【POJ1743】Musical Theme（后缀数组，二分）

题意：求一个字符串的不重叠最长相同变化的子串

n<=20000

思路：这是一道论文题

我们将原串两两之间作差，可以发现所求的相同变化的子串作出的差相同

问题就转化成了不重叠的最长重复子串

显然答案有二分性，二分答案，将问题转化为是否存在长度为k的相同子串

将后缀分成连续的若干组，每组相邻的height都不小于k

有希望满足条件的两个后缀一定在同一组

只要判断某组中的sa最大与最小值之差是否不小于k即可

有一组满足则k满足

 var a,b,wc,wd,x,y,height,sa,rank:array[..]of longint;
     n,i,l,r,mid,last,m:longint;
 
 function cmp(a,b,l:longint):boolean;
 begin
  exit((y[a]=y[b])and(y[a+l]=y[b+l]));
 end;
 
 procedure swap(var x,y:longint);
 var t:longint;
 begin
  t:=x; x:=y; y:=t;
 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
   begin
    if cmp(sa[i-],sa[i],j) then x[sa[i]]:=p-
     else begin x[sa[i]]:=p; inc(p); end;
   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 min(x,y:longint):longint;
 begin
  if x<y then exit(x);
  exit(y);
 end;
 
 function max(x,y:longint):longint;
 begin
  if x>y then exit(x);
  exit(y);
 end;
 
 function isok(x:longint):boolean;
 var l,r,i:longint;
 begin
  l:=sa[]; r:=sa[];
  for i:= to n- do
   if height[i]<x then
   begin
    l:=sa[i]; r:=sa[i];
   end
    else
    begin
     l:=min(l,sa[i]);
     r:=max(r,sa[i]);
     if r-l>=x then exit(true);
    end;
  exit(false);
 end;
 
 begin
  assign(input,'poj1743.in'); reset(input);
  assign(output,'poj1743.out'); rewrite(output);
  while not eof do
  begin
   fillchar(a,sizeof(a),);
   fillchar(b,sizeof(b),);
   fillchar(sa,sizeof(sa),);
   fillchar(rank,sizeof(rank),);
   fillchar(x,sizeof(x),);
   fillchar(y,sizeof(y),);
   fillchar(height,sizeof(height),);
   fillchar(wc,sizeof(wc),);
   fillchar(wd,sizeof(wd),);
   readln(n);
   if n= then break;
   for i:= to n- do read(b[i]);
   dec(n);
   for i:= to n- do a[i]:=b[i+]-b[i]+;
   a[n]:=; m:=;
   getsa(n+);
   getheight(n);
   l:=; r:=(n-) div ; last:=;
   while l<=r do
   begin
    mid:=(l+r)>>;
    if isok(mid) then begin last:=mid; l:=mid+; end
     else r:=mid-;
   end;
   if last< then writeln()
    else writeln(last+);
  // for i:= to n do write(sa[i]+,' ');
  // writeln;
  // for i:= to n do writeln(height[i]);
 
  end;
 
  close(input);
  close(output);
 end.