1195: [HNOI2006]最短母串 - BZOJ

Description

给定n个字符串（S1,S2,„,Sn），要求找到一个最短的字符串T，使得这n个字符串（S1,S2,„,Sn）都是T的子串。
Input

第一行是一个正整数n（n<=12），表示给定的字符串的个数。以下的n行，每行有一个全由大写字母组成的字符串。每个字符串的长度不超过50.
Output

只有一行，为找到的最短的字符串T。在保证最短的前提下，如果有多个字符串都满足要求，那么必须输出按字典序排列的第一个。
Sample Input

2

ABCD

BCDABC
Sample Output

ABCDABC

状压DP，f[i,s]表示以i开头状态为s的情况最短字符串有多长

为了比较字典序和方便的输出最终串，我们还要记录fa[i,s]表示f[i,s]的第二个字符串是哪个

 var
     str:array[..,..]of string;
     g:array[..,..]of longint;
     f,fa:array[..,..]of longint;
     a:array[..]of string;
     n:longint;

 function get(i,j:longint):string;
 var
     k,l:longint;
     flag:boolean;
 begin
     for k:= to length(a[i]) do
       begin
         if length(a[i])-k+>length(a[j]) then continue;
         flag:=true;
         for l:=k to length(a[i]) do
           if a[i][l]<>a[j][l-k+] then flag:=false;
         if flag then
         begin
           get:=a[i];
           for l:=length(a[i])-k+ to length(a[j]) do
             get:=get+a[j][l];
           g[i,j]:=length(a[i])-k+;
           exit(get);
         end;
       end;
     exit(a[i]+a[j]);
 end;

 procedure init;
 var
     i,j:longint;
 begin
     readln(n);
     for i:= to n do
       readln(a[i]);
     for i:= to n do
       for j:= to n do
         if i<>j then str[i,j]:=get(i,j);
 end;

 var
     d:array[..,..]of longint;

 procedure work;
 var
     i,j,k,head,tail,min,lastj:longint;
 begin
     head:=;
     tail:=;
     for i:= to n do
       begin
         inc(tail);
         f[i,<<(i-)]:=length(a[i]);
         d[tail,]:=i;
         d[tail,]:=<<(i-);
       end;
     while head<=tail do
       begin
         for i:= to n do
           if d[head,]and(<<(i-))= then
           begin
             if fa[i,d[head,]+<<(i-)]= then
             begin
               inc(tail);
               d[tail,]:=i;
               d[tail,]:=d[head,]+<<(i-);
               fa[i,d[head,]+<<(i-)]:=d[head,];
               f[i,d[head,]+<<(i-)]:=f[d[head,],d[head,]]+length(a[i])-g[i,d[head,]];
             end;
             if f[i,d[head,]+<<(i-)]>f[d[head,],d[head,]]+length(a[i])-g[i,d[head,]] then
             begin
               f[i,d[head,]+<<(i-)]:=f[d[head,],d[head,]]+length(a[i])-g[i,d[head,]];
               fa[i,d[head,]+<<(i-)]:=d[head,];
             end;
             if f[i,d[head,]+<<(i-)]=f[d[head,],d[head,]]+length(a[i])-g[i,d[head,]] then
             if str[i,fa[i,d[head,]+<<(i-)]]>str[i,d[head,]] then
             begin
               f[i,d[head,]+<<(i-)]:=f[d[head,],d[head,]]+length(a[i])-g[i,d[head,]];
               fa[i,d[head,]+<<(i-)]:=d[head,];
             end;
           end;
         inc(head);
       end;
     min:=;
     for i:= to n do
       if (f[i,<<n-]<min)or((f[i,<<n-]=min)and(str[i,fa[i,<<n-]]<str[j,fa[j,<<n-]])) then
       begin
         min:=f[i,<<n-];
         j:=i;
       end;
     write(a[j]);
     min:=<<n-;
     for i:= to n- do
       begin
         dec(min,<<(j-));
         lastj:=j;
         j:=fa[j,min+<<(j-)];
         for k:=g[lastj,j]+ to length(a[j]) do
           write(a[j][k]);
       end;
 end;

 begin
     init;
     work;
 end.