Merge remote-tracking branch 'upstream/master' into mypy-fix-other-lru_cache

Author: spazm

Diff for: .github/workflows/build.yml

@@ -21,7 +21,7 @@ jobs:
         run: |
           python -m pip install --upgrade pip setuptools six wheel
           python -m pip install mypy pytest-cov -r requirements.txt
-      - run: mypy --install-types --non-interactive .
+      - run: mypy .  # See `mypy.ini` for configuration settings.
       - name: Run tests
         run: pytest --doctest-modules --ignore=project_euler/ --ignore=scripts/validate_solutions.py --cov-report=term-missing:skip-covered --cov=. .
       - if: ${{ success() }}

Diff for: CONTRIBUTING.md

@@ -23,7 +23,7 @@ __Improving comments__ and __writing proper tests__ are also highly welcome.
 
 We appreciate any contribution, from fixing a grammar mistake in a comment to implementing complex algorithms. Please read this section if you are contributing your work.
 
-Your contribution will be tested by our [automated testing on Travis CI](https://travis-ci.org/TheAlgorithms/Python/pull_requests) to save time and mental energy.  After you have submitted your pull request, you should see the Travis tests start to run at the bottom of your submission page.  If those tests fail, then click on the ___details___ button try to read through the Travis output to understand the failure.  If you do not understand, please leave a comment on your submission page and a community member will try to help.
+Your contribution will be tested by our [automated testing on GitHub Actions](https://github.com/TheAlgorithms/Python/actions) to save time and mental energy.  After you have submitted your pull request, you should see the GitHub Actions tests start to run at the bottom of your submission page.  If those tests fail, then click on the ___details___ button try to read through the GitHub Actions output to understand the failure.  If you do not understand, please leave a comment on your submission page and a community member will try to help.
 
 Please help us keep our issue list small by adding fixes: #{$ISSUE_NO} to the commit message of pull requests that resolve open issues. GitHub will use this tag to auto-close the issue when the PR is merged.
 
@@ -170,7 +170,7 @@ We want your work to be readable by others; therefore, we encourage you to note
 - If possible, follow the standard *within* the folder you are submitting to.
 - If you have modified/added code work, make sure the code compiles before submitting.
 - If you have modified/added documentation work, ensure your language is concise and contains no grammar errors.
-- Do not update the README.md or DIRECTORY.md file which will be periodically autogenerated by our Travis CI processes.
+- Do not update the README.md or DIRECTORY.md file which will be periodically autogenerated by our GitHub Actions processes.
 - Add a corresponding explanation to [Algorithms-Explanation](https://github.com/TheAlgorithms/Algorithms-Explanation) (Optional but recommended).
 - All submissions will be tested with [__mypy__](http://www.mypy-lang.org) so we encourage you to add [__Python type hints__](https://docs.python.org/3/library/typing.html) where it makes sense to do so.
 

Diff for: DIRECTORY.md

@@ -4,6 +4,7 @@
   * [Gaussian Elimination](https://github.com/TheAlgorithms/Python/blob/master/arithmetic_analysis/gaussian_elimination.py)
   * [In Static Equilibrium](https://github.com/TheAlgorithms/Python/blob/master/arithmetic_analysis/in_static_equilibrium.py)
   * [Intersection](https://github.com/TheAlgorithms/Python/blob/master/arithmetic_analysis/intersection.py)
+  * [Jacobi Iteration Method](https://github.com/TheAlgorithms/Python/blob/master/arithmetic_analysis/jacobi_iteration_method.py)
   * [Lu Decomposition](https://github.com/TheAlgorithms/Python/blob/master/arithmetic_analysis/lu_decomposition.py)
   * [Newton Forward Interpolation](https://github.com/TheAlgorithms/Python/blob/master/arithmetic_analysis/newton_forward_interpolation.py)
   * [Newton Method](https://github.com/TheAlgorithms/Python/blob/master/arithmetic_analysis/newton_method.py)
@@ -39,6 +40,7 @@
   * [Binary Xor Operator](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/binary_xor_operator.py)
   * [Count 1S Brian Kernighan Method](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/count_1s_brian_kernighan_method.py)
   * [Count Number Of One Bits](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/count_number_of_one_bits.py)
+  * [Gray Code Sequence](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/gray_code_sequence.py)
   * [Reverse Bits](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/reverse_bits.py)
   * [Single Bit Manipulation Operations](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/single_bit_manipulation_operations.py)
 
@@ -63,7 +65,7 @@
   * [Baconian Cipher](https://github.com/TheAlgorithms/Python/blob/master/ciphers/baconian_cipher.py)
   * [Base16](https://github.com/TheAlgorithms/Python/blob/master/ciphers/base16.py)
   * [Base32](https://github.com/TheAlgorithms/Python/blob/master/ciphers/base32.py)
-  * [Base64 Encoding](https://github.com/TheAlgorithms/Python/blob/master/ciphers/base64_encoding.py)
+  * [Base64](https://github.com/TheAlgorithms/Python/blob/master/ciphers/base64.py)
   * [Base85](https://github.com/TheAlgorithms/Python/blob/master/ciphers/base85.py)
   * [Beaufort Cipher](https://github.com/TheAlgorithms/Python/blob/master/ciphers/beaufort_cipher.py)
   * [Bifid](https://github.com/TheAlgorithms/Python/blob/master/ciphers/bifid.py)
@@ -108,8 +110,10 @@
 
 ## Computer Vision
   * [Cnn Classification](https://github.com/TheAlgorithms/Python/blob/master/computer_vision/cnn_classification.py)
+  * [Flip Augmentation](https://github.com/TheAlgorithms/Python/blob/master/computer_vision/flip_augmentation.py)
   * [Harris Corner](https://github.com/TheAlgorithms/Python/blob/master/computer_vision/harris_corner.py)
   * [Mean Threshold](https://github.com/TheAlgorithms/Python/blob/master/computer_vision/mean_threshold.py)
+  * [Mosaic Augmentation](https://github.com/TheAlgorithms/Python/blob/master/computer_vision/mosaic_augmentation.py)
 
 ## Conversions
   * [Binary To Decimal](https://github.com/TheAlgorithms/Python/blob/master/conversions/binary_to_decimal.py)
@@ -219,6 +223,7 @@
   * Filters
     * [Bilateral Filter](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/filters/bilateral_filter.py)
     * [Convolve](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/filters/convolve.py)
+    * [Gabor Filter](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/filters/gabor_filter.py)
     * [Gaussian Filter](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/filters/gaussian_filter.py)
     * [Median Filter](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/filters/median_filter.py)
     * [Sobel Filter](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/filters/sobel_filter.py)
@@ -251,6 +256,7 @@
 
 ## Dynamic Programming
   * [Abbreviation](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/abbreviation.py)
+  * [All Construct](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/all_construct.py)
   * [Bitmask](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/bitmask.py)
   * [Catalan Numbers](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/catalan_numbers.py)
   * [Climbing Stairs](https://github.com/TheAlgorithms/Python/blob/master/dynamic_programming/climbing_stairs.py)
@@ -294,6 +300,7 @@
     * [Test Send File](https://github.com/TheAlgorithms/Python/blob/master/file_transfer/tests/test_send_file.py)
 
 ## Financial
+  * [Equated Monthly Installments](https://github.com/TheAlgorithms/Python/blob/master/financial/equated_monthly_installments.py)
   * [Interest](https://github.com/TheAlgorithms/Python/blob/master/financial/interest.py)
 
 ## Fractals
@@ -511,6 +518,7 @@
   * [Modular Exponential](https://github.com/TheAlgorithms/Python/blob/master/maths/modular_exponential.py)
   * [Monte Carlo](https://github.com/TheAlgorithms/Python/blob/master/maths/monte_carlo.py)
   * [Monte Carlo Dice](https://github.com/TheAlgorithms/Python/blob/master/maths/monte_carlo_dice.py)
+  * [Nevilles Method](https://github.com/TheAlgorithms/Python/blob/master/maths/nevilles_method.py)
   * [Newton Raphson](https://github.com/TheAlgorithms/Python/blob/master/maths/newton_raphson.py)
   * [Number Of Digits](https://github.com/TheAlgorithms/Python/blob/master/maths/number_of_digits.py)
   * [Numerical Integration](https://github.com/TheAlgorithms/Python/blob/master/maths/numerical_integration.py)
@@ -546,6 +554,7 @@
   * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/Python/blob/master/maths/sieve_of_eratosthenes.py)
   * [Sigmoid](https://github.com/TheAlgorithms/Python/blob/master/maths/sigmoid.py)
   * [Simpson Rule](https://github.com/TheAlgorithms/Python/blob/master/maths/simpson_rule.py)
+  * [Sock Merchant](https://github.com/TheAlgorithms/Python/blob/master/maths/sock_merchant.py)
   * [Softmax](https://github.com/TheAlgorithms/Python/blob/master/maths/softmax.py)
   * [Square Root](https://github.com/TheAlgorithms/Python/blob/master/maths/square_root.py)
   * [Sum Of Arithmetic Series](https://github.com/TheAlgorithms/Python/blob/master/maths/sum_of_arithmetic_series.py)
@@ -608,6 +617,7 @@
 
 ## Physics
   * [N Body Simulation](https://github.com/TheAlgorithms/Python/blob/master/physics/n_body_simulation.py)
+  * [Newtons Second Law Of Motion](https://github.com/TheAlgorithms/Python/blob/master/physics/newtons_second_law_of_motion.py)
 
 ## Project Euler
   * Problem 001
@@ -844,6 +854,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_135/sol1.py)
   * Problem 144
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_144/sol1.py)
+  * Problem 145
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_145/sol1.py)
   * Problem 173
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_173/sol1.py)
   * Problem 174
@@ -856,6 +868,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_191/sol1.py)
   * Problem 203
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_203/sol1.py)
+  * Problem 205
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_205/sol1.py)
   * Problem 206
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_206/sol1.py)
   * Problem 207
@@ -1014,6 +1028,7 @@
   * [Nasa Data](https://github.com/TheAlgorithms/Python/blob/master/web_programming/nasa_data.py)
   * [Random Anime Character](https://github.com/TheAlgorithms/Python/blob/master/web_programming/random_anime_character.py)
   * [Recaptcha Verification](https://github.com/TheAlgorithms/Python/blob/master/web_programming/recaptcha_verification.py)
+  * [Reddit](https://github.com/TheAlgorithms/Python/blob/master/web_programming/reddit.py)
   * [Search Books By Isbn](https://github.com/TheAlgorithms/Python/blob/master/web_programming/search_books_by_isbn.py)
   * [Slack Message](https://github.com/TheAlgorithms/Python/blob/master/web_programming/slack_message.py)
   * [Test Fetch Github Info](https://github.com/TheAlgorithms/Python/blob/master/web_programming/test_fetch_github_info.py)

Diff for: arithmetic_analysis/README.md

@@ -0,0 +1,7 @@
+# Arithmetic analysis
+
+Arithmetic analysis is a branch of mathematics that deals with solving linear equations.
+
+* <https://en.wikipedia.org/wiki/System_of_linear_equations>
+* <https://en.wikipedia.org/wiki/Gaussian_elimination>
+* <https://en.wikipedia.org/wiki/Root-finding_algorithms>

