【BZOJ4199&UOJ131】品酒大会（后缀数组，并查集）

题意：

两杯“r相似” （r>1）的酒同时也是“1 相似”、“2 相似”、……、“(r−1) 相似”的。

n<=300000 abs(a[i])<=10^9

思路：对于i,j两个后缀，它们的贡献只与它们的lcp有关

而lcp又是它们之间height的最小值

所以可以把height从大到小排序

然后用并查集合并最值，方案数之类的

每次合并的都是排名相邻的一对后缀，相当于一段不相交的线段

每个集合中的lcp即为height的最小值

将r相似的加到r-1相似中

被UOJ的extra卡了一发，原来是0相似的初始最大值忘记初始化了

 const oo=<<;
 var sum,f:array[..]of int64;
     sa,rank,height,id,mx,mn,size,a,fa,x,y,wc,wd,b:array[..]of longint;
     n,m,i,p,q,t:longint;
     ch:ansistring;
 procedure swap(var x,y:longint);
 var t:longint;
 begin
  t:=x; x:=y; y:=t;
 end;
 
 function max(x,y:int64):int64;
 begin
  if x>y then exit(x);
  exit(y);
 end;
 
 function min(x,y:longint):longint;
 begin
  if x<y then exit(x);
  exit(y);
 end;
 
 procedure qsort(l,r:longint);
 var i,j,mid:longint;
 begin
  i:=l; j:=r; mid:=height[id[(l+r)>>]];
  repeat
   while mid<height[id[i]] do inc(i);
   while mid>height[id[j]] do dec(j);
   if i<=j then
   begin
    swap(id[i],id[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 fa[k]<>k then fa[k]:=find(fa[k]);
  find:=fa[k];
 end;
 
 procedure merge(x,y:longint);
 begin
  size[y]:=size[y]+size[x];
  mx[y]:=max(mx[x],mx[y]);
  mn[y]:=min(mn[x],mn[y]);
  fa[x]:=y;
 end;
 
 function cmp(a,b,l:longint):boolean;
 begin
  exit((y[a]=y[b])and(y[a+l]=y[b+l]));
 end;
 
 procedure getsa(n:longint);
 var i,j,p:longint;
 begin
  for i:= to n- do
  begin
   x[i]:=a[i];
   inc(wc[a[i]]);
  end;
  for i:= to m- do wc[i]:=wc[i-]+wc[i];
  for i:=n- downto  do
  begin
   dec(wc[x[i]]);
   sa[wc[x[i]]]:=i;
  end;
  j:=; p:=;
  while p<n do
  begin
   p:=;
   for i:=n-j to n- do
   begin
    y[p]:=i; inc(p);
   end;
   for i:= to n- do
    if sa[i]>=j then begin y[p]:=sa[i]-j; inc(p); end;
   for i:= to n- do wd[i]:=x[y[i]];
   for i:= to m- do wc[i]:=;
   for i:= to n- do inc(wc[wd[i]]);
   for i:= to m- do wc[i]:=wc[i-]+wc[i];
   for i:=n- downto  do
   begin
    dec(wc[wd[i]]);
    sa[wc[wd[i]]]:=y[i];
   end;
   for i:= to n do swap(x[i],y[i]);
   p:=; x[sa[]]:=;
   for i:= to n- do
    if cmp(sa[i-],sa[i],j) then x[sa[i]]:=p-
     else
     begin
      x[sa[i]]:=p; inc(p);
     end;
   j:=j*;
   m:=p;
  end;
 end;
 
 procedure getheight(n:longint);
 var i,j,k:longint;
 begin
  for i:= to n do rank[sa[i]]:=i;
  k:=;
  for i:= to n- do
  begin
   if k> then dec(k);
   j:=sa[rank[i]-];
   while a[i+k]=a[j+k] do inc(k);
   height[rank[i]]:=k;
  end;
 end;
 
 begin
  assign(input,'bzoj4199.in'); reset(input);
  assign(output,'bzoj4199.out'); rewrite(output);
  readln(n);
  readln(ch);
  for i:= to n- do a[i]:=ord(ch[i+])-ord('a')+;
  a[n]:=; m:=;
  getsa(n+);
  getheight(n);
  for i:= to n- do read(b[i]);
  for i:= to n do
  begin
   fa[i]:=i;
   size[i]:=; mx[i]:=b[sa[i]]; mn[i]:=mx[i];
   f[i]:=-oo;
  end;
  f[]:=-oo;
  for i:= to n- do id[i]:=i+;
  qsort(,n-);
  for i:= to n- do
  begin
   p:=find(id[i]-); q:=find(id[i]);
   t:=height[id[i]];
   sum[t]:=sum[t]+int64(size[p])*size[q];
   f[t]:=max(f[t],int64(mx[p])*mx[q]);
   f[t]:=max(f[t],int64(mx[p])*mn[q]);
   f[t]:=max(f[t],int64(mn[p])*mx[q]);
   f[t]:=max(f[t],int64(mn[p])*mn[q]);
   merge(p,q);
  end;
  for i:=n- downto  do
  begin
   sum[i]:=sum[i]+sum[i+];
   f[i]:=max(f[i],f[i+]);
  end;
  for i:= to n- do
   if f[i]>-oo then writeln(sum[i],' ',f[i])
    else writeln(,' ',);
 
  close(input);
  close(output);
 end.