【NOIP2016练习&BZOJ2125】T3 sp （树上倍增，最短路）

题意：给一个N个点M条边的连通无向图，满足每条边最多属于一个环，有Q组询问，每次询问两点之间的最短路径。

对于80%的数据环的个数<=1

对于100%的数据N<=10000，Q<=10000

思路：bzoj原题

只会80，正解听说是仙人掌

对于80每个询问的最优解必定是一棵树或一棵树+一条边，因为环的个数<=1

倍增LCA求距离，枚举树上加哪条边即可

 var f,g:array[..,..]of longint;
     head,vet,next,fa,dep,a,b,c,len:array[..]of longint;
     n,i,tx,ty,tz,ans,w,tot,m,q,x,y,j:longint;

 function min(x,y:longint):longint;
 begin
  if x<y then exit(x);
  exit(y);
 end;

 procedure add(a,b,c:longint);
 begin
  inc(tot);
  next[tot]:=head[a];
  vet[tot]:=b;
  len[tot]:=c;
  head[a]:=tot;
 end;

 procedure swap(var x,y:longint);
 var t:longint;
 begin
  t:=x; x:=y; y:=t;
 end;

 function lca(x,y:longint):longint;
 var i,d:longint;
 begin
  if dep[x]<dep[y] then swap(x,y);
  d:=dep[x]-dep[y];
  for i:= to  do
   if d and (<<i)> then x:=f[x,i];
  for i:= downto  do
   if f[x,i]<>f[y,i] then
   begin
    x:=f[x,i]; y:=f[y,i];
   end;
  if x=y then exit(x);
  exit(f[x,]);
 end;

 function clac(x,y:longint):longint;
 var i,d:longint;
 begin
  if dep[x]<dep[y] then swap(x,y);
  d:=dep[x]-dep[y];
  clac:=;
  for i:= to  do
   if d and (<<i)> then
   begin
    clac:=clac+g[x,i];
    x:=f[x,i];
   end;
 end;

 function ask(x,y:longint):longint;
 var t:longint;
 begin
  t:=lca(x,y);
  exit(clac(x,t)+clac(y,t));
 end;

 function find(k:longint):longint;
 begin
  if fa[k]<>k then fa[k]:=find(fa[k]);
  exit(fa[k]);
 end;

 procedure dfs(u,pre:longint);
 var i,e,v:longint;
 begin
  for i:= to  do
  begin
   if dep[u]<<<i then break;
   f[u,i]:=f[f[u,i-],i-];
   g[u,i]:=g[u,i-]+g[f[u,i-],i-];
  end;
  e:=head[u];
  while e<> do
  begin
   v:=vet[e];
   if v<>pre then
   begin
    dep[v]:=dep[u]+;
    f[v,]:=u; g[v,]:=len[e];
    dfs(v,u);
   end;
   e:=next[e];
  end;
 end;

 begin
  assign(input,'sp.in'); reset(input);
  assign(output,'sp.out'); rewrite(output);
  readln(n,m,q);
  for i:= to n do fa[i]:=i;
  for i:= to m do
  begin
   readln(tx,ty,tz);
   x:=find(tx); y:=find(ty);
   if x<>y then
   begin
    fa[y]:=x;
    add(tx,ty,tz);
    add(ty,tx,tz);
   end
    else begin inc(w); a[w]:=tx; b[w]:=ty; c[w]:=tz; end;
  end;
  dfs(,-);
  for i:= to q do
  begin
   read(tx,ty);
   ans:=ask(tx,ty);
   for j:= to w do
   begin
    ans:=min(ans,ask(tx,a[j])+c[j]+ask(ty,b[j]));
    ans:=min(ans,ask(ty,a[j])+c[j]+ask(tx,b[j]));
   end;
   writeln(ans);
  end;
  close(input);
  close(output);
 end.