HDU 6115 Factory（虚树+根号分治）

Posted On 2019年4月28日

Factory

Solution

对于每个大小\(>size\)的集合\(O(n)\)预处理出其与其他集合的答案，这部分复杂度\(O(\frac{n}{size}\cdot n)\)

对于大小\(<size\)的集合在询问时建虚树\(O(size)\)解决即可，使用\(O(1)\)LCA时这部分复杂度\(O(size\cdot m)\)

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <bitset>
#include <algorithm>
#include <vector>
#include <tr1/unordered_map>
using namespace std;
using namespace std::tr1;
inline int read()
{
    int f=1,k=0;char c=getchar();
    while (c<'0'||c>'9')c=='-'&&(f=-1),c=getchar();
    while (c>='0'&&c<='9')k=k*10+c-'0',c=getchar();
    return k*f;
}
const int maxn=400000+100,inf=1e9;
int last[maxn],tmp[maxn],cnt[maxn],mn[maxn],upmn[maxn],Last[maxn],stk[maxn],tot,all,used[maxn],n;
vector<int>store[maxn],bel[maxn];
unordered_map<int,unordered_map<int,int> >ans;
unordered_map<int,unordered_map<int,bool> >vis;
pair<int,int>tp[maxn];
struct mc{int too,nxt,val;}e[maxn<<1],E[maxn<<1];
struct HLD
{
    int fa[maxn],top[maxn],dep[maxn],dfn[maxn],Time,mp[maxn],EULER,in[maxn],DEP[maxn],ALL,mn[maxn][20];
    void dfs(const int cur)
    {
        dfn[cur]=++Time;mp[in[cur]=++EULER]=cur;
        for (int i=last[cur];i;i=e[i].nxt)
            if (e[i].too!=fa[cur])
                dep[e[i].too]=dep[cur]+e[i].val,fa[e[i].too]=cur,mp[++EULER]=cur,DEP[e[i].too]=DEP[cur]+1,
                dfs(e[i].too);
    }
    inline int main(int a,int b)
    {
        int l=in[a],r=in[b];
        if (l>r)swap(l,r);
        int lg=log(r-l+1)/log(2),A=mn[l][lg],B=mn[r-(1<<lg)+1][lg];
        return DEP[A]<DEP[B]?A:B;
    }
    inline void pre()
    {
        EULER=Time=0;
        dfs(1);
        ALL=log(EULER)/log(2);
        for (int i=1;i<=EULER;i++)mn[i][0]=mp[i];
        for (int j=1;j<=ALL;j++)
        for (int i=1;i+(1<<j)-1<=EULER;i++)
        {
            int a=mn[i][j-1],b=mn[i+(1<<j-1)][j-1];
            if (DEP[a]<DEP[b])mn[i][j]=a;
            else mn[i][j]=b;
        }
    }
    inline int getdis(const int a,const int b,int lca=0)
    {
        if (!lca)lca=main(a,b);
        return dep[a]+dep[b]-dep[lca]*2;
    }
}LCA;
void dfs(int*last,mc*e,const int cur,const int fa)
{
    for (int i=last[cur];i;i=e[i].nxt)
        if (e[i].too!=fa)dfs(last,e,e[i].too,cur),mn[cur]=min(mn[cur],mn[e[i].too]+e[i].val);
}
void getup(int*last,mc*e,const int cur,const int fa)
{
    for (int i=last[cur];i;i=e[i].nxt)
        if (e[i].too!=fa)mn[e[i].too]=min(mn[e[i].too],mn[cur]+e[i].val),getup(last,e,e[i].too,cur);
}
inline void add(const int a,const int b,const int c)
{
    used[++all]=a;used[++all]=b;
    E[++tot]=(mc){b,Last[a],c};Last[a]=tot;
    E[++tot]=(mc){a,Last[b],c};Last[b]=tot;
}
inline void work()
{
    n=read();int m=read(),lg2=log(n)/log(2),siz=sqrt(n);siz/=10;
    memset(last,0,sizeof(int)*(n+1));
    for (int i=1;i<n;i++)
    {
        int a=read(),b=read();
        e[i<<1].too=b,e[i<<1].nxt=last[a],last[a]=i<<1;
        e[i<<1|1].too=a,e[i<<1|1].nxt=last[b],last[b]=i<<1|1;
        e[i<<1].val=e[i<<1|1].val=read();
    }
    LCA.pre();
    for (int i=1;i<=m;i++)
    {
        int N=read();
        for (int j=1;j<=N;j++)tmp[j]=read();
        sort(tmp+1,tmp+1+N);
        N=unique(tmp+1,tmp+1+N)-tmp-1;
        cnt[i]=N;
        for (int j=1;j<=N;j++)store[i].push_back(tmp[j]),bel[tmp[j]].push_back(i);
    }
    for (int i=1;i<=m;i++)
        if (cnt[i]>=siz)
        {
            memset(mn,0x3f,sizeof(int)*(n+1));
            for (int j=0;j<store[i].size();j++)
                mn[store[i][j]]=0;
            dfs(last,e,1,1);
            getup(last,e,1,1);
            for (int j=1;j<=n;j++)
            {
                int dis=mn[j];
                for (int k=0;k<bel[j].size();k++)
                {
                    int cur=bel[j][k];
                    if (!vis[cur][i])ans[cur][i]=ans[i][cur]=dis,vis[cur][i]=vis[i][cur]=1;
                    else ans[cur][i]=ans[i][cur]=min(ans[cur][i],dis);
                }
            }
        }
    memset(mn,0x3f,sizeof(mn));
    for (int Q=read();Q;Q--)
    {
        int a=read(),b=read();
        if (cnt[a]>=siz||cnt[b]>=siz)printf("%d\n",ans[a][b]);
        else 
        {
            int cnt=0,top=0;tot=0;all=0;
            for (int i=0,now;i<store[a].size();i++)now=store[a][i],tp[++cnt]=make_pair(LCA.dfn[now],now);
            for (int i=0,now;i<store[b].size();i++)now=store[b][i],tp[++cnt]=make_pair(LCA.dfn[now],now);
            sort(tp+1,tp+1+cnt);
            cnt=unique(tp+1,tp+1+cnt)-tp-1;
            stk[++top]=1;
            for (int i=1;i<=cnt;i++)
            {
                int now=tp[i].second;
                if (now==1)continue;
                if (top<=1)stk[++top]=tp[i].second;
                else
                {
                    int lca=LCA.main(now,stk[top]);
                    if (lca==stk[top])stk[++top]=now;
                    else
                    {
                        while (top>1&&LCA.dfn[lca]<=LCA.dfn[stk[top-1]])
                        add(stk[top],stk[top-1],LCA.getdis(stk[top],stk[top-1])),--top;
                        if (lca!=stk[top])add(stk[top],lca,LCA.getdis(lca,stk[top])),stk[top]=lca;
                        stk[++top]=now;
                    }
                }
            }
            for (int i=top;i>1;i--)add(stk[i],stk[i-1],LCA.getdis(stk[i],stk[i-1]));
            for (int i=1;i<=all;i++)mn[used[i]]=inf;
            for (int i=0;i<store[a].size();i++)
            mn[store[a][i]]=0;
            dfs(Last,E,1,1);
            getup(Last,E,1,1);
            int aw=inf;
            for (int i=0;i<store[b].size();i++)
            aw=min(aw,mn[store[b][i]]);
            printf("%d\n",aw);
            for (int i=1;i<=all;i++)Last[used[i]]=0;
        }
    }
    for (int i=1;i<=n;i++)store[i].clear(),ans[i].clear(),bel[i].clear(),vis[i].clear();
}
signed main()
{
    for (int T=read();T;T--)work();
}

