BZOJ 1787: [Ahoi2008]Meet 紧急集合（lca+贪心）

                                             [Ahoi2008]Meet 紧急集合

Description

 Input

 Output

Sample Input

6 4

1 2

2 3

2 4

4 5

5 6

4 5 6

6 3 1

2 4 4

6 6 6

Sample Output

5 2

2 5

4 1

6 0
HINT

 

分析：很简单的一道题，对于每次询问要分情况讨论，先求出两两之间的lca，如果为同一点，显然该点为集合点，如果有一个x不同于另外两个，则三者在一条链上，x为中间的一个，故x为集合点，如果三者互不相同，集合点可以是三者到共同lca路径上任何一点，或者干脆将三者共同lca作为集合点就行了。

代码：

program Meet;
type
  point=^node;
    node=record
       x:longint; next:point;
    end;
var
  a:array[0..500000]of point;
  f:array[0..20,0..500000]of longint;
  deep,s:array[0..500000]of longint;
  n,i,m,x,y,t,z,v1,v2,v3,ans:longint;
procedure add(x,y:longint);
var p:point;
begin
  new(p); p^.x:=y; p^.next:=a[x]; a[x]:=p;
end;
procedure dfs(x,k:longint);
var p:point;
begin
  new(p); p:=a[x];  f[0,x]:=k; deep[x]:=deep[k]+1;
  while p<>nil do
   begin
     if p^.x<>k then dfs(p^.x,x);p:=p^.next;
   end;
end;
procedure work;
var i,j:longint;
begin
  for i:=0 to trunc(ln(n)/ln(2))-1 do
   for j:=1 to n do
    f[i+1,j]:=f[i,f[i,j]];
end;
function lca(x,y:longint):longint;
var i,t:longint;
begin
  if deep[x]<deep[y] then begin t:=x; x:=y; y:=t; end;
  for i:=0 to trunc(ln(n)/ln(2)) do
   if ((deep[x]-deep[y])>>i) and 1=1 then x:=f[i,x];
  if x=y then exit(x);
  for i:=trunc(ln(n)/ln(2)) downto 0 do
   if f[i,x]<>f[i,y] then
    begin x:=f[i,x]; y:=f[i,y]; end;
  exit(f[0,x]);
end;
begin
  assign(input,'Meet.in');
reset(input);
assign(output,'Meet.out');
rewrite(output);
  readln(n,m);
  for i:=1 to n-1 do
   begin
     readln(x,y); add(x,y); add(y,x);
   end;
  deep[1]:=0;
  dfs(1,1);  work;
  for i:=1 to m do
   begin
     readln(x,y,z);
     v1:=lca(x,y);  v2:=lca(x,z); v3:=lca(z,y);
     if (v1=v2)and(v2=v3) then t:=v1
      else if v1=v2 then t:=v3
       else if v2=v3 then t:=v1
        else t:=v2;
     v1:=lca(x,t); v2:=lca(y,t); v3:=lca(z,t);
     ans:=deep[x]+deep[y]+deep[z]+deep[t]*3-2*(deep[v1]+deep[v2]+deep[v3]);
     writeln(t,' ',ans);
   end;
  close(input); close(output);
end.