uva-11324-SCC+dp

https://vjudge.net/problem/UVA-11324

给出一幅有向图，问最大能找到多少个节点，使得这些节点中任意两个节点之间都至少有一条可达路径。

找出SCC后缩点求权重最大路即可。

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<map>
 #include<set>
 #include<stack>
 #include<deque>
 #include<bitset>
 #include<unordered_map>
 #include<unordered_set>
 #include<queue>
 #include<cstdlib>
 #include<ctype.h>
 #include<ctime>
 #include<functional>
 #include<algorithm>
 #include<bits/stdc++.h>
 using namespace std;
 #define LL long long
 #define pii pair<int,int>
 #define mp make_pair
 #define pb push_back
 #define fi first
 #define se second
 #define inf 0x3f3f3f3f
 #define debug puts("debug")
 #define mid ((L+R)>>1)
 #define lc (id<<1)
 #define rc (id<<1|1)
 const int maxn=;
 const int maxm=;
 const double PI=acos(-1.0);
 const double eps=1e-;
 const LL mod=1e9+;
 LL gcd(LL a,LL b){return b==?a:gcd(b,a%b);}
 LL lcm(LL a,LL b){return a/gcd(a,b)*b;}
 LL qpow(LL a,LL b,LL c){LL r=; for(;b;b>>=,a=a*a%c)if(b&)r=r*a%c;return r;}
 template<class T>
 void prt(T v){for(auto x:v)cout<<x<<' ';cout<<endl;}
 struct Edge{int u,v,w,next;};

 vector<int>g[maxn],g2[maxn];
 int f[maxn],dfn[maxn],low[maxn],scc[maxn],tot[maxn],sum=,scc_cnt=;
 stack<int>S;
 void dfs(int u){
     dfn[u]=low[u]=++sum;
     S.push(u);
     for(int v:g[u]){
         if(!dfn[v]){
             dfs(v),low[u]=min(low[u],low[v]);
         }else if(!scc[v]){
             low[u]=min(low[u],dfn[v]);
         }
     }
     if(dfn[u]==low[u]){
         ++scc_cnt;
         for(;;){
             int x=S.top();S.pop();
             scc[x]=scc_cnt;
             tot[scc_cnt]++;
             if(x==u)break;
         }
     }
 }
 int cal(int u){
     if(f[u]!=-)return f[u];
     f[u]=tot[u];
     int maxx=;
     for(int v:g2[u]){
         maxx=max(maxx,cal(v));
     }
     return f[u]=f[u]+maxx;
 }
 int main(){
     int t,n,m,i,j,u,v;
     cin>>t;
     while(t--){
         scanf("%d%d",&n,&m);
         for(i=;i<=n;++i)g[i].clear(),g2[i].clear(),tot[i]=low[i]=dfn[i]=scc[i]=;
         sum=scc_cnt=;
         while(!S.empty())S.pop();
         while(m--){
             scanf("%d%d",&u,&v);
             g[u].pb(v);
         }
         for(i=;i<=n;++i){
             if(!dfn[i]){
                 dfs(i);
             }
         }
         memset(f,-,sizeof(f));
         for(u=;u<=n;++u){
             for(int v:g[u]){
                 if(scc[u]!=scc[v]){
                     //cout<<scc[v]<<' '<<scc[u]<<
                     g2[scc[v]].pb(scc[u]);
                 }
             }
         }
         int ans=;
         for(i=;i<=scc_cnt;++i){
             f[i]=cal(i);
             if(f[i]>ans)ans=f[i];
         }
         cout<<ans<<endl;
     }
     return ;
 }
 /*
 1
 5 5
 1 2
 2 3
 3 1
 4 1
 5 2

 */