath>#include<cstdlib>#include<iostream>#include<algorithm>#include<sstream>#include<vector>#include<map>#include<stack>#include<list>#include<set>#include<queue>#define LL long long#define lson l,m,rt<<1#define rson m+1,r,rt<<1 | 1using namespace std;const int maxn=55,maxe=10005,inf=1<<29;int n,m;int Map[maxn][maxn],p[maxn];bool EK_BFS(int s,int e){    queue<int>q;    bool vis[maxn];    memset(vis,0,sizeof(vis));    memset(p,-1,sizeof(p));    q.push(s);    vis[s]=1;    while(!q.empty())    {        int t=q.front();q.pop();        if(t==e) return 1;        for(int i=1;i<=n;i++)            if(Map[t][i]&&!vis[i]) vis[i]=1,p[i]=t,q.push(i);    }    return 0;}int EK_Max_Flow(int s,int e){    int ans=0,u,temp;    while(EK_BFS(s,e))    {        temp=inf;        u=e;        while(p[u]!=-1) temp=min(temp,Map[p[u]][u]),u=p[u];        ans+=temp;        u=e;        while(p[u]!=-1) Map[p[u]][u]-=temp,Map[u][p[u]]+=temp,u=p[u];    }    return ans;}int main(){    int t;    scanf("%d",&t);    for(int T=1;T<=t;T++)    {        memset(Map,0,sizeof(Map));        scanf("%d%d",&n,&m);        for(int i=0;i<m;i++)        {            int x,y,c;            scanf("%d%d%d",&x,&y,&c);            Map[x][y]+=c;        }        printf("Case %d: %d\n",T,EK_Max_Flow(1,n));    }    return 0;}

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SAP算法

<pre name="code" class="cpp">#include<cstdio>#include<cstring>#include<cmath>#include<cstdlib>#include<iostream>#include<algorithm>#include<sstream>#include<vector>#include<map>#include<stack>#include<list>#include<set>#include<queue>#define LL long long#define lson l,m,rt<<1#define rson m+1,r,rt<<1 | 1using namespace std;const int maxn=1005,maxe=10005,inf=1<<29;int n,m;struct edge{ int to,cap,rev;};vector<edge>G[maxn];int level[maxn],iter[maxn];bool vis[maxn];void add(int from,int to,int cap){    G[from].push_back((edge){to,cap,G[to].size()});    G[to].push_back((edge){from,0,G[from].size()-1});}void bfs(int s){    memset(level,-1,sizeof(level));    queue<int>q;    level[s]=0;    q.push(s);    while(!q.empty())    {        int v=q.front();q.pop();        for(int i=0;i<G[v].size();i++)        {            edge &e=G[v][i];            if(e.cap>0&&level[e.to]<0)            {                level[e.to]=level[v]+1;                q.push(e.to);            }        }    }}int dfs(int v,int t,int f){    if(v==t) return f;    for(int &i=iter[v];i<G[v].size();i++)    {        edge &e=G[v][i];        if(e.cap>0&&level[v]<level[e.to])        {            int d=dfs(e.to,t,min(f,e.cap));            if(d>0)            {                e.cap-=d;                G[e.to][e.rev].cap+=d;                return d;            }        }    }    return 0;}int max_flow(int s,int t){    int flow=0;    while(true)    {        bfs(s);        if(level[t]<0) return flow;        memset(iter,0,sizeof(iter));        int f;        while((f=dfs(s,t,inf))>0) flow+=f;    }}int main(){    int t;    scanf("%d",&t);    for(int T=1;T<=t;T++)    {        for(int i=0;i<=n;i++) G[i].clear();        scanf("%d%d",&n,&m);        for(int i=0;i<m;i++)        {            int x,y,c;            scanf("%d%d%d",&x,&y,&c);            add(x,y,c);        }        printf("Case %d: %d\n",T,max_flow(1,n));    }    return 0;}

----------------------------------------------------------------------------------------------------------------------------------DINIC算法

#include<cstdio>#include<cstring>#include<cmath>#include<cstdlib>#include<iostream>#include<algorithm>#include<sstream>#include<vector>#include<map>#include<stack>#include<list>#include<set>#include<queue>#define LL long long#define lson l,m,rt<<1#define rson m+1,r,rt<<1 | 1using namespace std;const int maxn=1005,maxe=100005,inf=1<<29;int n,m;int level[maxn];struct node{    int to,next,f;}edge[maxe];int head[maxn],cnt;void add(int from,int to,int f1,int f2){    edge[cnt].to=to;    edge[cnt].f=f1;    edge[cnt].next=head[from];    head[from]=cnt++;    edge[cnt].to=from;    edge[cnt].f=f2;    edge[cnt].next=head[to];    head[to]=cnt++;}bool makelevel(int s,int t){    memset(level,0,sizeof(level));    level[s]=1;    queue<int>q;    q.push(s);    while(!q.empty())    {        int top=q.front();q.pop();        if(top==t) return 1;        for(int i=head[top];i!=-1;i=edge[i].next)            if(!level[edge[i].to]&&edge[i].f) q.push(edge[i].to),level[edge[i].to]=level[top]+1;    }    return 0;}int dfs(int now,int Maxf,int t){    int ans=0;    if(now==t) return Maxf;    for(int i=head[now];i!=-1;i=edge[i].next)        if(edge[i].f&&level[edge[i].to]==level[now]+1)        {            int f=dfs(edge[i].to,min(Maxf-ans,edge[i].f),t);            edge[i].f-=f;            edge[i^1].f+=f;            ans+=f;            if(ans==Maxf) return ans;        }    return ans;}int dinic(int s,int t){    int ans=0;    while(makelevel(s,t)) ans+=dfs(s,inf,t);    return ans;}int main(){int t;    scanf("%d",&t);    for(int T=1;T<=t;T++)    {        cnt=0;        memset(head,-1,sizeof(head));        scanf("%d%d",&n,&m);        for(int i=0;i<m;i++)        {            int x,y,c;            scanf("%d%d%d",&x,&y,&c);            add(x,y,c,0);        }        printf("Case %d: %d\n",T,dinic(1,n));    }    return 0;}

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