Puzzle Square Hexa Prime 3x3

pengantar

Kami menganggap 3x3 kotak digit heksadesimal (dari 0ke F) seperti:

2 E 3    1 F 3
8 1 5    7 2 7
D D 5    B B 9

Kami mendefinisikan 3x3 Hexa Prime Square ( HPS3 ) sebagai kotak yang semua bilangan heksadesimalnya dibaca dari kiri ke kanan dan dari atas ke bawah adalah bilangan prima ganjil (yaitu bilangan prima lebih besar dari 2).

Ini berlaku untuk kuadrat kiri dan salah untuk kuadrat kanan:

2 E 3 --> 0x2E3 = 739       1 F 3 --> 0x1F3 = 499
8 1 5 --> 0x815 = 2069      7 2 7 --> 0x727 = 1831
D D 5 --> 0xDD5 = 3541      B B 9 --> 0xBB9 = 3001
| | |                       | | |
| | +---> 0x355 = 853       | | +---> 0x379 = 889 = 7 x 127
| +-----> 0xE1D = 3613      | +-----> 0xF2B = 3883 = 11 x 353
+-------> 0x28D = 653       +-------> 0x17B = 379

Tujuan

Diberikan daftar 9 digit heksadesimal, tujuan Anda adalah menemukan pengaturan yang membentuk HPS3.

Contoh:

Input: 123558DDE
Possible output: 2E3815DD5 (a flattened representation of the above left example)

Input output

Format input dan output fleksibel. Satu-satunya persyaratan adalah bahwa digit output dipesan dari kiri ke kanan dan dari atas ke bawah. Berikut adalah beberapa opsi yang mungkin:

"2E3815DD5"
[ 0x2, 0xE, 0x3, 0x8, 0x1, 0x5, 0xD, 0xD, 0x5 ]
[ "2", "E", "3", "8", "1", "5", "D", "D", "5" ]
[
  [ 0x2, 0xE, 0x3 ],
  [ 0x8, 0x1, 0x5 ],
  [ 0xD, 0xD, 0x5 ]
]
[ "2E3", "815", "DD5" ]
etc.

Tidak perlu menggunakan format yang sama untuk input dan output.

Aturan

• Ini adalah kode-golf, jadi jawaban tersingkat dalam byte menang. Celah standar dilarang.
• Algoritme Anda harus deterministik
• Anda tidak bisa hanya bogosort array sampai valid, bahkan dengan cara deterministik (dengan menggunakan seed acak konstan).
• Anda dapat mendaftar semua solusi yang mungkin untuk input yang diberikan, tetapi ini tidak diperlukan atau dikenakan bonus.
• Anda tidak diharuskan mendukung input yang tidak mengakui solusi apa pun. (Tidak apa-apa jika kode Anda berulang selamanya atau mogok dalam kasus itu.)

Uji kasus

Input       Possible output
---------------------------
123558dde   2e3815dd5
1155578ab   a7b851551
03bddffff   ffd0dfb3f
35899beff   8f99e3bf5
15899bbdf   581bb9fd9
14667799f   6f1469779
13378bcdd   78d1cd33b
24577bbdd   7274bd5db
1118bbddd   11b18dbdd
223556cdd   623c25dd5
12557899a   8a5295971
113579bbd   5b3db7191

05AB1E , 23 21 byte

Penggunaan pengodean CP-1252 .

œJvy3ôD€SøJìHDps2›*P—

Terlalu lambat untuk TIO.

