0000: 23 69 6e 63 6c 75 64 65 20 3c 69 6f 73 74 72 65 #include <iostre
0010: 61 6d 3e 0d 0a 23 69 6e 63 6c 75 64 65 20 3c 73 am>..#include <s
0020: 73 74 72 65 61 6d 3e 0d 0a 23 69 6e 63 6c 75 64 stream>..#includ
0030: 65 20 3c 69 6f 6d 61 6e 69 70 3e 0d 0a 23 69 6e e <iomanip>..#in
0040: 63 6c 75 64 65 20 3c 76 65 63 74 6f 72 3e 0d 0a clude <vector>..
0050: 23 69 6e 63 6c 75 64 65 20 3c 73 74 72 69 6e 67 #include <string
0060: 3e 0d 0a 23 69 6e 63 6c 75 64 65 20 3c 6d 61 70 >..#include <map
0070: 3e 0d 0a 23 69 6e 63 6c 75 64 65 20 3c 73 65 74 >..#include <set
0080: 3e 0d 0a 23 69 6e 63 6c 75 64 65 20 3c 61 6c 67 >..#include <alg
0090: 6f 72 69 74 68 6d 3e 0d 0a 23 69 6e 63 6c 75 64 orithm>..#includ
00a0: 65 20 3c 6e 75 6d 65 72 69 63 3e 0d 0a 23 69 6e e <numeric>..#in
00b0: 63 6c 75 64 65 20 3c 69 74 65 72 61 74 6f 72 3e clude <iterator>
00c0: 0d 0a 23 69 6e 63 6c 75 64 65 20 3c 66 75 6e 63 ..#include <func
00d0: 74 69 6f 6e 61 6c 3e 0d 0a 23 69 6e 63 6c 75 64 tional>..#includ
00e0: 65 20 3c 63 6f 6d 70 6c 65 78 3e 0d 0a 23 69 6e e <complex>..#in
00f0: 63 6c 75 64 65 20 3c 71 75 65 75 65 3e 0d 0a 23 clude <queue>..#
0100: 69 6e 63 6c 75 64 65 20 3c 73 74 61 63 6b 3e 0d include <stack>.
0110: 0a 23 69 6e 63 6c 75 64 65 20 3c 63 6d 61 74 68 .#include <cmath
0120: 3e 0d 0a 23 69 6e 63 6c 75 64 65 20 3c 63 61 73 >..#include <cas
0130: 73 65 72 74 3e 0d 0a 23 69 6e 63 6c 75 64 65 20 sert>..#include
0140: 3c 74 75 70 6c 65 3e 0d 0a 75 73 69 6e 67 20 6e <tuple>..using n
0150: 61 6d 65 73 70 61 63 65 20 73 74 64 3b 0d 0a 74 amespace std;..t
0160: 79 70 65 64 65 66 20 6c 6f 6e 67 20 6c 6f 6e 67 ypedef long long
0170: 20 4c 4c 3b 0d 0a 74 79 70 65 64 65 66 20 63 6f LL;..typedef co
0180: 6d 70 6c 65 78 3c 64 6f 75 62 6c 65 3e 20 43 4d mplex<double> CM
0190: 50 3b 0d 0a 0d 0a 63 6c 61 73 73 20 44 69 73 74 P;....class Dist
01a0: 69 6e 67 75 69 73 68 61 62 6c 65 53 65 74 44 69 inguishableSetDi
01b0: 76 31 20 7b 20 70 75 62 6c 69 63 3a 0d 0a 09 69 v1 { public:...i
01c0: 6e 74 20 63 6f 75 6e 74 28 76 65 63 74 6f 72 20 nt count(vector
01d0: 3c 73 74 72 69 6e 67 3e 20 61 6e 73 77 65 72 29 <string> answer)
01e0: 0d 0a 09 7b 0d 0a 09 09 69 6e 74 20 4e 20 3d 20 ...{....int N =
01f0: 61 6e 73 77 65 72 2e 73 69 7a 65 28 29 3b 0d 0a answer.size();..
