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• If you like cryptography and playing cards, have also a look at Card-Chameleon, a Cipher with Playing cards.
• And if you just like playing cards, have a look at Playing Cards Draw Order.

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As a secret agent, you need a method to transmit a message to another secret agent. But an encrypted text written on a notebook will be suspicious if you get caught. A simple deck of playing cards, however, is everything but suspicious...

With a deck of 52 playing cards, there are 52! different possible permutations to order it. And 52! is equal to 80658175170943878571660636856403766975289505440883277824000000000000. That's a number with 68 digits!

There are so many different possible permutations, we can assert with great confidence that if you shuffle the cards well and put them back together to form a deck, you are the first person in history to get that particular order. The number of possible permutations in a deck of cards is higher than the estimated number of atoms in planet Earth (which is a number with about 50 digits).

With a way to associate a permutation of the cards to a sequence of characters, we can hide a message in the deck by ordering it correctly.

Correspondence between message and permutation

Message

To compose our message, we will use an alphabet containing 27 characters: the space and the letters from A to Z. We give them the following values:

• space = 0
• A = 1
• B = 2
• ...
• Z = 26

We now have a numeral system with a base equal to 27. We can compute a numeric value corresponding to any message:

• "A " = 27
• "AA" = 28
• "AB" = 29
• "ABC" = 786
• etc.

Note: an empty message is considered equal to 0, as are messages composed only of spaces.

Permutation

Now we need a way to attribute a unique number to each of the possible permutations of our deck of playing cards.

There are few methods to enumerate permutations and assign a number to each of them, we will use the lexicographical order. For example, with three cards A, B, and C (with A < B < C) we have the ordering:

• ABC = 0
• ACB = 1
• BAC = 2
• BCA = 3
• CAB = 4
• CBA = 5

The first arrangement is ABC, and the last one is CBA. With our 52 playing cards – ranks sorted from the Ace to the King, and suits in alphabetical order (Clubs, Diamonds, Hearts, Spades) – the first arrangement (number 0) is:

and the last one (number 52! - 1) is:

To transmit a message, we will compute the permutation for which the unique number is the numeric value of the message.

Your task

Write two functions: encode, which converts a string into an ordered collection of strings representing a deck of playing cards, and decode, which does the reverse.

Cards are represented as strings of length two. The first character represents the rank, and the second character represents the suit.

AC 2C 3C 4C 5C 6C 7C 8C 9C TC JC QC KC for the Clubs AD 2D 3D 4D 5D 6D 7D 8D 9D TD JD QD KD for the Diamonds AH 2H 3H 4H 5H 6H 7H 8H 9H TH JH QH KH for the Hearts AS 2S 3S 4S 5S 6S 7S 8S 9S TS JS QS KS for the Spades

All provided inputs will be valid.

A preloaded function which prints the deck to the console has been provided:

Preload.print_deck(deck,unicode)

PlayingCardsOutput.printDeck(String[] deck, boolean unicode);

printDeck(deck, unicode);

printDeck(deck, unicode)

import { printDeck } from "./preloaded";

printDeck(deck, unicode);

import Preloaded.printDeck

printDeck(deck, unicode)

The first argument is the deck to print, the second one is a boolean value allowing the selection of the character set: regular or Unicode (for which a font containing the playing cards characters needs to be installed on your system).

Examples

Encoding

encode("ATTACK TONIGHT ON CODEWARS")

should return this array of 52 strings:

[
    "AC", "2C", "3C", "4C", "5C", "6C", "7C", "8C", "9C", "TC", "JC", "QC", "KC",
    "AD", "2D", "3D", "4D", "5D", "6D", "JD", "9D", "7S", "9S", "QD", "5S", "TH",
    "7D", "TS", "QS", "2H", "JS", "6H", "3S", "6S", "TD", "8S", "2S", "8H", "7H",
    "4S", "4H", "3H", "5H", "AS", "KH", "QH", "9H", "KD", "KS", "JH", "8D", "AH"
]

Decoding

decode([
    "AC", "2C", "3C", "4C", "5C", "6C", "7C", "8C", "9C", "TC", "JC", "QC", "KC",
    "AD", "2D", "3D", "4D", "5D", "6D", "7D", "8D", "9D", "TD", "JD", "QD", "KD",
    "AH", "2H", "3H", "4H", "8H", "9S", "3S", "2S", "8S", "TS", "QS", "9H", "7H",
    "KH", "AS", "JH", "4S", "KS", "JS", "5S", "TH", "7S", "6S", "5H", "QH", "6H"
])

should return the string:

"ATTACK APPROVED"

Have fun!

I hope you enjoy this kata! Feedback and translations are very welcome.

Further reading

Logarithm

The logarithm function can be used to obtain the number of digits required to represent a number in a given base. For example, log2(52!) = 225.58, so we can store 225 bits of information in a deck of cards (and 226 bits are needed to represent the value of 52!). Also, log27(52!) = 47.44, so we can store 47 characters of our alphabet in a deck of cards (and some message with 48 characters, but not all of them).