Penjelasan

œJ                     # all permutations of input as strings
  v                    # for each permutation
                       # EXAMPLE: 2E3815DD5
   y3ô                 # split in pieces of 3
                       # EXAMPLE: ['2E3','815','DD5']
      D                # duplicate
                       # EXAMPLE: ['2E3','815','DD5'], ['2E3','815','DD5']
       €SøJ            # zip the copy to swap rows and columns 
                       # EXAMPLE: ['2E3','815','DD5'], ['28D','E1D','355']
           ì           # attach them to the same list
                       # EXAMPLE: ['2E3','815','DD5','28D','E1D','355']
            H          # convert from base 16 to base 10
                       # EXAMPLE: [739, 2069, 3541, 653, 3613, 853]
             D         # duplicate
                       # EXAMPLE: [739, 2069, 3541, 653, 3613, 853],[739, 2069, 3541, 653, 3613, 853]
              p        # check first copy for primality
                       # EXAMPLE: [739, 2069, 3541, 653, 3613, 853],[1,1,1,1,1,1]
               s2›     # check that each in second copy is larger than 2
                       # EXAMPLE: [1,1,1,1,1,1],[1,1,1,1,1,1]
                  *    # pairwise multiplication
                       # EXAMPLE: [1,1,1,1,1,1]
                   P   # product (1 if all were primes larger than 2, else 0)
                       # EXAMPLE: 1
                    —  # if 1, print y
                       # EXAMPLE: 2E3815DD5

Python 2, 212 206 197 194 byte

Membutuhkan input yang dilampirkan dalam tanda kutip, seperti "123558dde"

from itertools import*
k,p,P=3,4,[]
while k<5e3:P+=[k][:p%k];p*=k;k+=1
print[s for s in map(''.join,permutations(input()))if all(int(s[3*i:][:3],16)in P and int(s[i::3],16)in P for i in(0,1,2))]

Menyimpan 9 dan 3 byte berkat Jonathan Allan

Menemukan filter prima baru dari xnor (memodifikasi kuadrat jauh, karena kami tidak ingin 2 sebagai prima di sini), filter perdana lama adalah dari Bob

Pyth, 23 21 byte

f*F}R-Pd2iR16sCBc3T.p

Waktu online, tetapi selesai dalam 1,5 menit di laptop saya. Mengambil input dalam tanda kutip.

Penjelasan

f*F}R-Pd2iR16sCBc3T.p
                   .pQ     permutations of input (implicit Q)
f                 T        filter each T:
                c3             divide into rows
              CB               make pair (rows, columns)
             s                 join those lists
         iR16                  interpret items as hex
   }R                          check if each number d is in
      Pd                           its prime factors
     -  2                          with twos removed
 *F                            product (also known as all)
                           implicitly print matches

Jelly , 34 30 byte

i@€ØH’
s3µ;ZÇ€ḅ⁴µ>2aÆPẠ
Œ!ÇÐfḢ

(Saya harus dapat menggunakan nfind untuk hanya mengambil pertandingan pertama, 1#sebagai gantinyaÐfḢ , dengan byte lebih sedikit dan lebih cepat, tetapi saya melihat kesalahan ketika saya mencoba. EDIT: menulis beberapa perubahan untuk mengimplementasikannya di Jelly.)

Pencarian paksa semua permutasi, difilter untuk kriteria, mengembalikan kecocokan pertama.
Terlalu lambat untuk TtyItOnline. Contoh output lokal:

C:\Jelly\jelly-master>python jelly -fu test.txt "123558DDE"
28DE1D355
C:\Jelly\jelly-master>python jelly -fu test.txt "1155578AB"
11B8A5557

Bagaimana?

i@€ØH’ - Link 1, convert from hexadecimal string to integer list: string
   ØH  - yield hexadecimal characters, "0123456789ABCDEF"
i@€    - index of €ach character of s in hex chars
     ’ - decrement (vectorises) (from 1 based jelly index to place value)

s3µ;ZÇ€ḅ⁴µ>2aÆPẠ - Link 2, check if a flattened square is "all prime": string
s3               - split into threes (rows)
  µ              - monadic chain separation
   ;             - concatenate with
    Z            - transpose (columns)
     Ç€          - call last link (1) as a monad for €ach string in the list
                       -> list of integer lists
       ḅ⁴        - convert from base 16 (vectorises) -> list of decimals
         µ       - monadic chain separation
          >2     - greater than 2
            a    - and
             ÆP  - isPrime? -> list of 1s and 0s
               Ạ - all truthy?

Œ!ÇÐfḢ  - Main link: string
Œ!      - all permutations of the string
   Ðf   - filter keeping entries that evaluate to truthily for
  Ç     - last link (3) as a monad
     Ḣ  - head - return first entry

J, 49 byte

[:(#~([:*/@(2&<*1&p:)@(,&dfh|:)_3]\])"{)i.@!@#A.]

Pencarian brute force yang menguji semua permutasi dan menghasilkan semua permutasi yang memenuhi kondisi untuk puzzle.

Performanya cukup baik untuk menghitung setiap test case dalam waktu sekitar 3 detik.

Pemakaian

   f =: [:(#~([:*/@(2&<*1&p:)@(,&dfh|:)_3]\])"{)i.@!@#A.]
   f '123558dde'
28de1d355
28de1d355
28de1d355
28de1d355
2e3815dd5
2e3815dd5
2e3815dd5
2e3815dd5
   timex 'f ''123558dde'''
3.68822

Penjelasan

[:(#~([:*/@(2&<*1&p:)@(,&dfh|:)_3]\])"{)i.@!@#A.]  Input: string S
                                             #     Length of S
                                           !@      Factorial
                                        i.@        Range [0, len(S)!)
                                                ]  Get S
                                              A.   Find the permutations of S by index
[:(                                    )           Operate on the permutations
     (                              )"{              For each permutation P
                                   ]                   Get P
                               _3]\                    Get sublists of size 3
      [:              (       )                        Operate on the sublists
                            |:                           Transpose
                        &dfh                             Convert both the transpose and
                                                         initial from hex to decimal
                       ,                                 Join them
           (        )                                  Operate on the decimals
                1&p:                                     Test each for primality
            2&<                                          Test each if greater than 2
               *                                         Multiply them (AND)
        */@                                            Reduce using multiplication
   #~                                                Filter the permutations by those
                                                     values and return

Mathematica, 115 byte

#<>""&@@Select[Permutations@#,And@@(PrimeQ@#&&#>2&)/@(FromDigits[#<>"",16]&/@#~Join~Transpose@#)&[#~Partition~3]&]&

Input harus berupa daftar karakter (mis. {"1", "2", "3", "5", "5", "8", "D", "D", "E"})

Ruby, 146 byte

Fungsi anonim mengambil array sembilan bilangan bulat, mengembalikan satu solusi sebagai array sembilan bilangan bulat. Mengandalkan fungsi pembantu gdan a require.

require'prime'
g=->x,y,z{(2<s=x<<8|y<<4|z)&&s.prime?}
->r{r.permutation{|i|a=1
3.times{|j|a&&=g[*i[j*3,3]]&&g[i[j],i[j+3],i[j+6]]}
a&&(return i)}}

Versi 140 byte ini mencetak semua solusi yang mungkin, dengan integer sebagai desimal (tidak yakin apakah itu dibolehkan.)

require'prime'
g=->x,y,z{(2<s=x<<8|y<<4|z)&&s.prime?}
->r{r.permutation{|i|a=1
3.times{|j|a&&=g[*i[j*3,3]]&&g[i[j],i[j+3],i[j+6]]}
a&&p(i)}}

Tidak digabungkan dalam program uji

require'prime'
g=->x,y,z{(2<s=x<<8|y<<4|z)&&   #combine 3 input values, check if >2
  s.prime?}                     #and check if prime
h=->r{
  r.permutation{|i|             #iterate over all permutations
    a=1                         #a=truthy
    3.times{|j|
      a&&=g[*i[j*3,3]]&&        #check rows (3 consecutive integers)
          g[i[j],i[j+3],i[j+6]] #and columns
    }
    a&&(return i)               #if a still truthy, return solution.
  }
}

