Ural1297Palindrome（后缀数组）

Posted 2020-08-31 myx12345

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]])

  1 var f:array[0..3000,0..11]of longint;
  2     x,y,sa,rank,height,a,wc,wd:array[0..3000]of longint;
  3     ch:ansistring;
  4     n,m,i,k,max,tmp,t,j:longint;
  5 
  6 function min(x,y:longint):longint;
  7 begin
  8  if x<y then exit(x);
  9  exit(y);
 10 end;
 11 
 12 procedure swap(var x,y:longint);
 13 var t:longint;
 14 begin
 15  t:=x; x:=y; y:=t;
 16 end;
 17 
 18 function cmp(a,b,l:longint):boolean;
 19 begin
 20  exit((y[a]=y[b])and(y[a+l]=y[b+l]));
 21 end;
 22 
 23 procedure getsa(n:longint);
 24 var i,j,p:longint;
 25 begin
 26  for i:=0 to n-1 do
 27  begin
 28   x[i]:=a[i];
 29   inc(wc[a[i]]);
 30  end;
 31  for i:=1 to m-1 do wc[i]:=wc[i-1]+wc[i];
 32  for i:=n-1 downto 0 do
 33  begin
 34   dec(wc[x[i]]);
 35   sa[wc[x[i]]]:=i;
 36  end;
 37  j:=1; p:=1;
 38  while p<n do
 39  begin
 40   p:=0;
 41   for i:=n-j to n-1 do
 42   begin
 43    y[p]:=i; inc(p);
 44   end;
 45   for i:=0 to n-1 do
 46    if sa[i]>=j then begin y[p]:=sa[i]-j; inc(p); end;
 47   for i:=0 to n-1 do wd[i]:=x[y[i]];
 48   for i:=0 to m-1 do wc[i]:=0;
 49   for i:=0 to n-1 do inc(wc[wd[i]]);
 50   for i:=1 to m-1 do wc[i]:=wc[i-1]+wc[i];
 51   for i:=n-1 downto 0 do
 52   begin
 53    dec(wc[wd[i]]);
 54    sa[wc[wd[i]]]:=y[i];
 55   end;
 56   for i:=0 to n do swap(x[i],y[i]);
 57   p:=1; x[sa[0]]:=0;
 58   for i:=1 to n-1 do
 59    if cmp(sa[i-1],sa[i],j) then x[sa[i]]:=p-1
 60     else begin x[sa[i]]:=p; inc(p); end;
 61   j:=j*2;
 62   m:=p;
 63  end;
 64 end;
 65 
 66 procedure getheight(n:longint);
 67 var i,j,k:longint;
 68 begin
 69  k:=0;
 70  for i:=1 to n do rank[sa[i]]:=i;
 71  for i:=0 to n-1 do
 72  begin
 73   if k>0 then dec(k);
 74   j:=sa[rank[i]-1];
 75   while a[i+k]=a[j+k] do inc(k);
 76   height[rank[i]]:=k;
 77  end;
 78 end;
 79 
 80 function query(x,y:longint):longint;
 81 var len,l:longint;
 82 begin
 83  len:=y-x+1; l:=trunc(ln(len)/ln(2));
 84  exit(min(f[x,l],f[y-(1<<l)+1,l]));
 85 end;
 86 
 87 function lcp(x,y:longint):longint;
 88 var i,j:longint;
 89 begin
 90  //inc(x); inc(y);
 91  i:=rank[x]; j:=rank[y];
 92  if i>j then swap(i,j);
 93  inc(i);
 94  exit(query(i,j));
 95 end;
 96 
 97 procedure init;
 98 begin
 99  fillchar(a,sizeof(a),0);
100  fillchar(height,sizeof(height),0);
101  fillchar(sa,sizeof(sa),0);
102  fillchar(rank,sizeof(rank),0);
103  fillchar(f,sizeof(f),0);
104  fillchar(x,sizeof(x),0);
105  fillchar(y,sizeof(y),0);
106  fillchar(wc,sizeof(wc),0);
107  fillchar(wd,sizeof(wd),0);
108 end;
109 
110 begin
111  assign(input,\'ural1297.in\'); reset(input);
112  assign(output,\'ural1297.out\'); rewrite(output);
113  while not eof do
114  begin
115   init;
116   readln(ch);
117   n:=length(ch);
118   if n=0 then break;
119   for i:=0 to n-1 do a[i]:=ord(ch[i+1]);
120   a[n]:=1; m:=300;
121   for i:=n+1 to 2*n do a[i]:=ord(ch[n-(i-n)+1]);
122   a[n*2+1]:=0;
123   getsa(n*2+2);
124   getheight(n*2+1);
125   m:=n*2+2;
126   t:=trunc(ln(m)/ln(2));
127   for i:=2 to m do f[i,0]:=height[i];
128   for i:=1 to t do
129    for j:=2 to m do
130     if j+(1<<(i-1))<=m then f[j,i]:=min(f[j,i-1],f[j+(1<<(i-1)),i-1]);
131   max:=0; k:=0;
132   for i:=0 to n-1 do
133   begin
134    tmp:=lcp(i,2*n-i)*2-1;
135    if tmp>max then
136    begin
137     max:=tmp;
138     k:=i;
139     end;
140    if i>0 then
141    begin
142     tmp:=lcp(i,n*2-i+1)*2;
143     if tmp>max then
144     begin
145      max:=tmp;
146      k:=i;
147     end;
148    end;
149   end;
150   if max mod 2=1 then
151    for j:=k-max div 2+1 to k+max div 2+1 do write(ch[j])
152     else
153      for j:=k-max div 2+1 to k+max div 2 do write(ch[j]);
154   writeln;
155  // for i:=2 to n*2+2 do writeln(height[i]);
156  // for i:=1 to n*2+2 do writeln(rank[i]);
157  // writeln;
158  end;
159 
160 
161 
162  close(input);
163  close(output);
164 end.