Merge branch 'TheAlgorithms:master' into master

Author: hash-ir

.github/workflows/build.yml

@@ -10,7 +10,7 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v4
-      - uses: astral-sh/setup-uv@v4
+      - uses: astral-sh/setup-uv@v5
         with:
           enable-cache: true
           cache-dependency-glob: uv.lock

.github/workflows/project_euler.yml

@@ -15,7 +15,7 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v4
-      - uses: astral-sh/setup-uv@v4
+      - uses: astral-sh/setup-uv@v5
       - uses: actions/setup-python@v5
         with:
           python-version: 3.x
@@ -25,7 +25,7 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v4
-      - uses: astral-sh/setup-uv@v4
+      - uses: astral-sh/setup-uv@v5
       - uses: actions/setup-python@v5
         with:
           python-version: 3.x

.github/workflows/ruff.yml

@@ -12,5 +12,5 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v4
-      - uses: astral-sh/setup-uv@v4
+      - uses: astral-sh/setup-uv@v5
       - run: uvx ruff check --output-format=github .

.github/workflows/sphinx.yml

@@ -23,10 +23,10 @@ concurrency:
 
 jobs:
   build_docs:
-    runs-on: ubuntu-latest
+    runs-on: ubuntu-24.04-arm
     steps:
       - uses: actions/checkout@v4
-      - uses: astral-sh/setup-uv@v4
+      - uses: astral-sh/setup-uv@v5
       - uses: actions/setup-python@v5
         with:
           python-version: 3.13

.pre-commit-config.yaml

@@ -16,13 +16,13 @@ repos:
       - id: auto-walrus
 
   - repo: https://github.com/astral-sh/ruff-pre-commit
-    rev: v0.8.1
+    rev: v0.9.6
     hooks:
       - id: ruff
       - id: ruff-format
 
   - repo: https://github.com/codespell-project/codespell
-    rev: v2.3.0
+    rev: v2.4.1
     hooks:
       - id: codespell
         additional_dependencies:
@@ -47,7 +47,7 @@ repos:
       - id: validate-pyproject
 
   - repo: https://github.com/pre-commit/mirrors-mypy
-    rev: v1.13.0
+    rev: v1.15.0
     hooks:
       - id: mypy
         args:

DIRECTORY.md

@@ -86,7 +86,7 @@
   * [Baconian Cipher](ciphers/baconian_cipher.py)
   * [Base16](ciphers/base16.py)
   * [Base32](ciphers/base32.py)
-  * [Base64](ciphers/base64.py)
+  * [Base64 Cipher](ciphers/base64_cipher.py)
   * [Base85](ciphers/base85.py)
   * [Beaufort Cipher](ciphers/beaufort_cipher.py)
   * [Bifid](ciphers/bifid.py)
@@ -142,6 +142,7 @@
   * [Haralick Descriptors](computer_vision/haralick_descriptors.py)
   * [Harris Corner](computer_vision/harris_corner.py)
   * [Horn Schunck](computer_vision/horn_schunck.py)
+  * [Intensity Based Segmentation](computer_vision/intensity_based_segmentation.py)
   * [Mean Threshold](computer_vision/mean_threshold.py)
   * [Mosaic Augmentation](computer_vision/mosaic_augmentation.py)
   * [Pooling Functions](computer_vision/pooling_functions.py)
@@ -169,6 +170,7 @@
   * [Prefix Conversions](conversions/prefix_conversions.py)
   * [Prefix Conversions String](conversions/prefix_conversions_string.py)
   * [Pressure Conversions](conversions/pressure_conversions.py)
+  * [Rectangular To Polar](conversions/rectangular_to_polar.py)
   * [Rgb Cmyk Conversion](conversions/rgb_cmyk_conversion.py)
   * [Rgb Hsv Conversion](conversions/rgb_hsv_conversion.py)
   * [Roman Numerals](conversions/roman_numerals.py)
@@ -273,15 +275,15 @@
     * [Singly Linked List](data_structures/linked_list/singly_linked_list.py)
     * [Skip List](data_structures/linked_list/skip_list.py)
     * [Swap Nodes](data_structures/linked_list/swap_nodes.py)
-  * Queue
-    * [Circular Queue](data_structures/queue/circular_queue.py)
-    * [Circular Queue Linked List](data_structures/queue/circular_queue_linked_list.py)
-    * [Double Ended Queue](data_structures/queue/double_ended_queue.py)
-    * [Linked Queue](data_structures/queue/linked_queue.py)
-    * [Priority Queue Using List](data_structures/queue/priority_queue_using_list.py)
-    * [Queue By List](data_structures/queue/queue_by_list.py)
-    * [Queue By Two Stacks](data_structures/queue/queue_by_two_stacks.py)
-    * [Queue On Pseudo Stack](data_structures/queue/queue_on_pseudo_stack.py)
+  * Queues
+    * [Circular Queue](data_structures/queues/circular_queue.py)
+    * [Circular Queue Linked List](data_structures/queues/circular_queue_linked_list.py)
+    * [Double Ended Queue](data_structures/queues/double_ended_queue.py)
+    * [Linked Queue](data_structures/queues/linked_queue.py)
+    * [Priority Queue Using List](data_structures/queues/priority_queue_using_list.py)
+    * [Queue By List](data_structures/queues/queue_by_list.py)
+    * [Queue By Two Stacks](data_structures/queues/queue_by_two_stacks.py)
+    * [Queue On Pseudo Stack](data_structures/queues/queue_on_pseudo_stack.py)
   * Stacks
     * [Balanced Parentheses](data_structures/stacks/balanced_parentheses.py)
     * [Dijkstras Two Stack Algorithm](data_structures/stacks/dijkstras_two_stack_algorithm.py)
@@ -375,6 +377,7 @@
   * [Longest Common Subsequence](dynamic_programming/longest_common_subsequence.py)
   * [Longest Common Substring](dynamic_programming/longest_common_substring.py)
   * [Longest Increasing Subsequence](dynamic_programming/longest_increasing_subsequence.py)
+  * [Longest Increasing Subsequence Iterative](dynamic_programming/longest_increasing_subsequence_iterative.py)
   * [Longest Increasing Subsequence O Nlogn](dynamic_programming/longest_increasing_subsequence_o_nlogn.py)
   * [Longest Palindromic Subsequence](dynamic_programming/longest_palindromic_subsequence.py)
   * [Matrix Chain Multiplication](dynamic_programming/matrix_chain_multiplication.py)
@@ -460,6 +463,8 @@
 