#test cases: uncomment to run. solutions do not always match example solution from OP.
a=10;b=11;c=12;d=13;e=14;f=15
#p h[[1,2,3,5,5,8,d,d,e]]   #2e3815dd5
#p h[[1,1,5,5,5,7,8,a,b]]   #a7b851551
#p h[[0,3,b,d,d,f,f,f,f]]   #ffd0dfb3f
#p h[[3,5,8,9,9,b,e,f,f]]   #8f99e3bf5
#p h[[1,5,8,9,9,b,b,d,f]]   #581bb9fd9
#p h[[1,4,6,6,7,7,9,9,f]]   #6f1469779
#p h[[1,3,3,7,8,b,c,d,d]]   #78d1cd33b
#p h[[2,4,5,7,7,b,b,d,d]]   #7274bd5db
#p h[[1,1,1,8,b,b,d,d,d]]   #11b18dbdd
#p h[[2,2,3,5,5,6,c,d,d]]   #623c25dd5
#p h[[1,2,5,5,7,8,9,9,a]]   #8a5295971
#p h[[1,1,3,5,7,9,b,b,d]]   #5b3db7191

Groovy, 134 Bytes

Temukan semua solusi yang mungkin dan kembalikan sebagai array, kembalikan []jika tidak ada solusi.

{it.toList().permutations().collect{it.collate(3).every{x=Integer.parseInt(it.join(),16);(2..x**0.5).every{x%it>0};}?it.join():0}-[0]}

Contoh input: 123558dde
Output:

[8235d5e1d, 2dd851e35, 815e352dd, 2e3d5518d, d2d3e5581, 853de5d21, 2dd3558e1, 2dd3e5581, 2e355d18d, 2518dd3e5, dd52e3185, e1d5d5283, 823ed1d55, 28d3e515d, 28d15de35, e351258dd, e5dd21853, 851d2d3e5, ed515d283, 2dd3e5185, 85de35d21, 5d1ed5823, 8dd355e21, d2d3e5815, d2d3e5851, 251e358dd, 2dde35851, 8235d5ed1, 2dde35815, e3585dd21, d2d8153e5, 85d5d12e3, 21dd85e35, d8521de35, 21d85d3e5, e1d5d5823, e35581d2d, 3e52dd581, dd52e3851, dd52e3815, 3e5281dd5, 8dd1253e5, 3e5815d2d, 3e55d128d, ed515d823, de5853d21, e218dd355, d8d1253e5, d8d251e35, d8d5512e3, 2dde35581, 3e52dd851, 5d1ed5283, e21dd5853, 3e5d2185d, 2513e58dd, 2dd3e5815, 2dd3e5851, e1d823d55, 3e52dd815, 581d2de35, e3515d28d, 2e318dd55, ed1823d55, dd52813e5, dd52e3581, 2e3515d8d, 28d3e55d1, 82355de1d, 82355ded1, 2dde35185, 3e5d8d125, 85d21de35, 281dd53e5, d21d85e35, d21e35d85, 2dd8e1355, 28d5d1e35, 85d15d2e3, 2813e5dd5, 3e5d2d185, 5d1e5d283, 3e5d2d581, e1dd55823, 3558e12dd, d55283e1d, 15dde5283, 5d128d3e5, 5518dd2e3, e5d28315d, 5d5823ed1, d2d1853e5, 823d55e1d, de521d853, d81d552e3, 5d5823e1d, 21ded5853, 823e1dd55, 3e52dd185, 5812dde35, d85e35d21, 3e585d21d, 8512dd3e5, 3e5251d8d, d2d8513e5, e1dd55283, 2e3d81d55, 853ed5d21, 2835d1ed5, 15d2e3d85, 5d1e3528d, 15dde5823, e35851d2d, 55d283e1d, 2e3551d8d, 8dd3e5125, 85d3e5d21, 8152e3dd5, 28de1d355, e1d55d823, 8dd3e5251, 5158dd2e3, e3521dd85, e1d35528d, 2e35d185d, 21de5d853, 823d55ed1, 5813e52dd, 8153e5d2d, e1d55d283, 21de3585d, d85d21e35, 5152e3d8d, 8513e5d2d, dd5e21853, 3552dd8e1, d552e318d, e5d2835d1, 2835d1e5d, 2835d1de5, 5d1e5d823, 8dde35125, 5d52e3d81, 3e5821dd5, 28d5d13e5, e35d21d85, dd51852e3, d2d185e35, 8dde35251, 8dd2513e5, e35d2d185, 2835d5e1d, 1852e3dd5, d85d213e5, 515d8d2e3, dd53e5821, d5518d2e3, 8dd5512e3, 283d55ed1, e5d5d1823, 28d355ed1, 3e58152dd, d812e3d55, e5d85321d, d8515d2e3, d2d581e35, 3e5581d2d, 85d21d3e5, 283d55e1d, dd53e5281, 851dd52e3, e35dd5821, 3e51258dd, dd58512e3, 28d355e1d, d8d2513e5, 125e358dd, e35dd5281, e35d2d851, d8d2e3515, e35d2d815, d21853ed5, d8d2e3551, 1852dd3e5, d21853e5d, 85dd213e5, d21853de5, 5d1283e5d, 823ed155d, 5d1283de5, ed521d853, 283e1dd55, d8d355e21, d8de35251, 5d1283ed5, e35d2d581, 3e528d15d, d55283ed1, 8512dde35, 3e5851d2d, 823ed15d5, 15d28de35, 15d3e528d, 2835d5ed1, 5d12e385d, 5d185d2e3, 5d5283e1d, 55d2e3d81, d2185de35, d55e1d283, ed582315d, 2dd8513e5, 853e5d21d, e352dd581, 851e352dd, 2dd5813e5, e352dd815, 853d21e5d, e352dd851, dd5821e35, ed155d283, 3e5d8d251, d8de35125, 2e3d8d551, 3e528d5d1, e5d21d853, dd5853e21, 853d21ed5, 85de3521d, e352518dd, 2e3d8d515, 125d8de35, e352dd185, 853d21de5, 8e13552dd, 1258dde35, 581e352dd, e21d8d355, ed155d823, e21853dd5, e3528d5d1, d2d851e35, 5512e38dd, 125d8d3e5, 2e3815dd5, 2513e5d8d, 21dde5853, 355d2d8e1, d55ed1283, 815dd52e3, 283ed1d55, 8152dd3e5, 281e35dd5, 28355de1d, 355e1d28d, ed182355d, 853dd5e21, e3528d15d, ed18235d5, 15d85d2e3, e351852dd, d55e1d823, 8e12dd355, 28355ded1, 2dd815e35, 581d2d3e5, d55ed1823, 15d283ed5, 821dd53e5, 2e35d518d, 5d5283ed1, 15d283e5d, 15d283de5, e1d28355d, e5d5d1283, 251d8d3e5, e1d2835d5, dd5281e35, ed15d5823, 21de35d85, dd58152e3, 2dd1853e5, 1258dd3e5, 5d5e1d283, 1253e58dd, 3e5d8521d, 18d2e3d55, e358152dd, 