【BZOJ4736】温暖会指引我们前行（LCT）

题意：有一张图，每条边有一个不同的编号，长度和权值，维护以下操作：

1.加边

2.修改边长

3.询问两点之间在最小权值最大的前提下的唯一路径长度

n<=100000 m<=300000

思路：RYZ作业

BZOJ上有四组数据的输入不完整，输出没问题

LCT维护最大生成树，维护子树和，和子树中权值最小的位置即可

 var t:array[..,..]of longint;
     sum:array[..]of int64;
     f:array[..,..]of longint;
     w,l1,mx,fa,q,rev:array[..]of longint;
     n,m,x,y,top,tot,id,i,len,s,ll,tt,j,tmp,now:longint;
     ch:string;

 procedure swap(var x,y:longint);
 var t:longint;
 begin
  t:=x; x:=y; y:=t;
 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(x:longint);
 var l,r:longint;
 begin
  l:=t[x,]; r:=t[x,];
  sum[x]:=sum[l]+sum[r]+l1[x];
  mx[x]:=x;
  if w[mx[l]]<w[mx[x]] then mx[x]:=mx[l];
  if w[mx[r]]<w[mx[x]] then mx[x]:=mx[r];
 end;

 procedure pushdown(x:longint);
 var l,r:longint;
 begin
  l:=t[x,]; r:=t[x,];
  if rev[x]> then
  begin
   rev[x]:=rev[x] xor ; rev[l]:=rev[l] xor ; rev[r]:=rev[r] xor ;
   swap(t[x,],t[x,]);
  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[y]:=x; fa[x]:=z; 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 k,y,z: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[x];
   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 last:longint;
 begin
  last:=;
  while x> do
  begin
   splay(x); t[x,]:=last; pushup(x);
   last:=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]:=;
 end;

 function findroot(x:longint):longint;
 var k:longint;
 begin
  access(x); splay(x);
  k:=x;
  while t[k,]<> do k:=t[k,];
  exit(k);
 end;

 begin
  assign(input,'bzoj4736.in'); reset(input);
  assign(output,'bzoj4736.out'); rewrite(output);
  readln(n,m);
  fillchar(w,sizeof(w),$7f);
  //fillchar(l,sizeof(l),$1f);
  for i:= to m do
  begin
   readln(ch); s:=; id:=; x:=; y:=; tt:=; ll:=;
   len:=length(ch);
   case ch[] of
    'f':
    begin
     for j:= to len do
     begin
      if ch[j]=' ' then begin inc(s); continue; end;
      tmp:=ord(ch[j])-ord('');
      case s of
       :id:=id*+tmp;
       :x:=x*+tmp;
       :y:=y*+tmp;
       :tt:=tt*+tmp;
       :ll:=ll*+tmp;
      end;
     end;
     inc(x); inc(y); inc(id);
     tot:=id+;
     w[tot]:=tt; l1[tot]:=ll; f[tot,]:=x; f[tot,]:=y;
     if findroot(x)<>findroot(y) then
     begin
      mx[tot]:=tot;
      link(x,tot); link(tot,y);
     end
      else
      begin
       split(x,y);
       now:=mx[y];
       if w[now]<tt then
       begin
        cut(f[now,],now); cut(now,f[now,]);
        mx[tot]:=tot;
        link(x,tot); link(tot,y);
       end;
      end;

    end;
    'm':
    begin
     for j:= to len do
     begin
      if ch[j]=' ' then begin inc(s); continue; end;
      tmp:=ord(ch[j])-ord('');
      case s of
       :x:=x*+tmp;
       :y:=y*+tmp;
      end;
     end;
     inc(x); inc(y);
     if findroot(x)<>findroot(y) then writeln(-)
      else
      begin
       split(x,y); writeln(sum[y]);
      end;
     end;
    'c':
    begin
     for j:= to len do
     begin
      if ch[j]=' ' then begin inc(s); continue; end;
      tmp:=ord(ch[j])-ord('');
      case s of
       :id:=id*+tmp;
       :ll:=ll*+tmp;
      end;
     end;
     inc(id); tot:=id+;
     splay(tot);
     l1[tot]:=ll;
     pushup(tot);
    end;
   end;
  end;
  close(input);
  close(output);
 end.

