Merge branch 'TheAlgorithms:master' into master

Author: Ramy-Badr-Ahmed

.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

@@ -26,7 +26,7 @@ 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: 3.13

.pre-commit-config.yaml

@@ -16,7 +16,7 @@ repos:
       - id: auto-walrus
 
   - repo: https://github.com/astral-sh/ruff-pre-commit
-    rev: v0.8.2
+    rev: v0.8.6
     hooks:
       - id: ruff
       - id: ruff-format
@@ -47,7 +47,7 @@ repos:
       - id: validate-pyproject
 
   - repo: https://github.com/pre-commit/mirrors-mypy
-    rev: v1.13.0
+    rev: v1.14.1
     hooks:
       - id: mypy
         args:

DIRECTORY.md

@@ -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)
@@ -460,6 +462,7 @@
 
 ## Graphics
   * [Bezier Curve](graphics/bezier_curve.py)
+  * [Digital Differential Analyzer Line](graphics/digital_differential_analyzer_line.py)
   * [Vector3 For 2D Rendering](graphics/vector3_for_2d_rendering.py)
 
 ## Graphs
@@ -506,6 +509,7 @@
   * [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 +664,7 @@
   * [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 +890,7 @@
   * [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)

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)

cellular_automata/wa_tor.py

@@ -1,9 +1,9 @@
 """
 Wa-Tor algorithm (1984)
 
-@ https://en.wikipedia.org/wiki/Wa-Tor
-@ https://beltoforion.de/en/wator/
-@ https://beltoforion.de/en/wator/images/wator_medium.webm
+| @ https://en.wikipedia.org/wiki/Wa-Tor
+| @ https://beltoforion.de/en/wator/
+| @ https://beltoforion.de/en/wator/images/wator_medium.webm
 
 This solution aims to completely remove any systematic approach
 to the Wa-Tor planet, and utilise fully random methods.
@@ -97,8 +97,8 @@ class WaTor:
 
     :attr time_passed: A function that is called every time
         time passes (a chronon) in order to visually display
-        the new Wa-Tor planet. The time_passed function can block
-        using time.sleep to slow the algorithm progression.
+        the new Wa-Tor planet. The `time_passed` function can block
+        using ``time.sleep`` to slow the algorithm progression.
 
     >>> wt = WaTor(10, 15)
     >>> wt.width
@@ -216,7 +216,7 @@ def get_surrounding_prey(self, entity: Entity) -> list[Entity]:
         """
         Returns all the prey entities around (N, S, E, W) a predator entity.
 
-        Subtly different to the try_to_move_to_unoccupied square.
+        Subtly different to the `move_and_reproduce`.
 
         >>> wt = WaTor(WIDTH, HEIGHT)
         >>> wt.set_planet([
@@ -260,7 +260,7 @@ def move_and_reproduce(
         """
         Attempts to move to an unoccupied neighbouring square
         in either of the four directions (North, South, East, West).
-        If the move was successful and the remaining_reproduction time is
+        If the move was successful and the `remaining_reproduction_time` is
         equal to 0, then a new prey or predator can also be created
         in the previous square.
 
@@ -351,12 +351,12 @@ def perform_prey_actions(
         Performs the actions for a prey entity
 
         For prey the rules are:
-          1. At each chronon, a prey moves randomly to one of the adjacent unoccupied
-            squares. If there are no free squares, no movement takes place.
-          2. Once a prey has survived a certain number of chronons it may reproduce.
-            This is done as it moves to a neighbouring square,
-            leaving behind a new prey in its old position.
-            Its reproduction time is also reset to zero.
+            1. At each chronon, a prey moves randomly to one of the adjacent unoccupied
+               squares. If there are no free squares, no movement takes place.
+            2. Once a prey has survived a certain number of chronons it may reproduce.
+               This is done as it moves to a neighbouring square,
+               leaving behind a new prey in its old position.
+               Its reproduction time is also reset to zero.
 