0200: 09 09 69 6e 74 20 51 20 3d 20 61 6e 73 77 65 72 ..int Q = answer
0210: 5b 30 5d 2e 73 69 7a 65 28 29 3b 0d 0a 09 09 76 [0].size();....v
0220: 65 63 74 6f 72 3c 62 6f 6f 6c 3e 20 6f 6b 28 31 ector<bool> ok(1
0230: 3c 3c 51 2c 20 74 72 75 65 29 3b 0d 0a 0d 0a 09 <<Q, true);.....
0240: 09 66 75 6e 63 74 69 6f 6e 3c 76 6f 69 64 28 69 .function<void(i
0250: 6e 74 29 3e 20 66 69 6c 6c 62 61 64 20 3d 20 5b nt)> fillbad = [
0260: 26 5d 28 69 6e 74 20 6d 29 20 7b 0d 0a 09 09 09 &](int m) {.....
0270: 69 66 28 21 6f 6b 5b 6d 5d 29 0d 0a 09 09 09 09 if(!ok[m])......
0280: 72 65 74 75 72 6e 3b 0d 0a 09 09 09 6f 6b 5b 6d return;.....ok[m
0290: 5d 20 3d 20 66 61 6c 73 65 3b 0d 0a 09 09 09 66 ] = false;.....f
02a0: 6f 72 28 69 6e 74 20 63 3d 30 3b 20 63 3c 51 3b or(int c=0; c<Q;
02b0: 20 2b 2b 63 29 20 69 66 28 6d 20 26 20 28 31 3c ++c) if(m & (1<
02c0: 3c 63 29 29 0d 0a 09 09 09 09 66 69 6c 6c 62 61 <c))......fillba
02d0: 64 28 6d 20 26 7e 20 28 31 3c 3c 63 29 29 3b 0d d(m &~ (1<<c));.
02e0: 0a 09 09 7d 3b 0d 0a 0d 0a 09 09 66 6f 72 28 69 ...};......for(i
02f0: 6e 74 20 69 3d 30 3b 20 69 3c 4e 3b 20 2b 2b 69 nt i=0; i<N; ++i
0300: 29 0d 0a 09 09 66 6f 72 28 69 6e 74 20 6b 3d 69 )....for(int k=i
0310: 2b 31 3b 20 6b 3c 4e 3b 20 2b 2b 6b 29 0d 0a 09 +1; k<N; ++k)...
0320: 09 7b 0d 0a 09 09 09 69 6e 74 20 62 61 64 73 65 .{.....int badse
0330: 74 20 3d 20 30 3b 0d 0a 09 09 09 66 6f 72 28 69 t = 0;.....for(i
0340: 6e 74 20 63 3d 30 3b 20 63 3c 51 3b 20 2b 2b 63 nt c=0; c<Q; ++c
0350: 29 0d 0a 09 09 09 09 69 66 28 61 6e 73 77 65 72 )......if(answer
0360: 5b 69 5d 5b 63 5d 20 3d 3d 20 61 6e 73 77 65 72 [i][c] == answer
0370: 5b 6b 5d 5b 63 5d 29 0d 0a 09 09 09 09 09 62 61 [k][c]).......ba
0380: 64 73 65 74 20 7c 3d 20 31 3c 3c 63 3b 0d 0a 09 dset |= 1<<c;...
0390: 09 09 66 69 6c 6c 62 61 64 28 62 61 64 73 65 74 ..fillbad(badset
03a0: 29 3b 0d 0a 09 09 7d 0d 0a 0d 0a 09 09 69 6e 74 );....}......int
03b0: 20 61 6e 73 20 3d 20 30 3b 0d 0a 09 09 66 6f 72 ans = 0;....for
03c0: 28 69 6e 74 20 6d 3d 30 3b 20 6d 3c 28 31 3c 3c (int m=0; m<(1<<
03d0: 51 29 3b 20 2b 2b 6d 29 0d 0a 09 09 09 69 66 28 Q); ++m).....if(
03e0: 6f 6b 5b 6d 5d 29 0d 0a 09 09 09 09 2b 2b 61 6e ok[m])......++an
03f0: 73 3b 0d 0a 09 09 72 65 74 75 72 6e 20 61 6e 73 s;....return ans
0400: 3b 0d 0a 09 7d 0d 0a 7d 3b 0d 0a 0d 0a 2f 2f 20 ;...}..};....//
0410: 42 45 47 49 4e 20 43 55 54 20 48 45 52 45 0d 0a BEGIN CUT HERE..
