update fork

DIRECTORY.md

@@ -29,7 +29,11 @@
   * [Binary Count Setbits](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/binary_count_setbits.py)
   * [Binary Count Trailing Zeros](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/binary_count_trailing_zeros.py)
   * [Binary Or Operator](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/binary_or_operator.py)
+  * [Binary Shifts](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/binary_shifts.py)
+  * [Binary Twos Complement](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/binary_twos_complement.py)
   * [Binary Xor Operator](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/binary_xor_operator.py)
+  * [Count Number Of One Bits](https://github.com/TheAlgorithms/Python/blob/master/bit_manipulation/count_number_of_one_bits.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)
 
 ## Blockchain
@@ -122,6 +126,7 @@
     * [Fenwick Tree](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/fenwick_tree.py)
     * [Lazy Segment Tree](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/lazy_segment_tree.py)
     * [Lowest Common Ancestor](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/lowest_common_ancestor.py)
+    * [Merge Two Binary Trees](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/merge_two_binary_trees.py)
     * [Non Recursive Segment Tree](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/non_recursive_segment_tree.py)
     * [Number Of Possible Binary Trees](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/number_of_possible_binary_trees.py)
     * [Red Black Tree](https://github.com/TheAlgorithms/Python/blob/master/data_structures/binary_tree/red_black_tree.py)
@@ -274,6 +279,8 @@
 
 ## Graphics
   * [Bezier Curve](https://github.com/TheAlgorithms/Python/blob/master/graphics/bezier_curve.py)
+  * [Koch Snowflake](https://github.com/TheAlgorithms/Python/blob/master/graphics/koch_snowflake.py)
+  * [Mandelbrot](https://github.com/TheAlgorithms/Python/blob/master/graphics/mandelbrot.py)
   * [Vector3 For 2D Rendering](https://github.com/TheAlgorithms/Python/blob/master/graphics/vector3_for_2d_rendering.py)
 
 ## Graphs
@@ -465,6 +472,7 @@
   * [Runge Kutta](https://github.com/TheAlgorithms/Python/blob/master/maths/runge_kutta.py)
   * [Segmented Sieve](https://github.com/TheAlgorithms/Python/blob/master/maths/segmented_sieve.py)
   * Series
+    * [Geometric Mean](https://github.com/TheAlgorithms/Python/blob/master/maths/series/geometric_mean.py)
     * [Geometric Series](https://github.com/TheAlgorithms/Python/blob/master/maths/series/geometric_series.py)
     * [Harmonic Series](https://github.com/TheAlgorithms/Python/blob/master/maths/series/harmonic_series.py)
     * [P Series](https://github.com/TheAlgorithms/Python/blob/master/maths/series/p_series.py)
@@ -520,6 +528,7 @@
   * [Frequency Finder](https://github.com/TheAlgorithms/Python/blob/master/other/frequency_finder.py)
   * [Game Of Life](https://github.com/TheAlgorithms/Python/blob/master/other/game_of_life.py)
   * [Gauss Easter](https://github.com/TheAlgorithms/Python/blob/master/other/gauss_easter.py)
+  * [Graham Scan](https://github.com/TheAlgorithms/Python/blob/master/other/graham_scan.py)
   * [Greedy](https://github.com/TheAlgorithms/Python/blob/master/other/greedy.py)
   * [Integeration By Simpson Approx](https://github.com/TheAlgorithms/Python/blob/master/other/integeration_by_simpson_approx.py)
   * [Largest Subarray Sum](https://github.com/TheAlgorithms/Python/blob/master/other/largest_subarray_sum.py)
@@ -752,6 +761,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_102/sol1.py)
   * Problem 107
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_107/sol1.py)
+  * Problem 109
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_109/sol1.py)
   * Problem 112
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_112/sol1.py)
   * Problem 113
@@ -840,6 +851,7 @@
   * [Merge Insertion Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/merge_insertion_sort.py)
   * [Merge Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/merge_sort.py)
   * [Natural Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/natural_sort.py)
+  * [Odd Even Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/odd_even_sort.py)
   * [Odd Even Transposition Parallel](https://github.com/TheAlgorithms/Python/blob/master/sorts/odd_even_transposition_parallel.py)
   * [Odd Even Transposition Single Threaded](https://github.com/TheAlgorithms/Python/blob/master/sorts/odd_even_transposition_single_threaded.py)
   * [Pancake Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/pancake_sort.py)
@@ -856,6 +868,7 @@
   * [Recursive Quick Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/recursive_quick_sort.py)
   * [Selection Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/selection_sort.py)
   * [Shell Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/shell_sort.py)
+  * [Slowsort](https://github.com/TheAlgorithms/Python/blob/master/sorts/slowsort.py)
   * [Stooge Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/stooge_sort.py)
   * [Strand Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/strand_sort.py)
   * [Tim Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/tim_sort.py)

