P4103 [HEOI2014]大工程
题目
P4103 [HEOI2014]大工程
化简题目:在树上选定\(k\)个点,求两两路径和,最大的一组路径,最小的一组路径
做法
关键点不多,建个虚树跑一边就好了
\(sum_i\)为\(i\)子树各关键点到根节点的距离和,\(small_i\)为其最小值,\(big_i\)为其最大值
My complete code
#include<cstdio>
#include<iostream>
#include<cstring>
#include<string>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long LL;
inline LL Read(){
LL x(0),f(1); char c=getchar();
while(c<'0'||c>'9'){
if(c=='-')f=-1; c=getchar();
}
while(c>='0'&&c<='9')
x=(x<<3)+(x<<1)+c-'0',c=getchar();
return x*f;
}
const LL maxn=2*1e6+9,inf=0x3f3f3f3f;
LL n,ans1,ans2,ans3;
LL a[maxn],sta[maxn];
struct Tree{
LL tot,num,head[maxn],dfn[maxn],dep[maxn],size[maxn],key[maxn],inc[maxn][25],fa[maxn];
LL sum[maxn],big[maxn],small[maxn];
struct node{
LL to,next,d;
}dis[maxn];
inline void Add(LL u,LL v,LL d){
dis[++num]=(node){v,head[u],d},head[u]=num;
}
void Fdfs(LL u){
dfn[u]=++tot;
inc[u][0]=fa[u];
for(LL i=1;i<=21;++i)
inc[u][i]=inc[inc[u][i-1]][i-1];
for(LL i=head[u];i;i=dis[i].next){
LL v(dis[i].to);
if(v==fa[u])
continue;
fa[v]=u,dep[v]=dep[u]+1,
Fdfs(v);
}
}
inline LL Lca(LL x,LL y){
if(dep[x]<dep[y])
swap(x,y);
for(LL i=20;i>=0;--i)
if(dep[inc[x][i]]>=dep[y])
x=inc[x][i];
if(x==y)
return x;
for(LL i=20;i>=0;--i)
if(inc[x][i]!=inc[y][i])
x=inc[x][i],y=inc[y][i];
return inc[x][0];
}
void Dfs(LL u){
size[u]=key[u],
sum[u]=big[u]=0,
small[u]=(key[u]==0)?inf:0;
for(LL i=head[u];i;i=dis[i].next){
LL v(dis[i].to),d(dis[i].d);
Dfs(v);
if(size[u]){
ans1+=size[u]*size[v]*d+size[u]*sum[v]+size[v]*sum[u],
ans2=min(ans2,small[u]+d+small[v]),
ans3=max(ans3,big[u]+d+big[v]);
}
sum[u]+=sum[v]+size[v]*d;
small[u]=min(small[u],small[v]+d),
big[u]=max(big[u],big[v]+d),
size[u]+=size[v];
}
head[u]=key[u]=0;
}
}T,X;
inline bool cmp1(LL x,LL y){
return T.dfn[x]<T.dfn[y];
}
inline void Solve(){
LL kase=Read();
while(kase--){
LL num(Read());
for(LL i=1;i<=num;++i)
a[i]=Read();
sort(a+1,a+1+num,cmp1);
LL tp; sta[tp=1]=1;
for(LL i=1;i<=num;++i){
X.key[a[i]]=1;
LL lca=T.Lca(a[i],sta[tp]);
while(T.dep[sta[tp]]>T.dep[lca])
if(T.dep[sta[tp-1]]<T.dep[lca])
X.Add(lca,sta[tp],T.dep[sta[tp]]-T.dep[lca]),sta[tp]=lca;
else
X.Add(sta[tp-1],sta[tp],T.dep[sta[tp]]-T.dep[sta[tp-1]]),--tp;
if(sta[tp]!=a[i])
sta[++tp]=a[i];
}
while(tp>1)
X.Add(sta[tp-1],sta[tp],T.dep[sta[tp]]-T.dep[sta[tp-1]]),--tp;
ans1=0,ans2=inf,ans3=0;
X.Dfs(1);
printf("%lld %lld %lld\n",ans1,ans2,ans3);
}
}
int main(){
n=Read();
for(LL i=1;i<n;++i){
LL u(Read()),v(Read());
T.Add(u,v,1),T.Add(v,u,1);
}
T.Fdfs(1);
Solve();
return 0;
}/*
*/