0420: 23 69 6e 63 6c 75 64 65 20 3c 63 74 69 6d 65 3e #include <ctime>
0430: 0d 0a 64 6f 75 62 6c 65 20 73 74 61 72 74 5f 74 ..double start_t
0440: 69 6d 65 3b 20 73 74 72 69 6e 67 20 74 69 6d 65 ime; string time
0450: 72 28 29 0d 0a 20 7b 20 6f 73 74 72 69 6e 67 73 r().. { ostrings
0460: 74 72 65 61 6d 20 6f 73 3b 20 6f 73 20 3c 3c 20 tream os; os <<
0470: 22 20 28 22 20 3c 3c 20 69 6e 74 28 28 63 6c 6f " (" << int((clo
0480: 63 6b 28 29 2d 73 74 61 72 74 5f 74 69 6d 65 29 ck()-start_time)
0490: 2f 43 4c 4f 43 4b 53 5f 50 45 52 5f 53 45 43 2a /CLOCKS_PER_SEC*
04a0: 31 30 30 30 29 20 3c 3c 20 22 20 6d 73 65 63 29 1000) << " msec)
04b0: 22 3b 20 72 65 74 75 72 6e 20 6f 73 2e 73 74 72 "; return os.str
04c0: 28 29 3b 20 7d 0d 0a 74 65 6d 70 6c 61 74 65 3c (); }..template<
04d0: 74 79 70 65 6e 61 6d 65 20 54 3e 20 6f 73 74 72 typename T> ostr
04e0: 65 61 6d 26 20 6f 70 65 72 61 74 6f 72 3c 3c 28 eam& operator<<(
04f0: 6f 73 74 72 65 61 6d 26 20 6f 73 2c 20 63 6f 6e ostream& os, con
0500: 73 74 20 76 65 63 74 6f 72 3c 54 3e 26 20 76 29 st vector<T>& v)
0510: 0d 0a 20 7b 20 6f 73 20 3c 3c 20 22 7b 20 22 3b .. { os << "{ ";
0520: 0d 0a 20 20 20 66 6f 72 28 74 79 70 65 6e 61 6d .. for(typenam
0530: 65 20 76 65 63 74 6f 72 3c 54 3e 3a 3a 63 6f 6e e vector<T>::con
0540: 73 74 5f 69 74 65 72 61 74 6f 72 20 69 74 3d 76 st_iterator it=v
0550: 2e 62 65 67 69 6e 28 29 3b 20 69 74 21 3d 76 2e .begin(); it!=v.
0560: 65 6e 64 28 29 3b 20 2b 2b 69 74 29 0d 0a 20 20 end(); ++it)..