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#include <iostream>

#include <cstdio>

#include <cstdlib>

#include <cmath>

#include <cstring>

#include <bitset>

#include <algorithm>

#include <vector>

#include <tr1/unordered_map>

using namespace std;

using namespace std::tr1;

inline int read()

{

int f=1,k=0;char c=getchar();

while (c<'0'||c>'9')c=='-'&&(f=-1),c=getchar();

while (c>='0'&&c<='9')k=k*10+c-'0',c=getchar();

return k*f;

}

const int maxn=400000+100,inf=1e9;

int last[maxn],tmp[maxn],cnt[maxn],mn[maxn],upmn[maxn],Last[maxn],stk[maxn],tot,all,used[maxn],n;

vector<int>store[maxn],bel[maxn];

unordered_map<int,unordered_map<int,int> >ans;

unordered_map<int,unordered_map<int,bool> >vis;

pair<int,int>tp[maxn];

struct mc{int too,nxt,val;}e[maxn<<1],E[maxn<<1];

struct HLD

{

int fa[maxn],top[maxn],dep[maxn],dfn[maxn],Time,mp[maxn],EULER,in[maxn],DEP[maxn],ALL,mn[maxn][20];

void dfs(const int cur)

{

dfn[cur]=++Time;mp[in[cur]=++EULER]=cur;

for (int i=last[cur];i;i=e[i].nxt)

if (e[i].too!=fa[cur])

dep[e[i].too]=dep[cur]+e[i].val,fa[e[i].too]=cur,mp[++EULER]=cur,DEP[e[i].too]=DEP[cur]+1,

dfs(e[i].too);

}

inline int main(int a,int b)

{

int l=in[a],r=in[b];

if (l>r)swap(l,r);

int lg=log(r-l+1)/log(2),A=mn[l][lg],B=mn[r-(1<<lg)+1][lg];

return DEP[A]<DEP[B]?A:B;

}

inline void pre()

{

EULER=Time=0;

dfs(1);

ALL=log(EULER)/log(2);

for (int i=1;i<=EULER;i++)mn[i][0]=mp[i];

for (int j=1;j<=ALL;j++)

for (int i=1;i+(1<<j)-1<=EULER;i++)

