Merge branch 'TheAlgorithms:master' into fix-mypy-errs-5

Author: tianyizheng02

Diff for: .github/stale.yml

@@ -45,7 +45,7 @@ pulls:
   closeComment: >
     Please reopen this pull request once you commit the changes requested
     or make improvements on the code. If this is not the case and you need
-    some help, feel free to seek help from our [Gitter](https://app.gitter.im/#/room/#TheAlgorithms_community:gitter.im)
+    some help, feel free to seek help from our [Gitter](https://gitter.im/TheAlgorithms/community)
     or ping one of the reviewers. Thank you for your contributions!
 
 issues:
@@ -59,5 +59,5 @@ issues:
   closeComment: >
     Please reopen this issue once you add more information and updates here.
     If this is not the case and you need some help, feel free to seek help
-    from our [Gitter](https://app.gitter.im/#/room/#TheAlgorithms_community:gitter.im) or ping one of the
+    from our [Gitter](https://gitter.im/TheAlgorithms/community) or ping one of the
     reviewers. Thank you for your contributions!

Diff for: CONTRIBUTING.md

@@ -2,7 +2,7 @@
 
 ## Before contributing
 
-Welcome to [TheAlgorithms/Python](https://github.com/TheAlgorithms/Python)! Before sending your pull requests, make sure that you __read the whole guidelines__. If you have any doubt on the contributing guide, please feel free to [state it clearly in an issue](https://github.com/TheAlgorithms/Python/issues/new) or ask the community in [Gitter](https://app.gitter.im/#/room/#TheAlgorithms_community:gitter.im).
+Welcome to [TheAlgorithms/Python](https://github.com/TheAlgorithms/Python)! Before sending your pull requests, make sure that you __read the whole guidelines__. If you have any doubt on the contributing guide, please feel free to [state it clearly in an issue](https://github.com/TheAlgorithms/Python/issues/new) or ask the community in [Gitter](https://gitter.im/TheAlgorithms/community).
 
 ## Contributing
 
@@ -176,7 +176,7 @@ We want your work to be readable by others; therefore, we encourage you to note
 
 - Most importantly,
   - __Be consistent in the use of these guidelines when submitting.__
-  - __Join__ us on [Discord](https://discord.com/invite/c7MnfGFGa6) and [Gitter](https://app.gitter.im/#/room/#TheAlgorithms_community:gitter.im) __now!__
+  - __Join__ us on [Discord](https://discord.com/invite/c7MnfGFGa6) and [Gitter](https://gitter.im/TheAlgorithms/community) __now!__
   - Happy coding!
 
 Writer [@poyea](https://github.com/poyea), Jun 2019.

Diff for: DIRECTORY.md

@@ -317,6 +317,7 @@
   * [Longest Sub Array](dynamic_programming/longest_sub_array.py)
   * [Matrix Chain Order](dynamic_programming/matrix_chain_order.py)
   * [Max Non Adjacent Sum](dynamic_programming/max_non_adjacent_sum.py)
+  * [Max Product Subarray](dynamic_programming/max_product_subarray.py)
   * [Max Sub Array](dynamic_programming/max_sub_array.py)
   * [Max Sum Contiguous Subsequence](dynamic_programming/max_sum_contiguous_subsequence.py)
   * [Min Distance Up Bottom](dynamic_programming/min_distance_up_bottom.py)
@@ -936,6 +937,8 @@
     * [Sol1](project_euler/problem_091/sol1.py)
   * Problem 092
     * [Sol1](project_euler/problem_092/sol1.py)
+  * Problem 094
+    * [Sol1](project_euler/problem_094/sol1.py)
   * Problem 097
     * [Sol1](project_euler/problem_097/sol1.py)
   * Problem 099
@@ -990,6 +993,8 @@
     * [Sol1](project_euler/problem_174/sol1.py)
   * Problem 180
     * [Sol1](project_euler/problem_180/sol1.py)
+  * Problem 187
+    * [Sol1](project_euler/problem_187/sol1.py)
   * Problem 188
     * [Sol1](project_euler/problem_188/sol1.py)
   * Problem 191
@@ -1014,6 +1019,8 @@
     * [Sol1](project_euler/problem_587/sol1.py)
   * Problem 686
     * [Sol1](project_euler/problem_686/sol1.py)
+  * Problem 800
+    * [Sol1](project_euler/problem_800/sol1.py)
 