Diff for: arithmetic_analysis/jacobi_iteration_method.py

@@ -0,0 +1,163 @@
+"""
+Jacobi Iteration Method - https://en.wikipedia.org/wiki/Jacobi_method
+"""
+from __future__ import annotations
+
+import numpy as np
+
+
+# Method to find solution of system of linear equations
+def jacobi_iteration_method(
+    coefficient_matrix: np.ndarray,
+    constant_matrix: np.ndarray,
+    init_val: list,
+    iterations: int,
+) -> list[float]:
+    """
+    Jacobi Iteration Method:
+    An iterative algorithm to determine the solutions of strictly diagonally dominant
+    system of linear equations
+
+    4x1 +  x2 +  x3 =  2
+     x1 + 5x2 + 2x3 = -6
+     x1 + 2x2 + 4x3 = -4
+
+    x_init = [0.5, -0.5 , -0.5]
+
+    Examples:
+
+    >>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
+    >>> constant = np.array([[2], [-6], [-4]])
+    >>> init_val = [0.5, -0.5, -0.5]
+    >>> iterations = 3
+    >>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
+    [0.909375, -1.14375, -0.7484375]
+
+
+    >>> coefficient = np.array([[4, 1, 1], [1, 5, 2]])
+    >>> constant = np.array([[2], [-6], [-4]])
+    >>> init_val = [0.5, -0.5, -0.5]
+    >>> iterations = 3
+    >>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
+    Traceback (most recent call last):
+    ...
+    ValueError: Coefficient matrix dimensions must be nxn but received 2x3
+
+    >>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
+    >>> constant = np.array([[2], [-6]])
+    >>> init_val = [0.5, -0.5, -0.5]
+    >>> iterations = 3
+    >>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
+    Traceback (most recent call last):
+    ...
+    ValueError: Coefficient and constant matrices dimensions must be nxn and nx1 but
+                received 3x3 and 2x1
+
+    >>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
+    >>> constant = np.array([[2], [-6], [-4]])
+    >>> init_val = [0.5, -0.5]
+    >>> iterations = 3
+    >>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
+    Traceback (most recent call last):
+    ...
+    ValueError: Number of initial values must be equal to number of rows in coefficient
+                matrix but received 2 and 3
+
+    >>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
+    >>> constant = np.array([[2], [-6], [-4]])
+    >>> init_val = [0.5, -0.5, -0.5]
+    >>> iterations = 0
+    >>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
+    Traceback (most recent call last):
+    ...
+    ValueError: Iterations must be at least 1
+    """
+
+    rows1, cols1 = coefficient_matrix.shape
+    rows2, cols2 = constant_matrix.shape
+
+    if rows1 != cols1:
+        raise ValueError(
+            f"Coefficient matrix dimensions must be nxn but received {rows1}x{cols1}"
+        )
+
+    if cols2 != 1:
+        raise ValueError(f"Constant matrix must be nx1 but received {rows2}x{cols2}")
+
+    if rows1 != rows2:
+        raise ValueError(
+            f"""Coefficient and constant matrices dimensions must be nxn and nx1 but
+            received {rows1}x{cols1} and {rows2}x{cols2}"""
+        )
+
+    if len(init_val) != rows1:
+        raise ValueError(
+            f"""Number of initial values must be equal to number of rows in coefficient
+            matrix but received {len(init_val)} and {rows1}"""
+        )
+
+    if iterations <= 0:
+        raise ValueError("Iterations must be at least 1")
+
+    table = np.concatenate((coefficient_matrix, constant_matrix), axis=1)
+
+    rows, cols = table.shape
+
+    strictly_diagonally_dominant(table)
+
+    # Iterates the whole matrix for given number of times
+    for i in range(iterations):
+        new_val = []
+        for row in range(rows):
+            temp = 0
+            for col in range(cols):
+                if col == row:
+                    denom = table[row][col]
+                elif col == cols - 1:
+                    val = table[row][col]
+                else:
+                    temp += (-1) * table[row][col] * init_val[col]
+            temp = (temp + val) / denom
+            new_val.append(temp)
+        init_val = new_val
+
+    return [float(i) for i in new_val]
+
+
+# Checks if the given matrix is strictly diagonally dominant
+def strictly_diagonally_dominant(table: np.ndarray) -> bool:
+    """
+    >>> table = np.array([[4, 1, 1, 2], [1, 5, 2, -6], [1, 2, 4, -4]])
+    >>> strictly_diagonally_dominant(table)
+    True
+
+    >>> table = np.array([[4, 1, 1, 2], [1, 5, 2, -6], [1, 2, 3, -4]])
+    >>> strictly_diagonally_dominant(table)
+    Traceback (most recent call last):
+    ...
+    ValueError: Coefficient matrix is not strictly diagonally dominant
+    """
+
+    rows, cols = table.shape
+
+    is_diagonally_dominant = True
+
+    for i in range(0, rows):
+        sum = 0
+        for j in range(0, cols - 1):
+            if i == j:
+                continue
+            else:
+                sum += table[i][j]
+
+        if table[i][i] <= sum:
+            raise ValueError("Coefficient matrix is not strictly diagonally dominant")
+
+    return is_diagonally_dominant
+
+
+# Test Cases
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

Diff for: audio_filters/README.md

@@ -0,0 +1,9 @@
+# Audio Filter
+
+Audio filters work on the frequency of an audio signal to attenuate unwanted frequency and amplify wanted ones.
+They are used within anything related to sound, whether it is radio communication or a hi-fi system.
+
+* <https://www.masteringbox.com/filter-types/>
+* <http://ethanwiner.com/filters.html>
+* <https://en.wikipedia.org/wiki/Audio_filter>
+* <https://en.wikipedia.org/wiki/Electronic_filter>

Diff for: backtracking/README.md

@@ -0,0 +1,8 @@
+# Backtracking
+
+Backtracking is a way to speed up the search process by removing candidates when they can't be the solution of a problem.
+
+* <https://en.wikipedia.org/wiki/Backtracking>
+* <https://en.wikipedia.org/wiki/Decision_tree_pruning>
+* <https://medium.com/@priyankmistry1999/backtracking-sudoku-6e4439e4825c>
+* <https://www.geeksforgeeks.org/sudoku-backtracking-7/>

Diff for: bit_manipulation/README.md

@@ -1,6 +1,11 @@
-* https://docs.python.org/3/reference/expressions.html#binary-bitwise-operations
-* https://docs.python.org/3/reference/expressions.html#unary-arithmetic-and-bitwise-operations
-* https://docs.python.org/3/library/stdtypes.html#bitwise-operations-on-integer-types
-* https://wiki.python.org/moin/BitManipulation
-* https://wiki.python.org/moin/BitwiseOperators
-* https://www.tutorialspoint.com/python3/bitwise_operators_example.htm
+# Bit manipulation
+
+Bit manipulation is the act of manipulating bits to detect errors (hamming code), encrypts and decrypts messages (more on that in the 'ciphers' folder) or just do anything at the lowest level of your computer.
+
+* <https://en.wikipedia.org/wiki/Bit_manipulation>
+* <https://docs.python.org/3/reference/expressions.html#binary-bitwise-operations>
+* <https://docs.python.org/3/reference/expressions.html#unary-arithmetic-and-bitwise-operations>
+* <https://docs.python.org/3/library/stdtypes.html#bitwise-operations-on-integer-types>
+* <https://wiki.python.org/moin/BitManipulation>
+* <https://wiki.python.org/moin/BitwiseOperators>
+* <https://www.tutorialspoint.com/python3/bitwise_operators_example.htm>

Diff for: boolean_algebra/README.md

@@ -0,0 +1,7 @@
+# Boolean Algebra
+
+Boolean algebra is used to do arithmetic with bits of values True (1) or False (0).
+There are three basic operations: 'and', 'or' and 'not'.
+
+* <https://en.wikipedia.org/wiki/Boolean_algebra>
+* <https://plato.stanford.edu/entries/boolalg-math/>