0570: 20 6f 73 20 3c 3c 20 27 5c 22 27 20 3c 3c 20 2a os << '\"' << *
0580: 69 74 20 3c 3c 20 27 5c 22 27 20 3c 3c 20 28 69 it << '\"' << (i
0590: 74 2b 31 3d 3d 76 2e 65 6e 64 28 29 20 3f 20 22 t+1==v.end() ? "
05a0: 22 20 3a 20 22 2c 20 22 29 3b 20 6f 73 20 3c 3c " : ", "); os <<
05b0: 20 22 20 7d 22 3b 20 72 65 74 75 72 6e 20 6f 73 " }"; return os
05c0: 3b 20 7d 0d 0a 76 6f 69 64 20 76 65 72 69 66 79 ; }..void verify
05d0: 5f 63 61 73 65 28 63 6f 6e 73 74 20 69 6e 74 26 _case(const int&
05e0: 20 45 78 70 65 63 74 65 64 2c 20 63 6f 6e 73 74 Expected, const
05f0: 20 69 6e 74 26 20 52 65 63 65 69 76 65 64 29 20 int& Received)
0600: 7b 0d 0a 20 62 6f 6f 6c 20 6f 6b 20 3d 20 28 45 {.. bool ok = (E
0610: 78 70 65 63 74 65 64 20 3d 3d 20 52 65 63 65 69 xpected == Recei
0620: 76 65 64 29 3b 0d 0a 20 69 66 28 6f 6b 29 20 63 ved);.. if(ok) c
0630: 65 72 72 20 3c 3c 20 22 50 41 53 53 45 44 22 20 err << "PASSED"
0640: 3c 3c 20 74 69 6d 65 72 28 29 20 3c 3c 20 65 6e << timer() << en
0650: 64 6c 3b 20 20 65 6c 73 65 20 7b 20 63 65 72 72 dl; else { cerr
0660: 20 3c 3c 20 22 46 41 49 4c 45 44 22 20 3c 3c 20 << "FAILED" <<
0670: 74 69 6d 65 72 28 29 20 3c 3c 20 65 6e 64 6c 3b timer() << endl;
0680: 0d 0a 20 63 65 72 72 20 3c 3c 20 22 5c 74 6f 3a .. cerr << "\to:
0690: 20 5c 22 22 20 3c 3c 20 45 78 70 65 63 74 65 64 \"" << Expected
06a0: 20 3c 3c 20 27 5c 22 27 20 3c 3c 20 65 6e 64 6c << '\"' << endl
06b0: 20 3c 3c 20 22 5c 74 78 3a 20 5c 22 22 20 3c 3c << "\tx: \"" <<
06c0: 20 52 65 63 65 69 76 65 64 20 3c 3c 20 27 5c 22 Received << '\"
06d0: 27 20 3c 3c 20 65 6e 64 6c 3b 20 7d 20 7d 0d 0a ' << endl; } }..
06e0: 23 64 65 66 69 6e 65 20 43 41 53 45 28 4e 29 20 #define CASE(N)
06f0: 7b 63 65 72 72 20 3c 3c 20 22 54 65 73 74 20 43 {cerr << "Test C
0700: 61 73 65 20 23 22 20 3c 3c 20 4e 20 3c 3c 20 22 ase #" << N << "
0710: 2e 2e 2e 22 20 3c 3c 20 66 6c 75 73 68 3b 20 73 ..." << flush; s
0720: 74 61 72 74 5f 74 69 6d 65 3d 63 6c 6f 63 6b 28 tart_time=clock(
0730: 29 3b 0d 0a 23 64 65 66 69 6e 65 20 45 4e 44 09 );..#define END.
0740: 20 76 65 72 69 66 79 5f 63 61 73 65 28 5f 2c 20 verify_case(_,
0750: 44 69 73 74 69 6e 67 75 69 73 68 61 62 6c 65 53 DistinguishableS
0760: 65 74 44 69 76 31 28 29 2e 63 6f 75 6e 74 28 61 etDiv1().count(a
0770: 6e 73 77 65 72 29 29 3b 7d 0d 0a 69 6e 74 20 6d nswer));}..int m
0780: 61 69 6e 28 29 7b 0d 0a 0d 0a 43 41 53 45 28 30 ain(){....CASE(0
0790: 29 0d 0a 09 73 74 72 69 6e 67 20 61 6e 73 77 65 )...string answe
07a0: 72 5f 5b 5d 20 3d 20 7b 22 41 41 22 2c 22 41 42 r_[] = {"AA","AB
07b0: 22 2c 22 43 43 22 7d 3b 0d 0a 09 20 20 76 65 63 ","CC"};... vec
07c0: 74 6f 72 20 3c 73 74 72 69 6e 67 3e 20 61 6e 73 tor <string> ans
07d0: 77 65 72 28 61 6e 73 77 65 72 5f 2c 20 61 6e 73 wer(answer_, ans
07e0: 77 65 72 5f 2b 73 69 7a 65 6f 66 28 61 6e 73 77 wer_+sizeof(answ
07f0: 65 72 5f 29 2f 73 69 7a 65 6f 66 28 2a 61 6e 73 er_)/sizeof(*ans
0800: 77 65 72 5f 29 29 3b 20 0d 0a 09 69 6e 74 20 5f wer_)); ...int _
0810: 20 3d 20 32 3b 20 0d 0a 45 4e 44 0d 0a 43 41 53 = 2; ..END..CAS
0820: 45 28 31 29 0d 0a 09 73 74 72 69 6e 67 20 61 6e E(1)...string an
0830: 73 77 65 72 5f 5b 5d 20 3d 20 7b 22 58 59 5a 22 swer_[] = {"XYZ"
0840: 2c 22 58 59 5a 22 2c 22 58 59 5a 22 7d 3b 0d 0a ,"XYZ","XYZ"};..
0850: 09 20 20 76 65 63 74 6f 72 20 3c 73 74 72 69 6e . vector <strin
0860: 67 3e 20 61 6e 73 77 65 72 28 61 6e 73 77 65 72 g> answer(answer
0870: 5f 2c 20 61 6e 73 77 65 72 5f 2b 73 69 7a 65 6f _, answer_+sizeo
0880: 66 28 61 6e 73 77 65 72 5f 29 2f 73 69 7a 65 6f f(answer_)/sizeo
0890: 66 28 2a 61 6e 73 77 65 72 5f 29 29 3b 20 0d 0a f(*answer_)); ..
08a0: 09 69 6e 74 20 5f 20 3d 20 30 3b 20 0d 0a 45 4e .int _ = 0; ..EN
08b0: 44 0d 0a 43 41 53 45 28 32 29 0d 0a 09 73 74 72 D..CASE(2)...str
08c0: 69 6e 67 20 61 6e 73 77 65 72 5f 5b 5d 20 3d 20 ing answer_[] =
08d0: 7b 22 41 41 41 41 22 2c 22 42 41 43 41 22 2c 22 {"AAAA","BACA","
08e0: 43 44 43 45 22 7d 3b 0d 0a 09 20 20 76 65 63 74 CDCE"};... vect
08f0: 6f 72 20 3c 73 74 72 69 6e 67 3e 20 61 6e 73 77 or <string> answ
0900: 65 72 28 61 6e 73 77 65 72 5f 2c 20 61 6e 73 77 er(answer_, answ
0910: 65 72 5f 2b 73 69 7a 65 6f 66 28 61 6e 73 77 65 er_+sizeof(answe
0920: 72 5f 29 2f 73 69 7a 65 6f 66 28 2a 61 6e 73 77 r_)/sizeof(*answ
0930: 65 72 5f 29 29 3b 20 0d 0a 09 69 6e 74 20 5f 20 er_)); ...int _
0940: 3d 20 31 31 3b 20 0d 0a 45 4e 44 0d 0a 43 41 53 = 11; ..END..CAS
0950: 45 28 33 29 0d 0a 09 73 74 72 69 6e 67 20 61 6e E(3)...string an
0960: 73 77 65 72 5f 5b 5d 20 3d 20 7b 22 58 59 5a 22 swer_[] = {"XYZ"
0970: 2c 22 58 41 42 22 2c 22 59 41 43 22 7d 3b 0d 0a ,"XAB","YAC"};..
0980: 09 20 20 76 65 63 74 6f 72 20 3c 73 74 72 69 6e . vector <strin
0990: 67 3e 20 61 6e 73 77 65 72 28 61 6e 73 77 65 72 g> answer(answer
09a0: 5f 2c 20 61 6e 73 77 65 72 5f 2b 73 69 7a 65 6f _, answer_+sizeo
09b0: 66 28 61 6e 73 77 65 72 5f 29 2f 73 69 7a 65 6f f(answer_)/sizeo
09c0: 66 28 2a 61 6e 73 77 65 72 5f 29 29 3b 20 0d 0a f(*answer_)); ..