 ## Quantum
   * [Bb84](quantum/bb84.py)

Diff for: README.md

@@ -16,7 +16,7 @@
   <a href="https://discord.gg/c7MnfGFGa6">
     <img src="https://img.shields.io/discord/808045925556682782.svg?logo=discord&colorB=7289DA&style=flat-square" height="20" alt="Discord chat">
   </a>
-  <a href="https://app.gitter.im/#/room/#TheAlgorithms_community:gitter.im">
+  <a href="https://gitter.im/TheAlgorithms/community">
     <img src="https://img.shields.io/badge/Chat-Gitter-ff69b4.svg?label=Chat&logo=gitter&style=flat-square" height="20" alt="Gitter chat">
   </a>
   <!-- Second row: -->
@@ -42,7 +42,7 @@ Read through our [Contribution Guidelines](CONTRIBUTING.md) before you contribut
 
 ## Community Channels
 
-We are on [Discord](https://discord.gg/c7MnfGFGa6) and [Gitter](https://app.gitter.im/#/room/#TheAlgorithms_community:gitter.im)! Community channels are a great way for you to ask questions and get help. Please join us!
+We are on [Discord](https://discord.gg/c7MnfGFGa6) and [Gitter](https://gitter.im/TheAlgorithms/community)! Community channels are a great way for you to ask questions and get help. Please join us!
 
 ## List of Algorithms
 

Diff for: arithmetic_analysis/lu_decomposition.py

@@ -1,62 +1,101 @@
-"""Lower-Upper (LU) Decomposition.
+"""
+Lower–upper (LU) decomposition factors a matrix as a product of a lower
+triangular matrix and an upper triangular matrix. A square matrix has an LU
+decomposition under the following conditions:
+    - If the matrix is invertible, then it has an LU decomposition if and only
+    if all of its leading principal minors are non-zero (see
+    https://en.wikipedia.org/wiki/Minor_(linear_algebra) for an explanation of
+    leading principal minors of a matrix).
+    - If the matrix is singular (i.e., not invertible) and it has a rank of k
+    (i.e., it has k linearly independent columns), then it has an LU
+    decomposition if its first k leading principal minors are non-zero.
+
+This algorithm will simply attempt to perform LU decomposition on any square
+matrix and raise an error if no such decomposition exists.
 
-Reference:
-- https://en.wikipedia.org/wiki/LU_decomposition
+Reference: https://en.wikipedia.org/wiki/LU_decomposition
 """
 from __future__ import annotations
 
 import numpy as np
-from numpy import float64
-from numpy.typing import ArrayLike
-
 
-def lower_upper_decomposition(
-    table: ArrayLike[float64],
-) -> tuple[ArrayLike[float64], ArrayLike[float64]]:
-    """Lower-Upper (LU) Decomposition
-
-    Example:
 
+def lower_upper_decomposition(table: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """
+    Perform LU decomposition on a given matrix and raises an error if the matrix
+    isn't square or if no such decomposition exists
     >>> matrix = np.array([[2, -2, 1], [0, 1, 2], [5, 3, 1]])
-    >>> outcome = lower_upper_decomposition(matrix)
-    >>> outcome[0]
+    >>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
+    >>> lower_mat
     array([[1. , 0. , 0. ],
            [0. , 1. , 0. ],
            [2.5, 8. , 1. ]])
-    >>> outcome[1]
+    >>> upper_mat
     array([[  2. ,  -2. ,   1. ],
            [  0. ,   1. ,   2. ],
            [  0. ,   0. , -17.5]])
 
