feat: Concatenate algorithm implementations

Author: CaedenPH

maths/find_max.py

@@ -25,6 +25,57 @@ def find_max(nums: list[int | float]) -> int | float:
     return max_num
 
 
+# Divide and Conquer algorithm
+def find_max_recursive(nums: list[int | float], left: int, right: int) -> int | float:
+    """
+    find max value in list
+    :param nums: contains elements
+    :param left: index of first element
+    :param right: index of last element
+    :return: max in nums
+
+    >>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
+    ...     find_max(nums, 0, len(nums) - 1) == max(nums)
+    True
+    True
+    True
+    True
+    >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    >>> find_max(nums, 0, len(nums) - 1) == max(nums)
+    True
+    >>> find_max([], 0, 0)
+    Traceback (most recent call last):
+        ...
+    ValueError: find_max() arg is an empty sequence
+    >>> find_max(nums, 0, len(nums)) == max(nums)
+    Traceback (most recent call last):
+        ...
+    IndexError: list index out of range
+    >>> find_max(nums, -len(nums), -1) == max(nums)
+    True
+    >>> find_max(nums, -len(nums) - 1, -1) == max(nums)
+    Traceback (most recent call last):
+        ...
+    IndexError: list index out of range
+    """
+    if len(nums) == 0:
+        raise ValueError("find_max() arg is an empty sequence")
+    if (
+        left >= len(nums)
+        or left < -len(nums)
+        or right >= len(nums)
+        or right < -len(nums)
+    ):
+        raise IndexError("list index out of range")
+    if left == right:
+        return nums[left]
+    mid = (left + right) >> 1  # the middle
+    left_max = find_max(nums, left, mid)  # find max in range[left, mid]
+    right_max = find_max(nums, mid + 1, right)  # find max in range[mid + 1, right]
+
+    return left_max if left_max >= right_max else right_max
+
+
 if __name__ == "__main__":
     import doctest
 

maths/find_max_recursion.py

@@ -28,6 +28,57 @@ def find_min(nums: list[int | float]) -> int | float:
     return min_num
 
 
+# