From 2df4a7e3f599d7fa5fe9af30bf66fcbccaf522c7 Mon Sep 17 00:00:00 2001
From: Ignacio G <garcia.nunez@tum.de>
Date: Sat, 22 Apr 2023 12:20:23 +0200
Subject: [PATCH 01/15] Add solution to project_euler/problem_060

---
 project_euler/problem_060/sol1.py | 191 ++++++++++++++++++++++++++++++
 1 file changed, 191 insertions(+)
 create mode 100644 project_euler/problem_060/sol1.py

diff --git a/project_euler/problem_060/sol1.py b/project_euler/problem_060/sol1.py
new file mode 100644
index 000000000000..4e5dc2fe60d7
--- /dev/null
+++ b/project_euler/problem_060/sol1.py
@@ -0,0 +1,191 @@
+"""
+Project Euler Problem 60: https://projecteuler.net/problem=60
+
+The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and
+concatenating them in any order the result will always be prime. For example,
+taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792,
+represents the lowest sum for a set of four primes with this property.
+
+Find the lowest sum for a set of five primes for which any two primes concatenate to
+produce another prime.
+
+On the algorithm:
+- Generate PRIMES_SIZE primes
+- Iterate through the primes, starting from the smallest available. On the top-level of
+the recursion, generate a list of primes that can be concatenated to the current prime.
+This list will be used for the next recursive calls.
+- Find all matches for that prime and store them in a list that will be used for the
+next recursive calls
+- Test matches for the next recursive calls, register the smallest sum found
+- Concatenation is done with arithmetic operations. String processing is generally
+slower.
+"""
+import collections.abc
+import math
+from time import time
+
+PRIMES_SIZE = 1.2e3
+COUNTER = False
+
+
+def get_order(n: int) -> int:
+    """
+    Get the order of a number n, in order to facilitate concatenation.
+    get_order(n) = x -> 10^x <= n < 10^(x+1)
+
+    >>> get_order(1)
+    0
+    >>> get_order(10)
+    1
+    >>> get_order(12345)
+    4
+    """
+
+    return int(math.log(n, 10))
+
+
+def test_concatenate(num1: int, num2: int) -> bool:
+    """
+    Test if two numbers concatenate to form a prime, for both possible arrangements.
+    Use arithmetic operations to concatenate.
+
+    >> test_concatenate(3, 7)
+    True
+    >>> test_concatenate(2, 10)
+    False
+    >>> test_concatenate(673, 109)
+    True
+    """
+
+    if not is_prime(num1 * 10 ** (get_order(num2) + 1) + num2):
+        return False
+
+    if not is_prime(num2 * 10 ** (get_order(num1) + 1) + num1):
+        return False
+
+    return True
+
+
+def is_prime(n) -> bool:
+    """
+    Simple prime test
+
+    >>> is_prime(2)
+    True
+    >>> is_prime(100000007)
+    True
+    >>> is_prime(10000007)
+    False
+    """
+    for divider in range(2, int(n**0.5) + 1):
+        if int(n) % divider == 0:
+            return False
+    return True
+
+
+def prime_generator() -> collections.abc.Iterator[int]:
+    """
+    Custom prime generator for primes used in this problem
+    Skip 2 and 5: no primes end with 2 or 5 except for 2 and 5, so they're not useful
+    for this problem
+
+    >>> [[next(x) for _ in range(5)] for x in [(prime_generator())]][0]
+    [3, 7, 11, 13, 17]
+    """
+
+    local_output: int = 3
+    yield local_output
+    local_output = 5
+
+    while True:
+        local_output += 2
+        if is_prime(local_output):
+            yield local_output
+
+
+def solution_helper(
+    depth: int, start_idx: int, to_test: list[int], matches: list[int]
+) -> list[int]:
+    """
+    Recursive helper function for solution(), search for more primes from
+    matches[start_idx:] that can be concatenated to all primes from to_test until
+    recursion reaches depth 0. Return the list of primes if a solution is found, False
+    otherwise.
+
+    >>> solution_helper(depth=3, start_idx=1, to_test=[3],matches=[3, 7, 100, 109, 673])
+    [3, 7, 109, 673]
+    >>> solution_helper(depth=2, start_idx=0, to_test=[7], matches=[10, 20, 30, 40, 50])
+    []
+    """
+
+    if depth == 0:
+        return to_test
+
+    for i in range(start_idx, len(matches)):
+        # Test all previous matches:
+        passes = True
+        for j in range(len(to_test)):
+            if not test_concatenate(matches[i], to_test[j]):
+                passes = False
+                break
+        if not passes:
+            continue
+        if output := solution_helper(depth - 1, i + 1, to_test + [matches[i]], matches):
+            return output
+    return []
+
+
+def solution(n_primes: int = 5) -> int:
+    """
+    This function behaves similarly to solution_helper, but it is not recursive and
+    defines some variables that are used in the recursive calls. It also defines a list
+    of matches for every prime it tests, optimizing search time.
+
+    >>> solution(n_primes=2)
+    14
+    >>> solution(n_primes=3)
+    405
+    >>> solution(n_primes=4)
+    3146
+    """
+
+    # Generate primes and start variables
+    start = time()
+    generator: collections.abc.Iterator[int] = prime_generator()
+    primes: list[int] = []
+    output: int = int(5e4)  # initialize with theoretical max value
+    for _ in range(int(PRIMES_SIZE)):
+        primes.append(next(generator))
+    if COUNTER:
+        print(f"{int(PRIMES_SIZE)} primes generated in {time() - start}s")
+
+    # Main loop
+    limit = output ** (1 / n_primes) * n_primes
+    for i in range(len(primes)):
+        # Break main loop if the current minimal number is larger than the 3rd root
+        # of the current output The reason for this is to not waste time trying to
+        # find solutions once the smallest prime in the search is already too large
+        # to be part of the solution
+        if primes[i] > limit:
+            break
+
+        # Iterate larger primes, store in matches. This should optimize the nested loops
+        matches: list[int] = []
+        prime: int = primes[i]
+        for j in range(i + 1, len(primes)):
+            if test_concatenate(prime, primes[j]):
+                matches.append(primes[j])
+
+        # Match every candidate with every other candidate until 5 are found
+        if found := solution_helper(
+            depth=n_primes - 1, start_idx=+1, to_test=[prime], matches=matches
+        ):
+            output = min(output, sum(found))
+
+    if COUNTER:
+        print(f"Done ({time() - start}s)")
+    return output
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")

From 8ccffdf98ef4e7f3942df25b06f204a6ab883e09 Mon Sep 17 00:00:00 2001
From: Ignacio G <garcia.nunez@tum.de>
Date: Sat, 22 Apr 2023 16:25:12 +0200
Subject: [PATCH 02/15] Reword algorith explanation on
 project_euler/problem_060

---
 project_euler/problem_060/sol1.py | 13 +++++++------
 1 file changed, 7 insertions(+), 6 deletions(-)

diff --git a/project_euler/problem_060/sol1.py b/project_euler/problem_060/sol1.py
index 4e5dc2fe60d7..8120484abe8c 100644
--- a/project_euler/problem_060/sol1.py
+++ b/project_euler/problem_060/sol1.py
@@ -25,7 +25,7 @@
 from time import time
 
 PRIMES_SIZE = 1.2e3
-COUNTER = False
+COUNTER = True
 
 
 def get_order(n: int) -> int:
@@ -162,10 +162,11 @@ def solution(n_primes: int = 5) -> int:
     # Main loop
     limit = output ** (1 / n_primes) * n_primes
     for i in range(len(primes)):
-        # Break main loop if the current minimal number is larger than the 3rd root
-        # of the current output The reason for this is to not waste time trying to
-        # find solutions once the smallest prime in the search is already too large
-        # to be part of the solution
+        # Break main loop if the current minimal number is larger than the nth root
+        # of the current output times n, with n being the amount of primes searched.
+        # The reason for this is to reduce the search space with a reasonable upper
+        # bound. Analysis with lower values for n_primes shows that this is a valid
+        # optimization.
         if primes[i] > limit:
             break
 
@@ -188,4 +189,4 @@ def solution(n_primes: int = 5) -> int:
 
 
 if __name__ == "__main__":
-    print(f"{solution() = }")
+    print(f"{solution(4) = }")

From 633593793a3dba2bea51c638983d3ac57e6b695a Mon Sep 17 00:00:00 2001
From: Ignacio G <garcia.nunez@tum.de>
Date: Sat, 22 Apr 2023 16:29:35 +0200
Subject: [PATCH 03/15] Disable timer on project_euler/problem_060/sol1.py

---
 project_euler/problem_060/sol1.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/project_euler/problem_060/sol1.py b/project_euler/problem_060/sol1.py
index 8120484abe8c..5542e47f24fa 100644
--- a/project_euler/problem_060/sol1.py
+++ b/project_euler/problem_060/sol1.py
@@ -25,7 +25,7 @@
 from time import time
 
 PRIMES_SIZE = 1.2e3
-COUNTER = True
+COUNTER = False
 
 
 def get_order(n: int) -> int:
@@ -189,4 +189,4 @@ def solution(n_primes: int = 5) -> int:
 
 
 if __name__ == "__main__":
-    print(f"{solution(4) = }")
+    print(f"{solution() = }")

From 8ab974590a548646637a310562f58bf259861609 Mon Sep 17 00:00:00 2001
From: Ignacio G <garcia.nunez@tum.de>
Date: Sat, 22 Apr 2023 16:34:52 +0200
Subject: [PATCH 04/15] Implement suggested formatting for
 project_euler/problem_060/sol1.py

---
 project_euler/problem_060/sol1.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/project_euler/problem_060/sol1.py b/project_euler/problem_060/sol1.py
index 5542e47f24fa..e29b2dbe0cd7 100644
--- a/project_euler/problem_060/sol1.py
+++ b/project_euler/problem_060/sol1.py
@@ -28,7 +28,7 @@
 COUNTER = False
 
 
-def get_order(n: int) -> int:
+def get_order(target: int) -> int:
     """
     Get the order of a number n, in order to facilitate concatenation.
     get_order(n) = x -> 10^x <= n < 10^(x+1)
@@ -41,7 +41,7 @@ def get_order(n: int) -> int:
     4
     """
 
-    return int(math.log(n, 10))
+    return int(math.log(target, 10))
 
 
 def test_concatenate(num1: int, num2: int) -> bool:
@@ -66,7 +66,7 @@ def test_concatenate(num1: int, num2: int) -> bool:
     return True
 
 
-def is_prime(n) -> bool:
+def is_prime(target: int) -> bool:
     """
     Simple prime test
 
@@ -77,8 +77,8 @@ def is_prime(n) -> bool:
     >>> is_prime(10000007)
     False
     """
-    for divider in range(2, int(n**0.5) + 1):
-        if int(n) % divider == 0:
+    for divider in range(2, int(target**0.5) + 1):
+        if int(target) % divider == 0:
             return False
     return True
 

From 2faf2e938ffec4ed1d4be599318354bf4922f313 Mon Sep 17 00:00:00 2001
From: Rohan Anand <96521078+rohan472000@users.noreply.github.com>
Date: Sat, 22 Apr 2023 20:58:07 +0530
Subject: [PATCH 05/15] Update linear_discriminant_analysis.py

---
 machine_learning/linear_discriminant_analysis.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/machine_learning/linear_discriminant_analysis.py b/machine_learning/linear_discriminant_analysis.py
index f4fb5ba76b64..1a5d15dca284 100644
--- a/machine_learning/linear_discriminant_analysis.py
+++ b/machine_learning/linear_discriminant_analysis.py
@@ -399,7 +399,7 @@ def main():
         if input("Press any key to restart or 'q' for quit: ").strip().lower() == "q":
             print("\n" + "GoodBye!".center(100, "-") + "\n")
             break
-        system("cls" if name == "nt" else "clear")
+        system('clear' if os.name == 'posix' else 'cls')
 
 
 if __name__ == "__main__":