+    >>> matrix = np.array([[4, 3], [6, 3]])
+    >>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
+    >>> lower_mat
+    array([[1. , 0. ],
+           [1.5, 1. ]])
+    >>> upper_mat
+    array([[ 4. ,  3. ],
+           [ 0. , -1.5]])
+
+    # Matrix is not square
     >>> matrix = np.array([[2, -2, 1], [0, 1, 2]])
-    >>> lower_upper_decomposition(matrix)
+    >>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
     Traceback (most recent call last):
         ...
     ValueError: 'table' has to be of square shaped array but got a 2x3 array:
     [[ 2 -2  1]
      [ 0  1  2]]
+
+    # Matrix is invertible, but its first leading principal minor is 0
+    >>> matrix = np.array([[0, 1], [1, 0]])
+    >>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
+    Traceback (most recent call last):
+    ...
+    ArithmeticError: No LU decomposition exists
+
+    # Matrix is singular, but its first leading principal minor is 1
+    >>> matrix = np.array([[1, 0], [1, 0]])
+    >>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
+    >>> lower_mat
+    array([[1., 0.],
+           [1., 1.]])
+    >>> upper_mat
+    array([[1., 0.],
+           [0., 0.]])
+
+    # Matrix is singular, but its first leading principal minor is 0
+    >>> matrix = np.array([[0, 1], [0, 1]])
+    >>> lower_mat, upper_mat = lower_upper_decomposition(matrix)
+    Traceback (most recent call last):
+    ...
+    ArithmeticError: No LU decomposition exists
     """
-    # Table that contains our data
-    # Table has to be a square array so we need to check first
+    # Ensure that table is a square array
     rows, columns = np.shape(table)
     if rows != columns:
         raise ValueError(
-            f"'table' has to be of square shaped array but got a {rows}x{columns} "
-            + f"array:\n{table}"
+            f"'table' has to be of square shaped array but got a "
+            f"{rows}x{columns} array:\n{table}"
         )
+
     lower = np.zeros((rows, columns))
     upper = np.zeros((rows, columns))
     for i in range(columns):
         for j in range(i):
-            total = 0
-            for k in range(j):
-                total += lower[i][k] * upper[k][j]
+            total = sum(lower[i][k] * upper[k][j] for k in range(j))
+            if upper[j][j] == 0:
+                raise ArithmeticError("No LU decomposition exists")
             lower[i][j] = (table[i][j] - total) / upper[j][j]
         lower[i][i] = 1
         for j in range(i, columns):
-            total = 0
-            for k in range(i):
-                total += lower[i][k] * upper[k][j]
+            total = sum(lower[i][k] * upper[k][j] for k in range(j))
             upper[i][j] = table[i][j] - total
     return lower, upper
 

Diff for: computer_vision/cnn_classification.py

@@ -93,7 +93,7 @@
     test_image = tf.keras.preprocessing.image.img_to_array(test_image)
     test_image = np.expand_dims(test_image, axis=0)
     result = classifier.predict(test_image)
-    training_set.class_indices
+    # training_set.class_indices
     if result[0][0] == 0:
         prediction = "Normal"
     if result[0][0] == 1:

Diff for: data_structures/linked_list/circular_linked_list.py

@@ -24,7 +24,7 @@ def __iter__(self) -> Iterator[Any]:
                 break
 
     def __len__(self) -> int:
-        return len(tuple(iter(self)))
+        return sum(1 for _ in self)
 
     def __repr__(self):
         return "->".join(str(item) for item in iter(self))

Diff for: data_structures/linked_list/doubly_linked_list.py

@@ -51,7 +51,7 @@ def __len__(self):
         >>> len(linked_list) == 5
         True
         """
-        return len(tuple(iter(self)))
+        return sum(1 for _ in self)
 
     def insert_at_head(self, data):
         self.insert_at_nth(0, data)
@@ -81,7 +81,9 @@ def insert_at_nth(self, index: int, data):
             ....
         IndexError: list index out of range
         """
-        if not 0 <= index <= len(self):
+        length = len(self)
+
+        if not 0 <= index <= length:
             raise IndexError("list index out of range")
         new_node = Node(data)
         if self.head is None:
@@ -90,7 +92,7 @@ def insert_at_nth(self, index: int, data):
             self.head.previous = new_node
             new_node.next = self.head
             self.head = new_node
-        elif index == len(self):
+        elif index == length:
             self.tail.next = new_node
             new_node.previous = self.tail
             self.tail = new_node
@@ -131,15 +133,17 @@ def delete_at_nth(self, index: int):
             ....
         IndexError: list index out of range
         """
-        if not 0 <= index <= len(self) - 1:
+        length = len(self)
+
+        if not 0 <= index <= length - 1:
             raise IndexError("list index out of range")
         delete_node = self.head  # default first node
-        if len(self) == 1:
+        if length == 1:
             self.head = self.tail = None
         elif index == 0:
             self.head = self.head.next
             self.head.previous = None
-        elif index == len(self) - 1:
+        elif index == length - 1:
             delete_node = self.tail
             self.tail = self.tail.previous
             self.tail.next = None

Diff for: data_structures/linked_list/merge_two_lists.py

@@ -44,7 +44,7 @@ def __len__(self) -> int:
         >>> len(SortedLinkedList(test_data_odd))
         8
         """
-        return len(tuple(iter(self)))
+        return sum(1 for _ in self)
 
     def __str__(self) -> str:
         """

Diff for: data_structures/linked_list/singly_linked_list.py

@@ -72,7 +72,7 @@ def __len__(self) -> int:
         >>> len(linked_list)
         0
         """
-        return len(tuple(iter(self)))
+        return sum(1 for _ in self)
 
     def __repr__(self) -> str:
         """