【Ural1297】Palindrome（后缀数组）

题意：求一个字符串的最长回文子串

n<=1000

思路：这是一道论文题

需要注意的细节：

1.奇偶分类

2.中间的分割符与最后的附加字母都是最小值，但两者不能相同，否则height可能会出现问题

答案即为min(height[rank[x]+1]...height[rank[y]])

 var f:array[..,..]of longint;
     x,y,sa,rank,height,a,wc,wd:array[..]of longint;
     ch:ansistring;
     n,m,i,k,max,tmp,t,j:longint;

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

 procedure swap(var x,y:longint);
 var t:longint;
 begin
  t:=x; x:=y; y:=t;
 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
  k:=;
  for i:= to n do rank[sa[i]]:=i;
  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;

 function query(x,y:longint):longint;
 var len,l:longint;
 begin
  len:=y-x+; l:=trunc(ln(len)/ln());
  exit(min(f[x,l],f[y-(<<l)+,l]));
 end;

 function lcp(x,y:longint):longint;
 var i,j:longint;
 begin
  //inc(x); inc(y);
  i:=rank[x]; j:=rank[y];
  if i>j then swap(i,j);
  inc(i);
  exit(query(i,j));
 end;

 procedure init;
 begin
  fillchar(a,sizeof(a),);
  fillchar(height,sizeof(height),);
  fillchar(sa,sizeof(sa),);
  fillchar(rank,sizeof(rank),);
  fillchar(f,sizeof(f),);
  fillchar(x,sizeof(x),);
  fillchar(y,sizeof(y),);
  fillchar(wc,sizeof(wc),);
  fillchar(wd,sizeof(wd),);
 end;

 begin
  assign(input,'ural1297.in'); reset(input);
  assign(output,'ural1297.out'); rewrite(output);
  while not eof do
  begin
   init;
   readln(ch);
   n:=length(ch);
   if n= then break;
   for i:= to n- do a[i]:=ord(ch[i+]);
   a[n]:=; m:=;
   for i:=n+ to *n do a[i]:=ord(ch[n-(i-n)+]);
   a[n*+]:=;
   getsa(n*+);
   getheight(n*+);
   m:=n*+;
   t:=trunc(ln(m)/ln());
   for i:= to m do f[i,]:=height[i];
   for i:= to t do
    for j:= to m do
     if j+(<<(i-))<=m then f[j,i]:=min(f[j,i-],f[j+(<<(i-)),i-]);
   max:=; k:=;
   for i:= to n- do
   begin
    tmp:=lcp(i,*n-i)*-;
    if tmp>max then
    begin
     max:=tmp;
     k:=i;
     end;
    if i> then
    begin
     tmp:=lcp(i,n*-i+)*;
     if tmp>max then
     begin
      max:=tmp;
      k:=i;
     end;
    end;
   end;
   if max mod = then
    for j:=k-max div + to k+max div + do write(ch[j])
     else
      for j:=k-max div + to k+max div  do write(ch[j]);
   writeln;
  // for i:= to n*+ do writeln(height[i]);
  // for i:= to n*+ do writeln(rank[i]);
  // writeln;
  end;

  close(input);
  close(output);
 end.