【BZOJ3669】魔法森林（LCT）

题意：有一张无向图，每条边有两个权值。求选取一些边使1和n连通，且max(a[i])+max(b[i])最小

2<=n<=50,000

0<=m<=100,000

1<=ai ,bi<=50,000

思路：LCT模板

将a[i]排序，维护路径上b[i]的最大值

因为是无向图且连通情况不变，不用findroot检查是否连通，并查集即可

也许是OI生涯最后一次打LCT

 var t:array[..,..]of longint;
     rev,fa,mx,w,a,b,f,q,x,y:array[..]of longint;
     n,m,i,j,u,v,ans,tmp,top:longint;

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

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

 function isroot(x:longint):boolean;
 begin
  if (t[fa[x],]<>x)and(t[fa[x],]<>x) then exit(true);
  exit(false);
 end;

 procedure pushup(p:longint);
 var l,r:longint;
 begin
  l:=t[p,]; r:=t[p,];
  mx[p]:=p;
  if w[mx[l]]>w[mx[p]] then mx[p]:=mx[l];
  if w[mx[r]]>w[mx[p]] then mx[p]:=mx[r];
 end;

 procedure pushdown(p:longint);
 var l,r:longint;
 begin
  l:=t[p,]; r:=t[p,];
  if rev[p]= then
  begin
   rev[p]:=; rev[l]:=rev[l] xor ; rev[r]:=rev[r] xor ;
   swap(t[p,],t[p,]);
  end;
 end;

 procedure rotate(x:longint);
 var y,z,l,r:longint;
 begin
  y:=fa[x]; z:=fa[y];
  if t[y,]=x then l:=
   else l:=;
  r:=l xor ;
  if not isroot(y) then
  begin
   if t[z,]=y then t[z,]:=x
    else t[z,]:=x;
  end;
  fa[x]:=z; fa[y]:=x; fa[t[x,r]]:=y;
  t[y,l]:=t[x,r]; t[x,r]:=y;
  pushup(y);
  pushup(x);
 end;

 procedure splay(x:longint);
 var y,z,k:longint;
 begin
  inc(top); q[top]:=x;
  k:=x;
  while not isroot(k) do
  begin
   inc(top); q[top]:=fa[k];
   k:=fa[k];
  end;
  while top> do
  begin
   pushdown(q[top]);
   dec(top);
  end;

  while not isroot(x) do
  begin
   y:=fa[x]; z:=fa[y];
   if not isroot(y) then
   begin
    if (t[y,]=x)xor(t[z,]=y) then rotate(x)
     else rotate(y);
   end;
   rotate(x);
  end;
 end;

 procedure access(x:longint);
 var k:longint;
 begin
  k:=;
  while x> do
  begin
   splay(x); t[x,]:=k; pushup(x);
   k:=x; x:=fa[x];
  end;
 end;

 procedure makeroot(x:longint);
 begin
  access(x); splay(x); rev[x]:=rev[x] xor ;
 end;

 procedure link(x,y:longint);
 begin
  makeroot(x); fa[x]:=y;
 end;

 procedure split(x,y:longint);
 begin
  makeroot(x); access(y); splay(y);
 end;

 procedure cut(x,y:longint);
 begin
  makeroot(x); access(y); splay(y); t[y,]:=; fa[x]:=;
  pushup(y);
 end;

 function query(x,y:longint):longint;
 begin
  split(x,y);
  exit(mx[y]);
 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(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;

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

 begin
  assign(input,'bzoj3669.in'); reset(input);
  assign(output,'bzoj3669.out'); rewrite(output);
  readln(n,m);
  for i:= to n do f[i]:=i;
  for i:= to m do read(x[i],y[i],a[i],b[i]);
  qsort(,m);
  ans:=maxlongint;

  for i:= to m do
  begin
   u:=x[i]; v:=y[i];
   if find(u)=find(v) then
   begin
    tmp:=query(u,v);
    if w[tmp]>b[i] then
    begin
     cut(tmp,x[tmp-n]);
     cut(tmp,y[tmp-n]);
    end
     else
     begin
      if find()=find(n) then
      begin
       tmp:=query(,n);
       ans:=min(ans,w[tmp]+a[i]);
      end;
      continue;
     end;
   end
    else f[find(u)]:=find(v);
   w[i+n]:=b[i]; mx[i+n]:=i+n;
   link(u,i+n); link(v,i+n);
   if find()=find(n) then
   begin
    tmp:=query(,n);
    ans:=min(ans,w[tmp]+a[i]);
   end;
  end;
  if ans=maxlongint then writeln(-)
   else writeln(ans);
  close(input);
  close(output);
 end.