bzoj3572

通过这题我知道了一个鬼故事，trunc(ln(128)/ln(2))=6……以后不敢轻易这么写了

好了言归正传，这题明显的构建虚树，但构建虚树后怎么树形dp呢？

由于虚树上的点不仅是议事会还有可能是议事会的LCA，所以

我们要先求出虚树上每个点是被那个议事会管理的，这我们可以通过两遍dfs求出（儿子更新父亲，父亲更新儿子）

然后我们考虑虚树上每条边所代表原数的结点归属就可以了，这个地方细节比较多，建议自己想，具体见代码注释

  1 type node=record
  2        po,next:longint;
  3      end;
  4      point=record
  5        fr,ds:longint;
  6      end;
  7
  8 var e:array[0..600010] of node;
  9     f,b,c,d,a,st,ans,p,s:array[0..300010] of longint;
 10     anc:array[0..300010,0..20] of longint;
 11     w:array[0..300010] of point;
 12     n,q,m,i,len,j,x,y,t,z:longint;
 13     v:array[0..300010] of boolean;
 14
 15 procedure swap(var a,b:longint);
 16   var c:longint;
 17   begin
 18     c:=a;
 19     a:=b;
 20     b:=c;
 21   end;
 22
 23 procedure add(x,y:longint);
 24   begin
 25     inc(len);
 26     e[len].po:=y;
 27     e[len].next:=p[x];
 28     p[x]:=len;
 29   end;
 30
 31 procedure dfs(x:longint);
 32   var i,y:longint;
 33   begin
 34     inc(t);
 35     a[x]:=t;
 36     s[x]:=1;
 37     i:=p[x];
 38     while i<>0 do
 39     begin
 40       y:=e[i].po;
 41       if s[y]=0 then
 42       begin
 43         anc[y,0]:=x;
 44         d[y]:=d[x]+1;
 45         dfs(y);
 46         s[x]:=s[x]+s[y];
 47       end;
 48       i:=e[i].next;
 49     end;
 50   end;
 51
 52 procedure sort(l,r:longint);
 53   var i,j,x:longint;
 54   begin
 55     i:=l;
 56     j:=r;
 57     x:=c[(l+r) shr 1];
 58     repeat
 59       while a[c[i]]<a[x] do inc(i);
 60       while a[x]<a[c[j]] do dec(j);
 61       if not(i>j) then
 62       begin
 63         swap(c[i],c[j]);
 64         inc(i);
 65         dec(j);
 66       end;
 67     until i>j;
 68     if l<j then sort(l,j);
 69     if i<r then sort(i,r);
 70   end;
 71
 72 function lca(x,y:longint):longint;
 73   var i:longint;
 74   begin
 75     if x=y then exit(x);
 76     if d[x]<d[y] then swap(x,y);
 77     if d[x]>d[y] then
 78     begin
 79       for i:=18 downto 0 do
 80         if d[x]-1 shl i>=d[y] then x:=anc[x,i];
 81     end;
 82     if x=y then exit(x);
 83     for i:=18 downto 0 do
 84       if anc[x,i]<>anc[y,i] then
 85       begin
 86         x:=anc[x,i];
 87         y:=anc[y,i];
 88       end;
 89     exit(anc[x,0]);
 90   end;
 91
 92 procedure get(var a:point;x,y:longint);
 93   begin
 94     if (a.ds>x) or (a.ds=x) and (a.fr>y) then
 95     begin
 96       a.ds:=x;
 97       a.fr:=y;
 98     end;
 99   end;
100
101 function find(x,h:longint):longint;
102   var i:longint;
103   begin
104     if h=0 then exit(x);
105     for i:=18 downto 0 do
106       if h-1 shl i>=0 then
107       begin
108         x:=anc[x,i];
109         h:=h-1 shl i;
110         if h=0 then break;
111       end;
112     exit(x);
113   end;
114
115 procedure work1(x:longint);
116   var i,y:longint;
117   begin
118     if v[x] then
119     begin
120       w[x].fr:=x;
121       w[x].ds:=0;