From bff2edf6f6de7e00e5b4b08d0a9d53af90a0e388 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sat, 22 Apr 2023 15:29:43 +0000
Subject: [PATCH 06/15] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 machine_learning/linear_discriminant_analysis.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/machine_learning/linear_discriminant_analysis.py b/machine_learning/linear_discriminant_analysis.py
index 1a5d15dca284..45da556701a3 100644
--- a/machine_learning/linear_discriminant_analysis.py
+++ b/machine_learning/linear_discriminant_analysis.py
@@ -399,7 +399,7 @@ def main():
         if input("Press any key to restart or 'q' for quit: ").strip().lower() == "q":
             print("\n" + "GoodBye!".center(100, "-") + "\n")
             break
-        system('clear' if os.name == 'posix' else 'cls')
+        system("clear" if os.name == "posix" else "cls")
 
 
 if __name__ == "__main__":

From 41220e746bfbbd5d987ea4c714013f40852d8b72 Mon Sep 17 00:00:00 2001
From: Rohan Anand <96521078+rohan472000@users.noreply.github.com>
Date: Sat, 22 Apr 2023 21:00:37 +0530
Subject: [PATCH 07/15] Update linear_discriminant_analysis.py

---
 machine_learning/linear_discriminant_analysis.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/machine_learning/linear_discriminant_analysis.py b/machine_learning/linear_discriminant_analysis.py
index 45da556701a3..4d65f1aa5336 100644
--- a/machine_learning/linear_discriminant_analysis.py
+++ b/machine_learning/linear_discriminant_analysis.py
@@ -399,7 +399,7 @@ def main():
         if input("Press any key to restart or 'q' for quit: ").strip().lower() == "q":
             print("\n" + "GoodBye!".center(100, "-") + "\n")
             break
-        system("clear" if os.name == "posix" else "cls")
+        system("clear" if name == "posix" else "cls")
 
 
 if __name__ == "__main__":

From de13a9af856f0329ba21e48356fed7051f46dacf Mon Sep 17 00:00:00 2001
From: Rohan Anand <96521078+rohan472000@users.noreply.github.com>
Date: Sat, 22 Apr 2023 20:48:35 +0530
Subject: [PATCH 08/15] Update rsa_cipher.py by replacing %s with {}

---
 ciphers/rsa_cipher.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/ciphers/rsa_cipher.py b/ciphers/rsa_cipher.py
index de26992f5eeb..0e3df87cb891 100644
--- a/ciphers/rsa_cipher.py
+++ b/ciphers/rsa_cipher.py
@@ -76,7 +76,7 @@ def encrypt_and_write_to_file(
     key_size, n, e = read_key_file(key_filename)
     if key_size < block_size * 8:
         sys.exit(
-            "ERROR: Block size is %s bits and key size is %s bits. The RSA cipher "
+            "ERROR: Block size is {} bits and key size is {} bits. The RSA cipher "
             "requires the block size to be equal to or greater than the key size. "
             "Either decrease the block size or use different keys."
             % (block_size * 8, key_size)
@@ -101,7 +101,7 @@ def read_from_file_and_decrypt(message_filename: str, key_filename: str) -> str:
 
     if key_size < block_size * 8:
         sys.exit(
-            "ERROR: Block size is %s bits and key size is %s bits. The RSA cipher "
+            "ERROR: Block size is {} bits and key size is {} bits. The RSA cipher "
             "requires the block size to be equal to or greater than the key size. "
             "Did you specify the correct key file and encrypted file?"
             % (block_size * 8, key_size)

From d91fc28cc22c8c4791ccbe87efe8ccfe5cb1b679 Mon Sep 17 00:00:00 2001
From: Rohan Anand <96521078+rohan472000@users.noreply.github.com>
Date: Sat, 22 Apr 2023 20:51:27 +0530
Subject: [PATCH 09/15] Update rsa_cipher.py