maths/series/arithmetic_mean.py

@@ -0,0 +1,66 @@
+"""
+ARITHMETIC MEAN : https://en.wikipedia.org/wiki/Arithmetic_mean
+
+"""
+
+
+def is_arithmetic_series(series: list) -> bool:
+    """
+    checking whether the input series is arithmetic series or not
+
+    >>> is_arithmetic_series([2, 4, 6])
+    True
+    >>> is_arithmetic_series([3, 6, 12, 24])
+    False
+    >>> is_arithmetic_series([1, 2, 3])
+    True
+    """
+    if len(series) == 1:
+        return True
+    common_diff = series[1] - series[0]
+    for index in range(len(series) - 1):
+        if series[index + 1] - series[index] != common_diff:
+            return False
+    return True
+
+
+def arithmetic_mean(series: list) -> float:
+    """
+    return the arithmetic mean of series
+
+    >>> arithmetic_mean([2, 4, 6])
+    4.0
+    >>> arithmetic_mean([3, 6, 9, 12])
+    7.5
+    >>> arithmetic_mean(4)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input series is not valid, valid series - [2, 4, 6]
+    >>> arithmetic_mean([4, 8, 1])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input list is not an arithmetic series
+    >>> arithmetic_mean([1, 2, 3])
+    2.0
+    >>> arithmetic_mean([])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input list must be a non empty list
+
+    """
+    if not isinstance(series, list):
+        raise ValueError("Input series is not valid, valid series - [2, 4, 6]")
+    if len(series) == 0:
+        raise ValueError("Input list must be a non empty list")
+    if not is_arithmetic_series(series):
+        raise ValueError("Input list is not an arithmetic series")
+    answer = 0
+    for val in series:
+        answer += val
+    return answer / len(series)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

maths/series/geometric_mean.py

@@ -0,0 +1,75 @@
+"""
+GEOMETRIC MEAN :  https://en.wikipedia.org/wiki/Geometric_mean
+"""
+
+
+def is_geometric_series(series: list) -> bool:
+    """
+    checking whether the input series is geometric series or not
+
+    >>> is_geometric_series([2, 4, 8])
+    True
+    >>> is_geometric_series([3, 6, 12, 24])
+    True
+    >>> is_geometric_series([1, 2, 3])
+    False
+    >>> is_geometric_series([0, 0, 3])
+    False
+
+    """
+    if len(series) == 1:
+        return True
+    try:
+        common_ratio = series[1] / series[0]
+        for index in range(len(series) - 1):
+            if series[index + 1] / series[index] != common_ratio:
+                return False
+    except ZeroDivisionError:
+        return False
+    return True
+
+
+def geometric_mean(series: list) -> float:
+    """
+    return the geometric mean of series
+
+    >>> geometric_mean([2, 4, 8])
+    3.9999999999999996
+    >>> geometric_mean([3, 6, 12, 24])
+    8.48528137423857
+    >>> geometric_mean([4, 8, 16])
+    7.999999999999999
+    >>> geometric_mean(4)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input series is not valid, valid series - [2, 4, 8]
+    >>> geometric_mean([1, 2, 3])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input list is not a geometric series
+    >>> geometric_mean([0, 2, 3])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input list is not a geometric series
+    >>> geometric_mean([])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input list must be a non empty list
+
+    """
+    if not isinstance(series, list):
+        raise ValueError("Input series is not valid, valid series - [2, 4, 8]")
+    if len(series) == 0:
+        raise ValueError("Input list must be a non empty list")
+    if not is_geometric_series(series):
+        raise ValueError("Input list is not a geometric series")
+    answer = 1
+    for value in series:
+        answer *= value
+    return pow(answer, 1 / len(series))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

