最小路径覆盖问题(网络流最大流)
题目
洛谷题目传送门
题解
网络流题目详讲
code
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#define rg register
#define il inline
#define lst long long
#define ldb long double
#define N 550
#define M 100050
using namespace std;
const int Inf=1e9;
il int read()
{
rg int s=0,m=0;rg char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')m=1;ch=getchar();}
while(ch>='0'&&ch<='9')s=(s<<3)+(s<<1)+(ch^48),ch=getchar();
return m?-s:s;
}
int n,m,S,T,ans;
int to[N],tag[N],dep[N];
int hd[N],cur[N],cnt=1;
struct EDGE{int to,nxt,c;}ljl[M<<1];
il void add(rg int p,rg int q,rg int o)
{
ljl[++cnt]=(EDGE){q,hd[p],o},hd[p]=cnt;
ljl[++cnt]=(EDGE){p,hd[q],0},hd[q]=cnt;
}
queue Q;
il bool BFS()
{
for(rg int i=S;i<=T;++i)dep[i]=0;
while(!Q.empty())Q.pop();
Q.push(S),dep[S]=1;
while(!Q.empty())
{
rg int now=Q.front();Q.pop();
for(rg int i=hd[now];i;i=ljl[i].nxt)
{
rg int qw=ljl[i].to;
if(!dep[qw]&&ljl[i].c>0)
{
dep[qw]=dep[now]+1;
Q.push(qw);
}
}
}
return dep[T];
}
int dfs(rg int now,rg int aim,rg int flow)
{
if(now==aim)return flow;
for(rg int &i=cur[now];i;i=ljl[i].nxt)
{
rg int qw=ljl[i].to;
if(ljl[i].c>0&&dep[qw]==dep[now]+1)
{
rg int kk=dfs(qw,aim,min(flow,ljl[i].c));
if(kk>0)
{
to[now]=qw;
if(now!=S)tag[qw-n]=1;
ljl[i].c-=kk,ljl[i^1].c+=kk;
return kk;
}
}
}
return 0;
}
il int Dinic()
{
rg int ans=0;
while(BFS())
{
for(rg int i=S;i<=T;++i)cur[i]=hd[i];
while(int kk=dfs(S,T,Inf))ans+=kk;
}
for(rg int i=1;i<=n;++i)
if(!tag[i])
{
rg int now=i;
printf("%d ",now);
while(to[now]&&to[now]!=T)
{
printf("%d ",to[now]-n);
now=to[now]-n;
}
puts("");
}
return ans;
}
int main()
{
n=read(),m=read();
S=0,T=2*n+1;
for(rg int i=1;i<=n;++i)
add(S,i,1),add(i+n,T,1);
for(rg int i=1;i<=m;++i)
{
rg int p=read(),q=read();
add(p,q+n,1);
}
printf("%d\n",n-Dinic());
return 0;
}