The International Statistical Classification of Diseases and Related Health Problems¹ (ICD) is a list of the World Health Organization² (WHO) containing more than 10.000 diseases and maladies that patients might present. In addition to a description, each disease or malady is also given a unique ICD-code that the medical community uses for record-keeping. For example, a patient admitted to the hospital with whooping cough would be logged in the database with ICD-code A37.

Some of the stranger complaints that can be found on the list:

However, without any doubt our favorite so far is "Burn due to water-skis on fire" (V91.07). It's a dangerous world. Be safe out there.

Assignment

The Hippocrates code is a cryptographic technique that makes use of ICD-codes. A message is encrypted by replacing each character with a Hippocrates-code of the form

<ICD-code>.$$n$$    ($$n \in \mathbb{N}$$)

The Hippocrates-code is chosen so that the $$n$$-th position in the description of the ICD-code is occupied by the encoded character. The positions of the characters are numbered from zero. The Hippocrates-codes are separated by a single space in the ciphertext. This way, the message

Eat wise, drop a size

is encrypted as

A75.0.0 K50.119.59 T43.2.75 V14.1.21 V42.1.54 E10.32.53 T21.70.5 T21.06.12 S59.239.62 M85.812.56 M85.812.34 Q95.3.27 V64.0.22 T37.3.61 S00.261.34 T49.4X6.76 F44.6.32 A02.24.23 V59.9.62 J10.89.41 O91.1.13

We see, for example, that the first letter (position 0) in the description of ICD-code A75.0 (Epidemic louse-borne typhus fever due to Rickettsia prowazekii) is occupied by the uppercase letter E and that a lowercase letter a occurs at position 59 in the description of ICD-code K50.119 (Crohn's disease of large intestine with unspecified complications). When encoding, uppercase and lowercase letters are considered different characters, and the spaces and punctuation marks are also replaced by a corresponding Hippocrates-code.

However, the encoding is not unique because the same character may occur at multiple positions and in multiple descriptions. As such, the same sentence may also be encoded as

W92.XXXD.0 I97.611.84 I97.611.38 S59.099.31 M90.832.38 V42.1.93 M61.25.29 I67.83.43 T37.92.67 W93.38 O22.23 V59.9.48 F04.23 C34.2.13 F44.6.43 A00.0.28 M85.812.5 A02.24.23 Z96.621.21 J10.89.41 N07.9.31

To encode and decode messages according to the Hippocrates code we use text files whose lines contain an ICD-code and the corresponding description, separated by a single space. These are the ICD-codes that are used for encoding and decoding. An ICD-code never contains spaces (dots are allowed). Your task:

• Write a function code2character that takes the location (str) of a text file containing ICD-codes. The function must return a dictionary (dict) that maps all possible Hippocrates-codes (str) for the given text file onto their corresponding character (str).
  

• Write a function decode that takes two arguments: i) a ciphertext (str) whose encoding is based on the Hippocrates code and ii) a dictionary (dict) as returned by the function code2character. The function must return the plaintext (str) corresponding to the given ciphertext. In case the first argument is no valid ciphertext for the Hippocrates code (second argument), a ValueError must be raised with the message invalid ciphertext.

• Write a function character2codes that takes the location (str) of a text file containing ICD-codes. The function must return a dictionary (dict) that maps each character (str) that occurs in at least one of the messages in the given text file onto the set of all Hippocrates-codes (str) that can be used to replace the character when encoding the Hippocrates code.

• Write a function encode that takes two arguments: i) a plaintext (str) and ii) a dictionary (dict) as returned by the function character2codes. The function must return a ciphertext (str) for the given plaintext, where encoding is based on the Hippocrates code. Each character of the plaintext must be replaced by randomly choosing among all possible Hippocrates-codes that encode the character. If the given plaintext contains characters that cannot be encoded by a Hippocrates-code, a ValueError must be raised with the message invalid plaintext.

Example

In the following interactive session we assume the text file ICD.txt³ to be located in the current directory.