         >>> wt = WaTor(WIDTH, HEIGHT)
         >>> reproducable_entity = Entity(True, coords=(0, 1))
@@ -382,15 +382,15 @@ def perform_predator_actions(
         :param occupied_by_prey_coords: Move to this location if there is prey there
 
         For predators the rules are:
-          1. At each chronon, a predator moves randomly to an adjacent square occupied
-            by a prey. If there is none, the predator moves to a random adjacent
-            unoccupied square. If there are no free squares, no movement takes place.
-          2. At each chronon, each predator is deprived of a unit of energy.
-          3. Upon reaching zero energy, a predator dies.
-          4. If a predator moves to a square occupied by a prey,
-            it eats the prey and earns a certain amount of energy.
-          5. Once a predator has survived a certain number of chronons
-          it may reproduce in exactly the same way as the prey.
+            1. At each chronon, a predator moves randomly to an adjacent square occupied
+               by a prey. If there is none, the predator moves to a random adjacent
+               unoccupied square. If there are no free squares, no movement takes place.
+            2. At each chronon, each predator is deprived of a unit of energy.
+            3. Upon reaching zero energy, a predator dies.
+            4. If a predator moves to a square occupied by a prey,
+               it eats the prey and earns a certain amount of energy.
+            5. Once a predator has survived a certain number of chronons
+               it may reproduce in exactly the same way as the prey.
 
         >>> wt = WaTor(WIDTH, HEIGHT)
         >>> wt.set_planet([[Entity(True, coords=(0, 0)), Entity(False, coords=(0, 1))]])
@@ -430,7 +430,7 @@ def perform_predator_actions(
 
     def run(self, *, iteration_count: int) -> None:
         """
-        Emulate time passing by looping iteration_count times
+        Emulate time passing by looping `iteration_count` times
 
         >>> wt = WaTor(WIDTH, HEIGHT)
         >>> wt.run(iteration_count=PREDATOR_INITIAL_ENERGY_VALUE - 1)
@@ -484,11 +484,9 @@ def visualise(wt: WaTor, iter_number: int, *, colour: bool = True) -> None:
     an ascii code in terminal to clear and re-print
     the Wa-Tor planet at intervals.
 
-    Uses ascii colour codes to colourfully display
-    the predators and prey.
-
-    (0x60f197) Prey = #
-    (0xfffff) Predator = x
+    Uses ascii colour codes to colourfully display the predators and prey:
+        * (0x60f197) Prey = ``#``
+        * (0xfffff) Predator = ``x``
 
     >>> wt = WaTor(30, 30)
     >>> wt.set_planet([

ciphers/autokey.py

@@ -1,5 +1,6 @@
 """
 https://en.wikipedia.org/wiki/Autokey_cipher
+
 An autokey cipher (also known as the autoclave cipher) is a cipher that
 incorporates the message (the plaintext) into the key.
 The key is generated from the message in some automated fashion,
@@ -10,8 +11,9 @@
 
 def encrypt(plaintext: str, key: str) -> str:
     """
-    Encrypt a given plaintext (string) and key (string), returning the
+    Encrypt a given `plaintext` (string) and `key` (string), returning the
     encrypted ciphertext.
+
     >>> encrypt("hello world", "coffee")
     'jsqqs avvwo'
     >>> encrypt("coffee is good as python", "TheAlgorithms")
@@ -74,8 +76,9 @@ def encrypt(plaintext: str, key: str) -> str:
 
 def decrypt(ciphertext: str, key: str) -> str:
     """
-    Decrypt a given ciphertext (string) and key (string), returning the decrypted
+    Decrypt a given `ciphertext` (string) and `key` (string), returning the decrypted
     ciphertext.
+
     >>> decrypt("jsqqs avvwo", "coffee")
     'hello world'
     >>> decrypt("vvjfpk wj ohvp su ddylsv", "TheAlgorithms")