 ## Graphics
   * [Bezier Curve](graphics/bezier_curve.py)
+  * [Butterfly Pattern](graphics/butterfly_pattern.py)
+  * [Digital Differential Analyzer Line](graphics/digital_differential_analyzer_line.py)
   * [Vector3 For 2D Rendering](graphics/vector3_for_2d_rendering.py)
 
 ## Graphs
@@ -506,6 +511,7 @@
   * [Kahns Algorithm Long](graphs/kahns_algorithm_long.py)
   * [Kahns Algorithm Topo](graphs/kahns_algorithm_topo.py)
   * [Karger](graphs/karger.py)
+  * [Lanczos Eigenvectors](graphs/lanczos_eigenvectors.py)
   * [Markov Chain](graphs/markov_chain.py)
   * [Matching Min Vertex Cover](graphs/matching_min_vertex_cover.py)
   * [Minimum Path Sum](graphs/minimum_path_sum.py)
@@ -660,6 +666,7 @@
   * [Gamma](maths/gamma.py)
   * [Gaussian](maths/gaussian.py)
   * [Gcd Of N Numbers](maths/gcd_of_n_numbers.py)
+  * [Geometric Mean](maths/geometric_mean.py)
   * [Germain Primes](maths/germain_primes.py)
   * [Greatest Common Divisor](maths/greatest_common_divisor.py)
   * [Hardy Ramanujanalgo](maths/hardy_ramanujanalgo.py)
@@ -885,6 +892,7 @@
   * [N Body Simulation](physics/n_body_simulation.py)
   * [Newtons Law Of Gravitation](physics/newtons_law_of_gravitation.py)
   * [Newtons Second Law Of Motion](physics/newtons_second_law_of_motion.py)
+  * [Period Of Pendulum](physics/period_of_pendulum.py)
   * [Photoelectric Effect](physics/photoelectric_effect.py)
   * [Potential Energy](physics/potential_energy.py)
   * [Rainfall Intensity](physics/rainfall_intensity.py)
@@ -1325,7 +1333,7 @@
   * [Title](strings/title.py)
   * [Top K Frequent Words](strings/top_k_frequent_words.py)
   * [Upper](strings/upper.py)
-  * [Wave](strings/wave.py)
+  * [Wave String](strings/wave_string.py)
   * [Wildcard Pattern Matching](strings/wildcard_pattern_matching.py)
   * [Word Occurrence](strings/word_occurrence.py)
   * [Word Patterns](strings/word_patterns.py)

audio_filters/iir_filter.py

@@ -10,13 +10,17 @@ class IIRFilter:
 
     Implementation details:
     Based on the 2nd-order function from
-     https://en.wikipedia.org/wiki/Digital_biquad_filter,
+    https://en.wikipedia.org/wiki/Digital_biquad_filter,
     this generalized N-order function was made.
 