5512e3d8d, e35251d8d, 853ed521d, 3e5dd5281, 5813e5d2d, ed15d5283, 18d55d2e3, 281dd5e35, 8dde21355, 1852dde35, 3e585dd21, d85e3521d, 581e35d2d, ed1283d55, d812e35d5, 2e35518dd, 5d128de35, 8153e52dd, ed55d1823, e5d82315d, e35d85d21, d812e355d, d853e521d, 8dd2e3551, 2e3581dd5, 15de5d823, 8dd2e3515, 185e35d2d, 125e35d8d, 581dd52e3, 5d5e1d823, 5812e3dd5, 5152e38dd, 3558e1d2d, 85d3e521d, 5d1d852e3, 823de55d1, 2e3d8155d, d213e585d, ed55d1283, 2e3dd5581, 2e3dd5815, 15d823ed5, 2e3dd5851, d552e3d81, 55de1d823, e5d8235d1, 21d853de5, de528315d, d21e3585d, 2e3d815d5, 21d853e5d, ed58235d1, 2e3dd5185, 21d853ed5, de52835d1, 15d823e5d, e1d28d355, 355ed128d, 5812dd3e5, 815d2d3e5, 15d823de5, 823de515d, 55de1d283, ed5853d21, 2dd8153e5, 2e3d855d1, 185dd52e3, 8e1355d2d, 2e3d55d81, d2d3558e1, d8521d3e5, e5d15d823, ed52835d1, 35528de1d, dd5e35281, 3e58dd251, 5d5ed1283, dd58213e5, e355d128d, 3e58dd125, 3e5125d8d, 8213e5dd5, 355e218dd, 2e3d8515d, 35528ded1, e5d15d283, 853e21dd5, 8dd125e35, 15ded5823, e358dd251, 2e315dd85, 851d2de35, 551d8d2e3, d2d5813e5, ed528315d, 2e3185dd5, 185d2de35, 8152dde35, e35d2185d, 15de3528d, e358dd125, 251e35d8d, 5d5ed1823, 821dd5e35, 251d8de35, 8512e3dd5, 5d1823de5, d2d815e35, 3e51852dd, 5d1823e5d, 82315dde5, 3e5dd5821, 82315de5d, 5d518d2e3, 1853e5d2d, 8dd251e35, ed128355d, e1d8235d5, 82315ded5, d21ed5853, 823ed515d, 2e38dd551, ed135528d, 2e38dd515, 5d1823ed5, 2e318d55d, 15de5d283, e1d82355d, ed1d55823, 2e3851dd5, d8d5152e3, 283de515d, 823ed55d1, 3e55812dd, dd5e35821, 15ded5283, e21355d8d, 21d85de35, 8dd5152e3, e35125d8d, e355812dd, 5d52e318d, 8e1d2d355, d8155d2e3, 3e5d21d85, 21d3e5d85, ed12835d5, de585321d, d2185d3e5, 85dd21e35, 2e318d5d5, d213e5d85, 2e385d5d1, 55d823ed1, 15d2e385d, 3e521dd85, 283de55d1, ed1d55283, d8de21355, de5d21853, 55d823e1d, d852e315d, 355d8de21, d852e35d1, 8513e52dd, 185d2d3e5, 853e5dd21, 21d3e585d, 2dd581e35, de582315d, 823e5d15d, de515d283, 185e352dd, 28de3515d, 3e5d2d815, d21de5853, 283ed155d, 3e5d2d851, 55d283ed1, 3558dde21, 283ed15d5, d815d52e3, 28de355d1, 851e35d2d, de515d823, 5d1de5823, 55dd812e3, 283e5d15d, dd55812e3, 823e5d5d1, 15dd852e3, d2de35185, 1253e5d8d, 2e35d5d81, 1853e52dd, 2e35158dd, 21dd853e5, e35185d2d, 283e5d5d1, 18dd552e3, e35281dd5, 5d13e528d, e1d283d55, 2e385d15d, 28315de5d, 85d2e35d1, 28315dde5, 2dd185e35, e3585d21d, 283ed55d1, 5d1de5283, 28315ded5, d55823ed1, 5d12e3d85, e5d853d21, e35d8d125, e358512dd, d55823e1d, 815e35d2d, e35d8d251, 18d5d52e3, 28ded1355, e3521d85d, 283ed515d, 821e35dd5, d2d3e5185, 85321de5d, d2de35815, e35d8521d, d55d812e3, e213558dd, e35815d2d, d855d12e3, 15d28d3e5, d21e5d853, 85d2e315d, 3e58512dd, d2de35851, ed128d355, 28d15d3e5, 3e52518dd, 18d2e355d, de55d1823, d2de35581, 85321ded5, d2d8e1355, d853e5d21, 18d2e35d5, 2e35d1d85, 85321dde5, 3e5185d2d, 853de521d, 355e21d8d, 5d5d812e3, 55ded1823, de55d1283, 8235d1ed5, e35821dd5, 2518dde35, 8235d1de5, 8235d1e5d, 3e521d85d, d8d125e35, 2e315d85d, ed5d21853, 55ded1283, 815d2de35, 283e1d55d, 823e1d55d, 2e355dd81, 3e5d85d21, d8d3e5125, 3e515d28d, d21d853e5, 283e1d5d5, ed585321d, 823e1d5d5, 55d2e318d, d8d3e5251, 55d18d2e3, de58235d1]

Contoh input: 222222222 Output:[]

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