YBT高效进阶3.4.3 洛谷P2272最大半连通子图
Title
思路
Tanjan缩点,拓扑DP
第一问
f[v]=f[u]+s[v],s[v]为缩点后每个点原来点的个数
ans=max(f[i])
第二问
( f [ u ] + s [ v ] > f [ v ] ) (f[u]+s[v]>f[v]) (f[u]+s[v]>f[v])
g [ v ] = g [ u ] ; g[v]=g[u]; g[v]=g[u];
( f [ u ] + s [ v ] = f [ v ] ) (f[u]+s[v]=f[v]) (f[u]+s[v]=f[v])
g [ v ] = ( g [ v ] + g [ u ] ) g[v]=(g[v]+g[u])%mods; g[v]=(g[v]+g[u])
a n s = ∑ i = 1 总 点 数 g [ i ] m o d x [ 条 件 ( f [ i ] = m i n ( f [ i ] ) ) ] ans=\sum _{i=1}^{总点数}g[i] \mod x [条件(f[i]=min(f[i]))] ans=∑i=1总点数g[i]modx[条件(f[i]=min(f[i]))]
CODE
#include<iostream>
#include<cstdio>
#include<stack>
#include<queue>
#include<algorithm>
using namespace std;
const long long maxn=1000010;
struct jgt
{
long long u,v,nxt;
} efirst[maxn],esd[maxn];
long long dfn[maxn],low[maxn],col[maxn],s[maxn],ins[maxn],f[maxn],g[maxn],cnt,len;
long long headfirst[maxn],totfirst;
long long headsd[maxn],totsd;
long long headdz[maxn],totdz;
stack<long long>stck;
queue<long long>que;
void Tanjan(long long x)
{
dfn[x]=low[x]=++cnt;
stck.push(x);
for(long long i=headfirst[x]; i; i=efirst[i].nxt)
if(!dfn[efirst[i].v])Tanjan(efirst[i].v),low[x]=min(low[x],low[efirst[i].v]);
else if(!col[efirst[i].v])low[x]=min(low[x],dfn[efirst[i].v]);
if(dfn[x]==low[x])
{
for(col[x]=++len,s[len]=1; stck.top()!=x; stck.top(),stck.pop())col[stck.top()]=len,s[len]++;
stck.pop();
}
return;
}
bool cmp(jgt t1,jgt t2)
{
if(col[t1.u]==col[t2.u])return col[t1.v]<col[t2.v];
return col[t1.u]<col[t2.u];
}
int main()
{
long long n,m,i,ans=0,ansg,mods,j,w,x,y;
ios::sync_with_stdio(false);
for(cin>>n>>m>>mods,i=1; i<=m; i++)cin>>efirst[i].u>>efirst[i].v,efirst[i].nxt=headfirst[efirst[i].u],headfirst[efirst[i].u]=i;
for(i=1; i<=n; i++)if(!dfn[i])Tanjan(i);
sort(efirst+1,efirst+1+m,cmp);
for(i=1; i<=m; i++)
{
x=col[efirst[i].u],y=col[efirst[i].v];
if(x!=y&&(x!=col[efirst[i-1].u]||y!=col[efirst[i-1].v]))
{
esd[++totsd].u=x,esd[totsd].v=y,esd[totsd].nxt=headsd[x],headsd[x]=totsd,ins[y]++;
}
}
for(j=1; j<=len; f[j]=s[j],g[j]=1,j++)
if(!ins[j])
que.push(j);
for(; que.size(); que.pop())
{
for(w=que.front(),ans=max(ans,f[w]),j=headsd[w]; j; j=esd[j].nxt)
{
if(f[w]+s[esd[j].v]>f[esd[j].v])f[esd[j].v]=f[w]+s[esd[j].v],g[esd[j].v]=g[w];
else if(f[w]+s[esd[j].v]==f[esd[j].v])g[esd[j].v]=(g[esd[j].v]+g[w])%mods;
if(!(--ins[esd[j].v]))que.push(esd[j].v);
}
}
for(ansg=0,i=1; i<=len; i++)
if(f[i]==ans)ansg=(ansg+g[i])%mods;
cout<<ans<<endl<<ansg<<endl;
return 0;
}