UVA-The Largest Clique 11324

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最大团，

problem:给一个有向图G，求一个节点数最大的点集，使得该点集中的任意两个节点至少要有一条路径

那么可知， G中的SCC要么都选，要么都不选（不选是因为这是有向图选了之后的无法纳入范围），那么问题就简单了

将每个SCC缩成一个点，变成在DAG上DP

code:

#include <stack>#include <cstdio>#include <cstring>#include <algorithm>using namespace std;#define N 50005#define next Next#define begin Begin#define mem(a) memset(a, 0, sizeof(a))#define rep(i, j, k) for(int i=j; i<=k; ++i)#define erep(i, u) for(int i=begin[u]; i; i=next[i])void read(int &x){char c=getchar();x=0;while(c<'0' || c>'9')c=getchar();while(c>='0' && c<='9')x=x*10+c-'0', c=getchar();}int begin[N<<1], to[N<<1], next[N<<1], e;void add(int x, int y){to[++e]=y;next[e]=begin[x];begin[x]=e;}int n, m, low[N], pre[N], sccid[N], scc_cnt, clock_;stack<int>s;void dfs(int u){pre[u]=low[u]=++clock_;s.push(u);erep(i, u){int v=to[i];if(!pre[v])dfs(v),low[u]=min(low[u], low[v]);else if(!sccid[v])low[u]=min(low[u], pre[v]);//notice! array low can only reach the point which is in the same SCC;   }if(pre[u] == low[u]){scc_cnt++;while(1){int x=s.top();s.pop();sccid[x]=scc_cnt;if(x == u)break;}}}void solve(){clock_ = scc_cnt = 0;mem(pre);mem(sccid);rep(i, 1, n)if(!pre[i])dfs(i);}int f[1005], w[1005];bool p[1005],vis[1005][1005];int dp(int u){if(f[u]>=0)return f[u];f[u]=w[u];rep(v, 1, scc_cnt)if(v!=u && vis[u][v])f[u]=max(f[u], w[u]+dp(v));return f[u];}int main(){#ifndef ONLINE_JUDGEfreopen("data.in", "r", stdin);freopen("result.out", "w", stdout);#endifint _;read(_);while(_--){e=0;mem(begin);memset(f, -1, sizeof(f));mem(vis);mem(w);read(n);read(m);rep(i, 1, m){int u, v;read(u);read(v);add(u, v);}solve();rep(i, 1, n){w[sccid[i]]++;erep(j, i)vis[sccid[i]][sccid[to[j]]]=true;}int res=0;rep(i, 1, scc_cnt)res=max(res, dp(i));printf("%d\n", res);}return 0;}

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