---
 ciphers/rsa_cipher.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/ciphers/rsa_cipher.py b/ciphers/rsa_cipher.py
index 0e3df87cb891..aa59630b5645 100644
--- a/ciphers/rsa_cipher.py
+++ b/ciphers/rsa_cipher.py
@@ -79,7 +79,7 @@ def encrypt_and_write_to_file(
             "ERROR: Block size is {} bits and key size is {} bits. The RSA cipher "
             "requires the block size to be equal to or greater than the key size. "
             "Either decrease the block size or use different keys."
-            % (block_size * 8, key_size)
+            .format(block_size * 8, key_size)
         )
 
     encrypted_blocks = [str(i) for i in encrypt_message(message, (n, e), block_size)]
@@ -104,7 +104,7 @@ def read_from_file_and_decrypt(message_filename: str, key_filename: str) -> str:
             "ERROR: Block size is {} bits and key size is {} bits. The RSA cipher "
             "requires the block size to be equal to or greater than the key size. "
             "Did you specify the correct key file and encrypted file?"
-            % (block_size * 8, key_size)
+            .format(block_size * 8, key_size)
         )
 
     encrypted_blocks = []

From 69015fb3ec9df08078511e254e4675ff1359510e Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sat, 22 Apr 2023 15:21:57 +0000
Subject: [PATCH 10/15] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 ciphers/rsa_cipher.py | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/ciphers/rsa_cipher.py b/ciphers/rsa_cipher.py
index aa59630b5645..9c41cdc5d472 100644
--- a/ciphers/rsa_cipher.py
+++ b/ciphers/rsa_cipher.py
@@ -78,8 +78,9 @@ def encrypt_and_write_to_file(
         sys.exit(
             "ERROR: Block size is {} bits and key size is {} bits. The RSA cipher "
             "requires the block size to be equal to or greater than the key size. "
-            "Either decrease the block size or use different keys."
-            .format(block_size * 8, key_size)
+            "Either decrease the block size or use different keys.".format(
+                block_size * 8, key_size
+            )
         )
 
     encrypted_blocks = [str(i) for i in encrypt_message(message, (n, e), block_size)]
@@ -103,8 +104,9 @@ def read_from_file_and_decrypt(message_filename: str, key_filename: str) -> str:
         sys.exit(
             "ERROR: Block size is {} bits and key size is {} bits. The RSA cipher "
             "requires the block size to be equal to or greater than the key size. "
-            "Did you specify the correct key file and encrypted file?"
-            .format(block_size * 8, key_size)
+            "Did you specify the correct key file and encrypted file?".format(
+                block_size * 8, key_size
+            )
         )
 
     encrypted_blocks = []

From 24a73e756419b1f9129e99eea9e203b8510d075b Mon Sep 17 00:00:00 2001
From: Ignacio G <garcia.nunez@tum.de>
Date: Sun, 23 Apr 2023 19:35:40 +0200
Subject: [PATCH 11/15] Remove system command to clear console on
 machine_learning/linear_discriminant_analysis.py

---
 machine_learning/linear_discriminant_analysis.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/machine_learning/linear_discriminant_analysis.py b/machine_learning/linear_discriminant_analysis.py
index 4d65f1aa5336..b0ece521ecb9 100644
--- a/machine_learning/linear_discriminant_analysis.py
+++ b/machine_learning/linear_discriminant_analysis.py
@@ -44,7 +44,6 @@
 """
 from collections.abc import Callable
 from math import log
-from os import name, system
 from random import gauss, seed
 from typing import TypeVar
 
@@ -399,7 +398,7 @@ def main():
         if input("Press any key to restart or 'q' for quit: ").strip().lower() == "q":
             print("\n" + "GoodBye!".center(100, "-") + "\n")
             break
-        system("clear" if name == "posix" else "cls")
+        # system("clear" if name == "posix" else "cls")
 
 
 if __name__ == "__main__":

From 57ee3772a4b5833b77fed55e5dccabfdaf6f9400 Mon Sep 17 00:00:00 2001
From: Rohan Anand <96521078+rohan472000@users.noreply.github.com>
Date: Mon, 24 Apr 2023 10:58:30 +0530
Subject: [PATCH 12/15] Update linear_discriminant_analysis.py and
 rsa_cipher.py (#8680)

* Update rsa_cipher.py by replacing %s with {}

* Update rsa_cipher.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update linear_discriminant_analysis.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update linear_discriminant_analysis.py

