【CF733F】Drivers Dissatisfaction（最小瓶颈生成树，倍增）

题意：给出一个图，每条边有权值和花费c，每次花费ｃ能使的权值-1。给出一个预算，求减完权值后的一个最小生成树。

思路：感谢CC大神

有这样一个结论：最佳方案里必定存在一种，预算全部花费全部分配在一条边上。证明显然，对于任意一组解，都可以在内部再分配预算使总费用更小或不变。

于是先求出原图的最小生成树，枚举每条边。

对于在生成树中的，判断使这条边减费是否更优。

不在生成树上的，找出树上从x[i]到y[i]的路径（唯一）上a[i]最大的边，判断删除那条边并加入减费后的(x[i],y[i])是否更优。

 type yjs=record
           a:longint;
           s:int64;
          end;
 var f,q,g:array[..,..]of longint;
     head,vet,next,len,num,a,b,c,x,y,dep,fa,inq,ya,yb:array[..]of longint;
     hth,mst,s:int64;
     tot,n,m,i,del,k,tx,ty:longint;
     t:yjs;

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

 procedure qsort(l,r:longint);
 var i,j,mid:longint;
 begin
  i:=l; j:=r; mid:=a[(l+r)>>];
  repeat
   while mid>a[i] do inc(i);
   while mid<a[j] do dec(j);
   if i<=j then
   begin
    swap(a[i],a[j]); swap(b[i],b[j]); swap(c[i],c[j]);
    swap(x[i],x[j]); swap(y[i],y[j]);
    inc(i); dec(j);
   end;
  until i>j;
  if l<j then qsort(l,j);
  if i<r then qsort(i,r);
 end;

 procedure add(a,b,c,d:longint);
 begin
  inc(tot);
  next[tot]:=head[a];
  vet[tot]:=b;
  len[tot]:=c;
  num[tot]:=d;
  head[a]:=tot;
 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:=q[x,i];
  for i:= downto  do
   if q[x,i]<>q[y,i] then
   begin
    x:=q[x,i]; y:=q[y,i];
   end;
  if x=y then exit(x);
  exit(q[x,]);
 end;

 function clac(x,y:longint):yjs;
 var i,d:longint;
     cc:yjs;
 begin
  if dep[x]<dep[y] then swap(x,y);
  d:=dep[x]-dep[y];
  cc.a:=; cc.s:=-maxlongint;
  for i:= downto  do
   if d and (<<i)> then
   begin
    if f[x,i]>cc.s then
    begin
     cc.a:=g[x,i];
     cc.s:=f[x,i];
    end;
    x:=q[x,i];
   end;
  exit(cc);
 end;

 function ask(x,y:longint):yjs;
 var t:longint;
     t1,t2:yjs;
 begin
  t:=lca(x,y);
  t1:=clac(x,t);
  t2:=clac(y,t);
  if t1.s>t2.s then exit(t1);
  exit(t2);
 end;

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

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

 begin

  readln(n,m);
  for i:= to m do read(a[i]);
  for i:= to m do read(b[i]);
  for i:= to m do c[i]:=i;
  for i:= to m do readln(x[i],y[i]);
  readln(s);
  ya:=a; yb:=b;
  qsort(,m);
  for i:= to n do fa[i]:=i;
  for i:= to m do
  begin
   tx:=find(x[i]); ty:=find(y[i]);
   if tx<>ty then
   begin
    fa[ty]:=tx;
    hth:=hth+a[i];
    inq[c[i]]:=;
    add(x[i],y[i],a[i],c[i]);
    add(y[i],x[i],a[i],c[i]);
   end;
  end;
  dfs(,-);
  mst:=hth;
  for i:= to m do
   if inq[c[i]]= then
   begin
    if mst-s div b[i]<hth then
    begin
     hth:=mst-s div b[i];
     k:=c[i];
    end;
   end
    else
    begin
     t:=ask(x[i],y[i]);
     if mst-ya[t.a]+a[i]-s div b[i]<hth then
     begin
      hth:=mst-ya[t.a]+a[i]-s div b[i];
      k:=c[i];
      del:=t.a;
     end;
    end;
  writeln(hth);
  for i:= to m do
  begin
   if i=del then continue;
   if i=k then begin writeln(i,' ',ya[i]-s div yb[i]); continue; end;
   if inq[i]= then writeln(i,' ',ya[i]);
  end;

 end.