{

int a=mn[i][j-1],b=mn[i+(1<<j-1)][j-1];

if (DEP[a]<DEP[b])mn[i][j]=a;

else mn[i][j]=b;

}

inline int getdis(const int a,const int b,int lca=0)

{

if (!lca)lca=main(a,b);

return dep[a]+dep[b]-dep[lca]*2;

}

}LCA;

void dfs(int*last,mc*e,const int cur,const int fa)

{

for (int i=last[cur];i;i=e[i].nxt)

if (e[i].too!=fa)dfs(last,e,e[i].too,cur),mn[cur]=min(mn[cur],mn[e[i].too]+e[i].val);

}

void getup(int*last,mc*e,const int cur,const int fa)

{

for (int i=last[cur];i;i=e[i].nxt)

if (e[i].too!=fa)mn[e[i].too]=min(mn[e[i].too],mn[cur]+e[i].val),getup(last,e,e[i].too,cur);

}

inline void add(const int a,const int b,const int c)

{

used[++all]=a;used[++all]=b;

E[++tot]=(mc){b,Last[a],c};Last[a]=tot;

E[++tot]=(mc){a,Last[b],c};Last[b]=tot;

}

inline void work()

{

n=read();int m=read(),lg2=log(n)/log(2),siz=sqrt(n);siz/=10;

memset(last,0,sizeof(int)*(n+1));

for (int i=1;i<n;i++)

{

int a=read(),b=read();

e[i<<1].too=b,e[i<<1].nxt=last[a],last[a]=i<<1;

e[i<<1|1].too=a,e[i<<1|1].nxt=last[b],last[b]=i<<1|1;

e[i<<1].val=e[i<<1|1].val=read();

}

LCA.pre();

for (int i=1;i<=m;i++)

{

int N=read();

for (int j=1;j<=N;j++)tmp[j]=read();

sort(tmp+1,tmp+1+N);

N=unique(tmp+1,tmp+1+N)-tmp-1;

cnt[i]=N;

for (int j=1;j<=N;j++)store[i].push_back(tmp[j]),bel[tmp[j]].push_back(i);

}

for (int i=1;i<=m;i++)

if (cnt[i]>=siz)

{

memset(mn,0x3f,sizeof(int)*(n+1));

for (int j=0;j<store[i].size();j++)

mn[store[i][j]]=0;

dfs(last,e,1,1);

getup(last,e,1,1);

for (int j=1;j<=n;j++)

{

int dis=mn[j];

for (int k=0;k<bel[j].size();k++)

{

int cur=bel[j][k];

if (!vis[cur][i])ans[cur][i]=ans[i][cur]=dis,vis[cur][i]=vis[i][cur]=1;

else ans[cur][i]=ans[i][cur]=min(ans[cur][i],dis);

}

memset(mn,0x3f,sizeof(mn));

for (int Q=read();Q;Q--)

{

int a=read(),b=read();

if (cnt[a]>=siz||cnt[b]>=siz)printf("%d\n",ans[a][b]);

else

{

int cnt=0,top=0;tot=0;all=0;

for (int i=0,now;i<store[a].size();i++)now=store[a][i],tp[++cnt]=make_pair(LCA.dfn[now],now);

for (int i=0,now;i<store[b].size();i++)now=store[b][i],tp[++cnt]=make_pair(LCA.dfn[now],now);

sort(tp+1,tp+1+cnt);

cnt=unique(tp+1,tp+1+cnt)-tp-1;

stk[++top]=1;

for (int i=1;i<=cnt;i++)

{

int now=tp[i].second;

if (now==1)continue;

if (top<=1)stk[++top]=tp[i].second;

else

{

int lca=LCA.main(now,stk[top]);

if (lca==stk[top])stk[++top]=now;

else

{

while (top>1&&LCA.dfn[lca]<=LCA.dfn[stk[top-1]])

add(stk[top],stk[top-1],LCA.getdis(stk[top],stk[top-1])),--top;

if (lca!=stk[top])add(stk[top],lca,LCA.getdis(lca,stk[top])),stk[top]=lca;

stk[++top]=now;

}

for (int i=top;i>1;i--)add(stk[i],stk[i-1],LCA.getdis(stk[i],stk[i-1]));

for (int i=1;i<=all;i++)mn[used[i]]=inf;

for (int i=0;i<store[a].size();i++)

mn[store[a][i]]=0;

dfs(Last,E,1,1);

getup(Last,E,1,1);

int aw=inf;

for (int i=0;i<store[b].size();i++)

aw=min(aw,mn[store[b][i]]);

printf("%d\n",aw);

for (int i=1;i<=all;i++)Last[used[i]]=0;

}

for (int i=1;i<=n;i++)store[i].clear(),ans[i].clear(),bel[i].clear(),vis[i].clear();

}

signed main()

{

for (int T=read();T;T--)work();

}

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