>>> c2k = code2character('ICD.txt4')
>>> c2k['A00.0']
'C'
>>> c2k['A00.2']
'o'
>>> c2k['A00.0.33']
','
>>> c2k['A00.2.33']
Traceback (most recent call last):
KeyError: 'A00.2.33'

>>> decode('A75.0.0 K50.119.59 T43.2.75 V14.1.21 V42.1.54 E10.32.53 T21.70.5 T21.06.12 S59.239.62 M85.812.56 M85.812.34 Q95.3.27 V64.0.22 T37.3.61 S00.261.34 T49.4X6.76 F44.6.32 A02.24.23 V59.9.62 J10.89.41 O91.1.13', c2k)
'Eat wise, drop a size'
>>> decode('W92.XXXD.0 I97.611.84 I97.611.38 S59.099.31 M90.832.38 V42.1.93 M61.25.29 I67.83.43 T37.92.67 W93.38 O22.23 V59.9.48 F04.23 C34.2.13 F44.6.43 A00.0.28 M85.812.5 A02.24.23 Z96.621.21 J10.89.41 N07.9.31', c2k)
'Eat wise, drop a size'
>>> decode('X66.6 Q99.99 Z12.34', c2k)
Traceback (most recent call last):
ValueError: invalid ciphertext

>>> k2c = character2codes('ICD.txt5')
>>> k2c['V']
{'O22.0', 'A00.1.15', 'I83.218.0', 'A00.0.15'}
>>> k2c['v']
{'I67.83.12', 'V59.9.50', 'V64.0.76', 'H59.121.12', 'M50.022.3', 'S44.8X9.19', 'T37.92.46', 'S44.8X9.51', 'V42.1.68', 'S66.911.68', 'T37.3.16', 'T37.1X.16', 'V04.92.67', 'M67.971.28', 'B08.04.4', 'Q95.3.53', 'V49.60.69', 'V64.0.3', 'T43.2.16', 'V64.0.26', 'E10.32.49', 'B57.30.40', 'A00.0.38', 'V64.0.13', 'I89.9.10', 'I83.218.9', 'V04.92.54', 'F44.6.3', 'I89.9.35', 'W24.0.23', 'M67.232.4', 'B57.30.43', 'S90.464.16', 'N13.9', 'V52.1.88', 'S14.9.25', 'V52.1.30', 'S78.922.54', 'V92.16.45', 'V14.1.51', 'S00.261.16', 'B57.30.28', 'V59.9.13', 'W93.19', 'W92.XXXD.19', 'V64.0.63', 'M50.022.34', 'J10.89.44', 'A00.1.38', 'A75.0.30', 'V14.1.64', 'T37.1X5.2'}
>>> k2c['.']
{'Z68.35.29', 'Z68.35.24', 'Z68.42.29', 'Z68.36.29', 'Z68.42.24', 'Z68.36.24', 'Z68.43.27'}
>>> k2c['xxx']
Traceback (most recent call last):
KeyError: 'xxx'
>>> k2c['!']
Traceback (most recent call last):
KeyError: '!'

>>> encode('Eat wise, drop a size', k2c)
'A75.0.0 K50.119.59 T43.2.75 V14.1.21 V42.1.54 E10.32.53 T21.70.5 T21.06.12 S59.239.62 M85.812.56 M85.812.34 Q95.3.27 V64.0.22 T37.3.61 S00.261.34 T49.4X6.76 F44.6.32 A02.24.23 V59.9.62 J10.89.41 O91.1.13'
>>> encode('Eat wise, drop a size', k2c)
'W92.XXXD.0 I97.611.84 I97.611.38 S59.099.31 M90.832.38 V42.1.93 M61.25.29 I67.83.43 T37.92.67 W93.38 O22.23 V59.9.48 F04.23 C34.2.13 F44.6.43 A00.0.28 M85.812.5 A02.24.23 Z96.621.21 J10.89.41 N07.9.31'
>>> encode('Eat wise, drop a size!', k2c)
Traceback (most recent call last):
ValueError: invalid plaintext