     Using the following transfer function
-    H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+...+b_{k}z^{-k}}{a_{0}+a_{1}z^{-1}+a_{2}z^{-2}+...+a_{k}z^{-k}}
+        .. math:: H(z)=\frac{b_{0}+b_{1}z^{-1}+b_{2}z^{-2}+...+b_{k}z^{-k}}
+                  {a_{0}+a_{1}z^{-1}+a_{2}z^{-2}+...+a_{k}z^{-k}}
+
     we can rewrite this to
-    y[n]={\frac{1}{a_{0}}}\left(\left(b_{0}x[n]+b_{1}x[n-1]+b_{2}x[n-2]+...+b_{k}x[n-k]\right)-\left(a_{1}y[n-1]+a_{2}y[n-2]+...+a_{k}y[n-k]\right)\right)
+        .. math:: y[n]={\frac{1}{a_{0}}}
+                  \left(\left(b_{0}x[n]+b_{1}x[n-1]+b_{2}x[n-2]+...+b_{k}x[n-k]\right)-
+                  \left(a_{1}y[n-1]+a_{2}y[n-2]+...+a_{k}y[n-k]\right)\right)
     """
 
     def __init__(self, order: int) -> None:
@@ -34,17 +38,19 @@ def __init__(self, order: int) -> None:
 
     def set_coefficients(self, a_coeffs: list[float], b_coeffs: list[float]) -> None:
         """
-        Set the coefficients for the IIR filter. These should both be of size order + 1.
-        a_0 may be left out, and it will use 1.0 as default value.
+        Set the coefficients for the IIR filter.
+        These should both be of size `order` + 1.
+        :math:`a_0` may be left out, and it will use 1.0 as default value.
 
         This method works well with scipy's filter design functions
-            >>> # Make a 2nd-order 1000Hz butterworth lowpass filter
-            >>> import scipy.signal
-            >>> b_coeffs, a_coeffs = scipy.signal.butter(2, 1000,
-            ...                                          btype='lowpass',
-            ...                                          fs=48000)
-            >>> filt = IIRFilter(2)
-            >>> filt.set_coefficients(a_coeffs, b_coeffs)
+
+        >>> # Make a 2nd-order 1000Hz butterworth lowpass filter
+        >>> import scipy.signal
+        >>> b_coeffs, a_coeffs = scipy.signal.butter(2, 1000,
+        ...                                          btype='lowpass',
+        ...                                          fs=48000)
+        >>> filt = IIRFilter(2)
+        >>> filt.set_coefficients(a_coeffs, b_coeffs)
         """
         if len(a_coeffs) < self.order:
             a_coeffs = [1.0, *a_coeffs]
@@ -68,7 +74,7 @@ def set_coefficients(self, a_coeffs: list[float], b_coeffs: list[float]) -> None
 
     def process(self, sample: float) -> float:
         """
-        Calculate y[n]
+        Calculate :math:`y[n]`
 
         >>> filt = IIRFilter(2)
         >>> filt.process(0)

backtracking/all_combinations.py

@@ -12,6 +12,8 @@
 
 def combination_lists(n: int, k: int) -> list[list[int]]:
     """
+    Generates all possible combinations of k numbers out of 1 ... n using itertools.
+
     >>> combination_lists(n=4, k=2)
     [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
     """
@@ -20,6 +22,8 @@ def combination_lists(n: int, k: int) -> list[list[int]]:
 
 def generate_all_combinations(n: int, k: int) -> list[list[int]]:
     """
+    Generates all possible combinations of k numbers out of 1 ... n using backtracking.
+
     >>> generate_all_combinations(n=4, k=2)
     [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
     >>> generate_all_combinations(n=0, k=0)
@@ -34,6 +38,14 @@ def generate_all_combinations(n: int, k: int) -> list[list[int]]:
     ValueError: n must not be negative
     >>> generate_all_combinations(n=5, k=4)
     [[1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 4, 5], [1, 3, 4, 5], [2, 3, 4, 5]]
+    >>> generate_all_combinations(n=3, k=3)
+    [[1, 2, 3]]
+    >>> generate_all_combinations(n=3, k=1)
+    [[1], [2], [3]]
+    >>> generate_all_combinations(n=1, k=0)
+    [[]]
+    >>> generate_all_combinations(n=1, k=1)
+    [[1]]
     >>> from itertools import combinations
     >>> all(generate_all_combinations(n, k) == combination_lists(n, k)
     ...     for n in range(1, 6) for k in range(1, 6))
@@ -56,6 +68,28 @@ def create_all_state(
     current_list: list[int],
     total_list: list[list[int]],
 ) -> None:
+    """
+    Helper function to recursively build all combinations.
+
+    >>> create_all_state(1, 4, 2, [], result := [])
+    >>> result
+    [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
+    >>> create_all_state(1, 3, 3, [], result := [])
+    >>> result
+    [[1, 2, 3]]
+    >>> create_all_state(2, 2, 1, [1], result := [])
+    >>> result
+    [[1, 2]]
+    >>> create_all_state(1, 0, 0, [], result := [])
+    >>> result
+    [[]]
+    >>> create_all_state(1, 4, 0, [1, 2], result := [])
+    >>> result
+    [[1, 2]]
+    >>> create_all_state(5, 4, 2, [1, 2], result := [])
+    >>> result
+    []
+    """
     if level == 0:
         total_list.append(current_list[:])
         return