Add solution for Project Euler problem 59 (TheAlgorithms#4031)

* Added solution for Project Euler problem 59

* updating DIRECTORY.md

* Formatting, type hints, no more evil map functions

* Doctests

* Added doctests for Project Euler problem 59

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

Author: fpringle

Diff for: DIRECTORY.md

@@ -345,6 +345,7 @@
 
 ## Linear Algebra
   * Src
+    * [Conjugate Gradient](https://github.com/TheAlgorithms/Python/blob/master/linear_algebra/src/conjugate_gradient.py)
     * [Lib](https://github.com/TheAlgorithms/Python/blob/master/linear_algebra/src/lib.py)
     * [Polynom For Points](https://github.com/TheAlgorithms/Python/blob/master/linear_algebra/src/polynom_for_points.py)
     * [Power Iteration](https://github.com/TheAlgorithms/Python/blob/master/linear_algebra/src/power_iteration.py)
@@ -695,6 +696,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_057/sol1.py)
   * Problem 058
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_058/sol1.py)
+  * Problem 059
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_059/sol1.py)
   * Problem 062
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_062/sol1.py)
   * Problem 063

Diff for: project_euler/problem_059/__init__.py

@@ -0,0 +1 @@
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Diff for: project_euler/problem_059/p059_cipher.txt

@@ -0,0 +1,128 @@
+"""
+Each character on a computer is assigned a unique code and the preferred standard is
+ASCII (American Standard Code for Information Interchange).
+For example, uppercase A = 65, asterisk (*) = 42, and lowercase k = 107.
+
+A modern encryption method is to take a text file, convert the bytes to ASCII, then
+XOR each byte with a given value, taken from a secret key. The advantage with the
+XOR function is that using the same encryption key on the cipher text, restores
+the plain text; for example, 65 XOR 42 = 107, then 107 XOR 42 = 65.
+
+For unbreakable encryption, the key is the same length as the plain text message, and
+the key is made up of random bytes. The user would keep the encrypted message and the
+encryption key in different locations, and without both "halves", it is impossible to
+decrypt the message.
+
+Unfortunately, this method is impractical for most users, so the modified method is
+to use a password as a key. If the password is shorter than the message, which is
+likely, the key is repeated cyclically throughout the message. The balance for this
+method is using a sufficiently long password key for security, but short enough to
+be memorable.
+
+Your task has been made easy, as the encryption key consists of three lower case
+characters. Using p059_cipher.txt (right click and 'Save Link/Target As...'), a
+file containing the encrypted ASCII codes, and the knowledge that the plain text
+must contain common English words, decrypt the message and find the sum of the ASCII
+values in the original text.
+"""
+
+
+import string
+from itertools import cycle, product
+from pathlib import Path
+from typing import List, Optional, Set, Tuple
+
+VALID_CHARS: str = (
+    string.ascii_letters + string.digits + string.punctuation + string.whitespace
+)
+LOWERCASE_INTS: List[int] = [ord(letter) for letter in string.ascii_lowercase]
+VALID_INTS: Set[int] = {ord(char) for char in VALID_CHARS}
+
+COMMON_WORDS: List[str] = ["the", "be", "to", "of", "and", "in", "that", "have"]
+
+
+def try_key(ciphertext: List[int], key: Tuple[int, ...]) -> Optional[str]:
+    """
+    Given an encrypted message and a possible 3-character key, decrypt the message.
+    If the decrypted message contains a invalid character, i.e. not an ASCII letter,
+    a digit, punctuation or whitespace, then we know the key is incorrect, so return
+    None.
+    >>> try_key([0, 17, 20, 4, 27], (104, 116, 120))
+    'hello'
+    >>> try_key([68, 10, 300, 4, 27], (104, 116, 120)) is None
+    True
+    """
+    decoded: str = ""
+    keychar: int
+    cipherchar: int
+    decodedchar: int
+
+    for keychar, cipherchar in zip(cycle(key), ciphertext):
+        decodedchar = cipherchar ^ keychar
+        if decodedchar not in VALID_INTS:
+            return None
+        decoded += chr(decodedchar)
+
+    return decoded
+
+
+def filter_valid_chars(ciphertext: List[int]) -> List[str]:
+    """
+    Given an encrypted message, test all 3-character strings to try and find the
+    key. Return a list of the possible decrypted messages.
+    >>> from itertools import cycle
+    >>> text = "The enemy's gate is down"
+    >>> key = "end"
+    >>> encoded = [ord(k) ^ ord(c) for k,c in zip(cycle(key), text)]
+    >>> text in filter_valid_chars(encoded)
+    True
+    """
+    possibles: List[str] = []
+    for key in product(LOWERCASE_INTS, repeat=3):
+        encoded = try_key(ciphertext, key)
+        if encoded is not None:
+            possibles.append(encoded)
+    return possibles
+
+
+def filter_common_word(possibles: List[str], common_word: str) -> List[str]:
+    """
+    Given a list of possible decoded messages, narrow down the possibilities
+    for checking for the presence of a specified common word. Only decoded messages
+    containing common_word will be returned.
+    >>> filter_common_word(['asfla adf', 'I am here', '   !?! #a'], 'am')
+    ['I am here']
+    >>> filter_common_word(['athla amf', 'I am here', '   !?! #a'], 'am')
+    ['athla amf', 'I am here']
+    """
+    return [possible for possible in possibles if common_word in possible.lower()]
+
+
+def solution(filename: str = "p059_cipher.txt") -> int:
+    """
+    Test the ciphertext against all possible 3-character keys, then narrow down the
+    possibilities by filtering using common words until there's only one possible
+    decoded message.
+    >>> solution("test_cipher.txt")
+    3000
+    """
+    ciphertext: List[int]
+    possibles: List[str]
+    common_word: str
+    decoded_text: str
+    data: str = Path(__file__).parent.joinpath(filename).read_text(encoding="utf-8")
+
+    ciphertext = [int(number) for number in data.strip().split(",")]
+
+    possibles = filter_valid_chars(ciphertext)
+    for common_word in COMMON_WORDS:
+        possibles = filter_common_word(possibles, common_word)
+        if len(possibles) == 1:
+            break
+
+    decoded_text = possibles[0]
+    return sum([ord(char) for char in decoded_text])
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")

Diff for: project_euler/problem_059/sol1.py

@@ -0,0 +1 @@
+63,13,28,75,0,23,14,8,0,76,22,89,12,4,13,14,69,16,24,69,29,4,18,23,69,69,59,14,69,11,14,4,29,18