【POJ2406】Power Strings（KMP，后缀数组）

题意：

n<=1000000，cas较大

 

思路：这是一道论文题

 

后缀数组已弃疗，强行需要DC3构造，懒得（不会）写

var a,x,y,sa,rank,height,dp,wc,wd:array[0..1000010]of longint;
    n,m,i,j,len,ans,st:longint;
    ch:ansistring;
    flag:boolean;

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

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:=0 to m do wc[i]:=0;
 for i:=0 to n-1 do
 begin
  x[i]:=a[i];
  inc(wc[a[i]]);
 end;
 for i:=1 to m-1 do wc[i]:=wc[i-1]+wc[i];
 for i:=n-1 downto 0 do
 begin
  dec(wc[x[i]]);
  sa[wc[x[i]]]:=i;
 end;
 j:=1; p:=1;
 while p<n do
 begin
  p:=0;
  for i:=n-j to n-1 do
  begin
   y[p]:=i; inc(p);
  end;
  for i:=0 to n-1 do
   if sa[i]>=j then begin y[p]:=sa[i]-j; inc(p); end;
  for i:=0 to n-1 do wd[i]:=x[y[i]];
  for i:=0 to m-1 do wc[i]:=0;
  for i:=0 to n-1 do inc(wc[wd[i]]);
  for i:=1 to m-1 do wc[i]:=wc[i-1]+wc[i];
  for i:=n-1 downto 0 do
  begin
   dec(wc[wd[i]]);
   sa[wc[wd[i]]]:=y[i];
  end;
  for i:=0 to n do swap(x[i],y[i]);
  p:=1; x[sa[0]]:=0;
  for i:=1 to n-1 do
   if cmp(sa[i-1],sa[i],j) then x[sa[i]]:=p-1
    else begin x[sa[i]]:=p; inc(p); end;
  j:=j*2;
  m:=p;
 end;
end;

procedure getheight(n:longint);
var i,j,k:longint;
begin
 for i:=1 to n do rank[sa[i]]:=i;
 k:=0;
 for i:=0 to n-1 do
 begin
  if k>0 then dec(k);
  j:=sa[rank[i]-1];
  while a[i+k]=a[j+k] do inc(k);
  height[rank[i]]:=k;
 end;
end;

{procedure init;
begin
 fillchar(a,sizeof(a),0);
 fillchar(x,sizeof(x),0);
 fillchar(y,sizeof(y),0);
 fillchar(sa,sizeof(sa),0);
 fillchar(rank,sizeof(rank),0);
 fillchar(height,sizeof(height),0);
 fillchar(dp1,sizeof(dp1),0);
 fillchar(dp2,sizeof(dp2),0);
end;     }

begin
 assign(input,'data.in'); reset(input);
 assign(output,'poj2406.out'); rewrite(output);
 while not eof do
 begin
  //init;
  readln(ch);
  n:=length(ch);
  if ch='.' then break;
  for i:=0 to n do
  begin
   height[i]:=0; sa[i]:=0; rank[i]:=0;
   dp[i]:=0;
  end;
  for i:=0 to n-1 do a[i]:=ord(ch[i+1]);
  a[n]:=1; m:=200;
  getsa(n+1);
  getheight(n);
  dp[rank[0]]:=maxlongint;
  for i:=rank[0]+1 to n do dp[i]:=min(height[i],dp[i-1]);
  for i:=rank[0]-1 downto 0 do dp[i]:=min(height[i+1],dp[i+1]);
  ans:=1;
  for i:=1 to n div 2 do
   if n mod i=0 then
   begin
    st:=n-i;
    if dp[rank[i]]=n-i then begin ans:=n div i; break; end;
   end;
  writeln(ans);
 end;
end.

 显然钦定的算法是KMP

var a:ansistring;
    next:array[0..2000000]of longint;
    n,i,j:longint;
 
begin
 
 while not eof do
 begin
  readln(a);
  if a='.' then break;
  n:=length(a);
  i:=0; j:=1;
  next[1]:=0;
  while j<=n do
  begin
   if (i=0)or(a[i]=a[j]) then
   begin
    inc(i); inc(j);
    next[j]:=i;
   end
    else i:=next[i];
  end;
  if n mod (n-next[n+1]+1)=0 then
   writeln(n div (n-next[n+1]+1))
    else writeln(1);
  for i:=0 to n+1 do next[i]:=0;
 end;
  
end.