卧薪尝胆,厚积薄发。
HEOI2014 大工程
Date: Tue Nov 20 18:22:56 CST 2018 In Category: NoCategory

Description:

给一棵树和树上的 $k$ 个点,求出这些点两两之间的路径的和,最大值,最小值。
$1\leqslant n\leqslant10^6,\sum k\leqslant 2n$

Solution:

虚树 $+$ 树形 $DP$ 。

Code:


#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<vector>
#include<cctype>
#include<cstring>
using namespace std;
inline int rd()
{
register int res = 0,f = 1;
register char c = getchar();
while(!isdigit(c))
{
if(c == '-')f = -1;
c = getchar();
}
while(isdigit(c))
{
res = (res << 1) + (res << 3) + c - '0';
c = getchar();
}
return res * f;
}
int n,m;
#define MAXN 1000010
struct edge
{
int to,nxt;
}e[MAXN << 1];
int edgenum = 0;
int lin[MAXN] = {0};
inline void add(int a,int b)
{
e[++edgenum] = (edge){b,lin[a]};lin[a] = edgenum;
e[++edgenum] = (edge){a,lin[b]};lin[b] = edgenum;
return;
}
int fa[MAXN],dep[MAXN],top[MAXN],son[MAXN],siz[MAXN];
int dfn[MAXN],tot = 0;
#define R register
void dfs1(int k,int depth)
{
dfn[k] = ++tot;
dep[k] = depth;
siz[k] = 1;
for(R int i = lin[k];i != 0;i = e[i].nxt)
{
if(e[i].to != fa[k])
{
fa[e[i].to] = k;
dfs1(e[i].to,depth + 1);
siz[k] += siz[e[i].to];
if(son[k] == 0 || siz[e[i].to] > siz[son[k]])
{
son[k] = e[i].to;
}
}
}
return;
}
void dfs2(int k,int tp)
{
top[k] = tp;
if(son[k] == 0)return;
dfs2(son[k],tp);
for(R int i = lin[k];i != 0;i = e[i].nxt)
{
if(e[i].to != fa[k] && e[i].to != son[k])
{
dfs2(e[i].to,e[i].to);
}
}
return;
}
inline int LCA(int a,int b)
{
while(top[a] != top[b])
{
if(dep[top[a]] < dep[top[b]])swap(a,b);
a = fa[top[a]];
}
return (dep[a] < dep[b] ? a : b);
}
int v[MAXN];
vector<int> g[MAXN];
bool cmp_dfn(int a,int b){return dfn[a] < dfn[b];}
int s[MAXN],tp = 0;
typedef long long ll;
ll ans1,ans2,ans3;
ll f1[MAXN],f2[MAXN];
bool tag[MAXN];
int dp(int k)
{
R int siz = 0;
if(tag[k])siz = 1;
f2[k] = 0x3f3f3f3f;
if(tag[k])f2[k] = 0;
f1[k] = 0;
for(R vector<int>::iterator i = g[k].begin();i != g[k].end();++i)
{
R int sson = dp(*i);
siz += sson;
ans1 += 1ll * (dep[*i] - dep[k]) * (v[0] - sson) * sson;
ans2 = min(ans2,f2[k] + f2[*i] + dep[*i] - dep[k]);
f2[k] = min(f2[k],f2[*i] + dep[*i] - dep[k]);
ans3 = max(ans3,f1[k] + f1[*i] + dep[*i] - dep[k]);
f1[k] = max(f1[k],f1[*i] + dep[*i] - dep[k]);
}
g[k].clear();
return siz;
}
int main()
{
scanf("%d",&n);
for(R int i = 1;i < n;++i)add(rd(),rd());
dfs1(1,1);dfs2(1,1);
scanf("%d",&m);
while(m--)
{
v[0] = rd();
for(R int i = 1;i <= v[0];++i)v[i] = rd();
sort(v + 1,v + 1 + v[0],cmp_dfn);
tp = 0;s[++tp] = v[1];
for(R int i = 1;i <= v[0];++i)tag[v[i]] = true;
for(R int i = 2;i <= v[0];++i)
{
if(v[i] == v[i - 1])continue;
R int lca = LCA(s[tp],v[i]);
if(lca == s[tp])
{
s[++tp] = v[i];
continue;
}
while(tp >= 2)
{
if(dfn[lca] < dfn[s[tp - 1]])
{
g[s[tp - 1]].push_back(s[tp]);
--tp;
}
else
{
g[lca].push_back(s[tp]);
--tp;
break;
}
}
if(tp == 1 && dfn[lca] < dfn[s[tp]])
{
g[lca].push_back(s[tp]);
s[tp] = lca;
}
if(lca != s[tp])s[++tp] = lca;
s[++tp] = v[i];
}
while(tp >= 2)
{
g[s[tp - 1]].push_back(s[tp]);
--tp;
}
ans1 = 0;ans2 = 0x3f3f3f3f3f3f3f3f;ans3 = 0xc0c0c0c0c0c0c0c0;
dp(s[tp]);
printf("%lld %lld %lld\n",ans1,ans2,ans3);
for(int i = 1;i <= v[0];++i)tag[v[i]] = false;
}
return 0;
}
In tag: 树-虚树
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