other/graham_scan.py

@@ -0,0 +1,171 @@
+"""
+This is a pure Python implementation of the merge-insertion sort algorithm
+Source: https://en.wikipedia.org/wiki/Graham_scan
+
+For doctests run following command:
+python3 -m doctest -v graham_scan.py
+"""
+
+from __future__ import annotations
+
+from collections import deque
+from enum import Enum
+from math import atan2, degrees
+from sys import maxsize
+
+
+def graham_scan(points: list[list[int, int]]) -> list[list[int, int]]:
+    """Pure implementation of graham scan algorithm in Python
+
+    :param points: The unique points on coordinates.
+    :return: The points on convex hell.
+
+    Examples:
+    >>> graham_scan([(9, 6), (3, 1), (0, 0), (5, 5), (5, 2), (7, 0), (3, 3), (1, 4)])
+    [(0, 0), (7, 0), (9, 6), (5, 5), (1, 4)]
+
+    >>> graham_scan([(0, 0), (1, 0), (1, 1), (0, 1)])
+    [(0, 0), (1, 0), (1, 1), (0, 1)]
+
+    >>> graham_scan([(0, 0), (1, 1), (2, 2), (3, 3), (-1, 2)])
+    [(0, 0), (1, 1), (2, 2), (3, 3), (-1, 2)]
+
+    >>> graham_scan([(-100, 20), (99, 3), (1, 10000001), (5133186, -25), (-66, -4)])
+    [(5133186, -25), (1, 10000001), (-100, 20), (-66, -4)]
+    """
+
+    if len(points) <= 2:
+        # There is no convex hull
+        raise ValueError("graham_scan: argument must contain more than 3 points.")
+    if len(points) == 3:
+        return points
+    # find the lowest and the most left point
+    minidx = 0
+    miny, minx = maxsize, maxsize
+    for i, point in enumerate(points):
+        x = point[0]
+        y = point[1]
+        if y < miny:
+            miny = y
+            minx = x
+            minidx = i
+        if y == miny:
+            if x < minx:
+                minx = x
+                minidx = i
+
+    # remove the lowest and the most left point from points for preparing for sort
+    points.pop(minidx)
+
+    def angle_comparer(point: list[int, int], minx: int, miny: int) -> float:
+        """Return the angle toward to point from (minx, miny)
+
+        :param point: The target point
+               minx: The starting point's x
+               miny: The starting point's y
+        :return: the angle
+
+        Examples:
+        >>> angle_comparer([1,1], 0, 0)
+        45.0
+
+        >>> angle_comparer([100,1], 10, 10)
+        -5.710593137499642
+
+        >>> angle_comparer([5,5], 2, 3)
+        33.690067525979785
+        """
+        # sort the points accorgind to the angle from the lowest and the most left point
+        x = point[0]
+        y = point[1]
+        angle = degrees(atan2(y - miny, x - minx))
+        return angle
+
+    sorted_points = sorted(points, key=lambda point: angle_comparer(point, minx, miny))
+    # This insert actually costs complexity,
+    # and you should insteadly add (minx, miny) into stack later.
+    # I'm using insert just for easy understanding.
+    sorted_points.insert(0, (minx, miny))
+
+    # traversal from the lowest and the most left point in anti-clockwise direction
+    # if direction gets right, the previous point is not the convex hull.
+    class Direction(Enum):
+        left = 1
+        straight = 2
+        right = 3
+
+    def check_direction(
+        starting: list[int, int], via: list[int, int], target: list[int, int]
+    ) -> Direction:
+        """Return the direction toward to the line from via to target from starting
+
+        :param starting: The starting point
+               via: The via point
+               target: The target point
+        :return: the Direction
+
+        Examples:
+        >>> check_direction([1,1], [2,2], [3,3])
+        Direction.straight
+
+        >>> check_direction([60,1], [-50,199], [30,2])
+        Direction.left
+
+        >>> check_direction([0,0], [5,5], [10,0])
+        Direction.right
+        """
+        x0, y0 = starting
+        x1, y1 = via
+        x2, y2 = target
+        via_angle = degrees(atan2(y1 - y0, x1 - x0))
+        if via_angle < 0:
+            via_angle += 360
+        target_angle = degrees(atan2(y2 - y0, x2 - x0))
+        if target_angle < 0:
+            target_angle += 360
+        # t-
+        #  \ \
+        #   \ v
+        #    \|
+        #     s
+        # via_angle is always lower than target_angle, if direction is left.
+        # If they are same, it means they are on a same line of convex hull.
+        if target_angle > via_angle:
+            return Direction.left
+        if target_angle == via_angle:
+            return Direction.straight
+        if target_angle < via_angle:
+            return Direction.right
+
+    stack = deque()
+    stack.append(sorted_points[0])
+    stack.append(sorted_points[1])
+    stack.append(sorted_points[2])
+    # In any ways, the first 3 points line are towards left.
+    # Because we sort them the angle from minx, miny.
+    current_direction = Direction.left
+
+    for i in range(3, len(sorted_points)):
+        while True:
+            starting = stack[-2]
+            via = stack[-1]
+            target = sorted_points[i]
+            next_direction = check_direction(starting, via, target)
+
+            if next_direction == Direction.left:
+                current_direction = Direction.left
+                break
+            if next_direction == Direction.straight:
+                if current_direction == Direction.left:
+                    # We keep current_direction as left.
+                    # Because if the straight line keeps as straight,
+                    # we want to know if this straight line is towards left.
+                    break
+                elif current_direction == Direction.right:
+                    # If the straight line is towards right,
+                    # every previous points on those straigh line is not convex hull.
+                    stack.pop()
+            if next_direction == Direction.right:
+                stack.pop()
+        stack.append(sorted_points[i])
+    return list(stack)