2017.3.9

突然发现前一个代码splay打错了一个字母导致退化成类似单旋的东西

神TM单旋也能过

 var t:array[..,..]of longint;
     sum:array[..]of int64;
     f:array[..,..]of longint;
     w,l1,mx,fa,q,rev:array[..]of longint;
     n,m,x,y,top,tot,id,i,len,s,ll,tt,j,tmp,now:longint;
     ch:string;

 procedure swap(var x,y:longint);
 var t:longint;
 begin
  t:=x; x:=y; y:=t;
 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(x:longint);
 var l,r:longint;
 begin
  l:=t[x,]; r:=t[x,];
  sum[x]:=sum[l]+sum[r]+l1[x];
  mx[x]:=x;
  if w[mx[l]]<w[mx[x]] then mx[x]:=mx[l];
  if w[mx[r]]<w[mx[x]] then mx[x]:=mx[r];
 end;

 procedure pushdown(x:longint);
 var l,r:longint;
 begin
  l:=t[x,]; r:=t[x,];
  if rev[x]> then
  begin
   rev[x]:=rev[x] xor ; rev[l]:=rev[l] xor ; rev[r]:=rev[r] xor ;
   swap(t[x,],t[x,]);
  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[y]:=x; fa[x]:=z; 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 k,y,z: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 last:longint;
 begin
  last:=;
  while x> do
  begin
   splay(x); t[x,]:=last; pushup(x);
   last:=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]:=;
 end;

 function findroot(x:longint):longint;
 var k:longint;
 begin
  access(x); splay(x);
  k:=x;
  while t[k,]<> do k:=t[k,];
  exit(k);
 end;

 begin
  assign(input,'bzoj4736.in'); reset(input);
  assign(output,'bzoj4736.out'); rewrite(output);
  readln(n,m);
  fillchar(w,sizeof(w),$7f);
  //fillchar(l,sizeof(l),$1f);
  for i:= to m do
  begin
   readln(ch); s:=; id:=; x:=; y:=; tt:=; ll:=;
   len:=length(ch);
   case ch[] of
    'f':
    begin
     for j:= to len do
     begin
      if ch[j]=' ' then begin inc(s); continue; end;
      tmp:=ord(ch[j])-ord('');
      case s of
       :id:=id*+tmp;
       :x:=x*+tmp;
       :y:=y*+tmp;
       :tt:=tt*+tmp;
       :ll:=ll*+tmp;
      end;
     end;
     inc(x); inc(y); inc(id);
     tot:=id+;
     w[tot]:=tt; l1[tot]:=ll; f[tot,]:=x; f[tot,]:=y;
     if findroot(x)<>findroot(y) then
     begin
      mx[tot]:=tot;
      link(x,tot); link(tot,y);
     end
      else
      begin
       split(x,y);
       now:=mx[y];
       if w[now]<tt then
       begin
        cut(f[now,],now); cut(now,f[now,]);
        mx[tot]:=tot;
        link(x,tot); link(tot,y);
       end;
      end;

    end;
    'm':
    begin
     for j:= to len do
     begin
      if ch[j]=' ' then begin inc(s); continue; end;
      tmp:=ord(ch[j])-ord('');
      case s of
       :x:=x*+tmp;
       :y:=y*+tmp;
      end;
     end;
     inc(x); inc(y);
     if findroot(x)<>findroot(y) then writeln(-)
      else
      begin
       split(x,y); writeln(sum[y]);
      end;
     end;
    'c':
    begin
     for j:= to len do
     begin
      if ch[j]=' ' then begin inc(s); continue; end;
      tmp:=ord(ch[j])-ord('');
      case s of
       :id:=id*+tmp;
       :ll:=ll*+tmp;
      end;
     end;
     inc(id); tot:=id+;
     splay(tot);
     l1[tot]:=ll;
     pushup(tot);
    end;
   end;
  end;
  close(input);
  close(output);
 end.