09d0: 09 69 6e 74 20 5f 20 3d 20 35 3b 20 0d 0a 45 4e .int _ = 5; ..EN
09e0: 44 0d 0a 43 41 53 45 28 34 29 0d 0a 09 73 74 72 D..CASE(4)...str
09f0: 69 6e 67 20 61 6e 73 77 65 72 5f 5b 5d 20 3d 20 ing answer_[] =
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0a30: 4c 4c 47 43 43 54 4a 4a 53 53 4e 44 46 48 54 48 LLGCCTJJSSNDFHTH
0a40: 47 4f 42 4a 22 2c 22 49 4d 4c 59 45 44 48 45 48 GOBJ","IMLYEDHEH
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0a60: 48 49 48 41 50 50 51 51 42 59 45 4d 59 4a 53 47 HIHAPPQQBYEMYJSG
0a70: 4e 5a 22 2c 22 52 5a 55 51 51 55 51 44 42 44 48 NZ","RZUQQUQDBDH
0a80: 45 44 51 4e 4d 53 45 44 49 22 2c 22 58 45 49 42 EDQNMSEDI","XEIB
0a90: 52 48 4d 4c 50 42 4d 49 42 48 5a 52 42 52 57 45 RHMLPBMIBHZRBRWE
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0ab0: 45 45 4f 4e 54 5a 43 22 2c 22 55 4c 4d 56 55 4c EEONTZC","ULMVUL
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63f0: 6e 73 77 65 72 28 61 6e 73 77 65 72 5f 2c 20 61 nswer(answer_, a
6400: 6e 73 77 65 72 5f 2b 73 69 7a 65 6f 66 28 61 6e nswer_+sizeof(an
6410: 73 77 65 72 5f 29 2f 73 69 7a 65 6f 66 28 2a 61 swer_)/sizeof(*a
6420: 6e 73 77 65 72 5f 29 29 3b 20 0d 0a 09 69 6e 74 nswer_)); ...int
6430: 20 5f 20 3d 20 31 30 34 33 30 37 30 3b 20 0d 0a _ = 1043070; ..
6440: 45 4e 44 0d 0a 2f 2a 0d 0a 43 41 53 45 28 35 29 END../*..CASE(5)
6450: 0d 0a 09 73 74 72 69 6e 67 20 61 6e 73 77 65 72 ...string answer
6460: 5f 5b 5d 20 3d 20 3b 0d 0a 09 20 20 76 65 63 74 _[] = ;... vect
6470: 6f 72 20 3c 73 74 72 69 6e 67 3e 20 61 6e 73 77 or <string> answ
6480: 65 72 28 61 6e 73 77 65 72 5f 2c 20 61 6e 73 77 er(answer_, answ
6490: 65 72 5f 2b 73 69 7a 65 6f 66 28 61 6e 73 77 65 er_+sizeof(answe
64a0: 72 5f 29 2f 73 69 7a 65 6f 66 28 2a 61 6e 73 77 r_)/sizeof(*answ
64b0: 65 72 5f 29 29 3b 20 0d 0a 09 69 6e 74 20 5f 20 er_)); ...int _
64c0: 3d 20 3b 20 0d 0a 45 4e 44 0d 0a 43 41 53 45 28 = ; ..END..CASE(
64d0: 36 29 0d 0a 09 73 74 72 69 6e 67 20 61 6e 73 77 6)...string answ
64e0: 65 72 5f 5b 5d 20 3d 20 3b 0d 0a 09 20 20 76 65 er_[] = ;... ve
64f0: 63 74 6f 72 20 3c 73 74 72 69 6e 67 3e 20 61 6e ctor <string> an
6500: 73 77 65 72 28 61 6e 73 77 65 72 5f 2c 20 61 6e swer(answer_, an
6510: 73 77 65 72 5f 2b 73 69 7a 65 6f 66 28 61 6e 73 swer_+sizeof(ans
6520: 77 65 72 5f 29 2f 73 69 7a 65 6f 66 28 2a 61 6e wer_)/sizeof(*an
6530: 73 77 65 72 5f 29 29 3b 20 0d 0a 09 69 6e 74 20 swer_)); ...int
6540: 5f 20 3d 20 3b 20 0d 0a 45 4e 44 0d 0a 2a 2f 0d _ = ; ..END..*/.
6550: 0a 7d 0d 0a 2f 2f 20 45 4e 44 20 43 55 54 20 48 .}..// END CUT H
6560: 45 52 45 0d 0a ERE..