122     end
123     else begin
124       w[x].fr:=n+1;
125       w[x].ds:=10000010;
126     end;
127     f[x]:=s[x];
128     i:=p[x];
129     while i<>0 do
130     begin
131       y:=e[i].po;
132       f[x]:=f[x]-s[find(y,d[y]-d[x]-1)];
133       work1(y);
134       get(w[x],w[y].ds+d[y]-d[x],w[y].fr);
135       i:=e[i].next;
136     end;
137   end;
138
139 procedure work2(x:longint);
140   var i,y:longint;
141   begin
142     i:=p[x];
143     while i<>0 do
144     begin
145       y:=e[i].po;
146       get(w[y],w[x].ds+d[y]-d[x],w[x].fr);
147       work2(y);
148       i:=e[i].next;
149     end;
150   end;
151
152 procedure calc(x:longint);
153   var i,y,l,h:longint;
154   begin
155     inc(ans[b[w[x].fr]],f[x]);  //我们先单独考虑边的端点
156     i:=p[x];
157     while i<>0 do
158     begin
159       y:=e[i].po;
160       if w[x].fr=w[y].fr then
161         inc(ans[b[w[x].fr]],s[find(y,d[y]-d[x]-1)]-s[y])
162       else begin
163         l:=w[x].ds+w[y].ds+d[y]-d[x];
164         h:=l div 2-w[y].ds;  //均分
165         if (l mod 2=0) and (w[x].fr<w[y].fr) then dec(h);  //注意临界情况
166         h:=find(y,h);  //寻找向上d个单位的点
167         inc(ans[b[w[x].fr]],s[find(y,d[y]-d[x]-1)]-s[h]);  //注意这里的结点归属
168         inc(ans[b[w[y].fr]],s[h]-s[y]);
169       end;
170       calc(y);
171       i:=e[i].next;
172     end;
173     p[x]:=0;
174   end;
175
176 begin
177   readln(n);
178   for i:=1 to n-1 do
179   begin
180     readln(x,y);
181     add(x,y);
182     add(y,x);
183   end;
184   dfs(1);
185   for j:=1 to trunc(ln(n)/ln(2)) do
186     for i:=1 to n do
187     begin
188       x:=anc[i,j-1];
189       anc[i,j]:=anc[x,j-1];
190     end;
191
192   len:=0;
193   fillchar(p,sizeof(p),0);
194   readln(m);
195   while m>0 do
196   begin
197     dec(m);
198     len:=0;
199     readln(q);
200     for i:=1 to q do
201     begin
202       read(c[i]);
203       b[c[i]]:=i;
204       v[c[i]]:=true;
205     end;
206     sort(1,q);
207     st[1]:=1;
208     t:=1;
209     for i:=1 to q do
210     begin
211       x:=c[i];
212       z:=lca(x,st[t]);
213       while d[z]<d[st[t]] do
214       begin
215         if d[z]>=d[st[t-1]] then
216         begin
217           add(z,st[t]);
218           dec(t);
219           if st[t]<>z then
220           begin
221             inc(t);
222             st[t]:=z;
223           end;
224           break;
225         end;
226         add(st[t-1],st[t]);
227         dec(t);
228       end;
229       if st[t]<>x then
230       begin
231         inc(t);
232         st[t]:=x;
233       end;
234     end;
235     while t>1 do
236     begin
237       add(st[t-1],st[t]);
238       dec(t);
239     end;
240     work1(1);
241     work2(1);
242     calc(1);
243     for i:=1 to q do
244     begin
245       write(ans[i],‘ ‘);
246       ans[i]:=0;
247       b[c[i]]:=0;
248       v[c[i]]:=false;
249     end;
250     writeln;
251   end;
252 end.