* Update linear_discriminant_analysis.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update linear_discriminant_analysis.py

* Update linear_discriminant_analysis.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update linear_discriminant_analysis.py

* Update machine_learning/linear_discriminant_analysis.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update linear_discriminant_analysis.py

* updated

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
---
 machine_learning/linear_discriminant_analysis.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/machine_learning/linear_discriminant_analysis.py b/machine_learning/linear_discriminant_analysis.py
index b0ece521ecb9..5469c6decc9d 100644
--- a/machine_learning/linear_discriminant_analysis.py
+++ b/machine_learning/linear_discriminant_analysis.py
@@ -398,7 +398,7 @@ def main():
         if input("Press any key to restart or 'q' for quit: ").strip().lower() == "q":
             print("\n" + "GoodBye!".center(100, "-") + "\n")
             break
-        # system("clear" if name == "posix" else "cls")
+        system("clear" if name == "posix" else "cls")  # noqa: S605
 
 
 if __name__ == "__main__":

From 296239187b1eeec9b3902466b543eec8df09c383 Mon Sep 17 00:00:00 2001
From: Rohan Anand <96521078+rohan472000@users.noreply.github.com>
Date: Sat, 22 Apr 2023 20:51:27 +0530
Subject: [PATCH 13/15] Update rsa_cipher.py

---
 ciphers/rsa_cipher.py | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/ciphers/rsa_cipher.py b/ciphers/rsa_cipher.py
index 9c41cdc5d472..762337a2d119 100644
--- a/ciphers/rsa_cipher.py
+++ b/ciphers/rsa_cipher.py
@@ -78,9 +78,14 @@ def encrypt_and_write_to_file(
         sys.exit(
             "ERROR: Block size is {} bits and key size is {} bits. The RSA cipher "
             "requires the block size to be equal to or greater than the key size. "
+<<<<<<< HEAD
             "Either decrease the block size or use different keys.".format(
                 block_size * 8, key_size
             )
+=======
+            "Either decrease the block size or use different keys."
+            .format(block_size * 8, key_size)
+>>>>>>> d91fc28 (Update rsa_cipher.py)
         )
 
     encrypted_blocks = [str(i) for i in encrypt_message(message, (n, e), block_size)]

From c5960166000f04fdc85b4b4f70c31c17a32a7e25 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sat, 22 Apr 2023 15:21:57 +0000
Subject: [PATCH 14/15] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 ciphers/rsa_cipher.py | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/ciphers/rsa_cipher.py b/ciphers/rsa_cipher.py
index 762337a2d119..9c41cdc5d472 100644
--- a/ciphers/rsa_cipher.py
+++ b/ciphers/rsa_cipher.py
@@ -78,14 +78,9 @@ def encrypt_and_write_to_file(
         sys.exit(
             "ERROR: Block size is {} bits and key size is {} bits. The RSA cipher "
             "requires the block size to be equal to or greater than the key size. "
-<<<<<<< HEAD
             "Either decrease the block size or use different keys.".format(
                 block_size * 8, key_size
             )
-=======
-            "Either decrease the block size or use different keys."
-            .format(block_size * 8, key_size)
->>>>>>> d91fc28 (Update rsa_cipher.py)
         )
 
     encrypted_blocks = [str(i) for i in encrypt_message(message, (n, e), block_size)]

From 19086945b1b4bbee5e17262d027f5324f592990f Mon Sep 17 00:00:00 2001
From: Ignacio G <garcia.nunez@tum.de>
Date: Mon, 24 Apr 2023 09:41:09 +0200
Subject: [PATCH 15/15] Rollback changes

---
 machine_learning/linear_discriminant_analysis.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/machine_learning/linear_discriminant_analysis.py b/machine_learning/linear_discriminant_analysis.py
index 5469c6decc9d..c0a477be10c7 100644
--- a/machine_learning/linear_discriminant_analysis.py
+++ b/machine_learning/linear_discriminant_analysis.py
@@ -44,6 +44,7 @@
 """
 from collections.abc import Callable
 from math import log
+from os import name, system
 from random import gauss, seed
 from typing import TypeVar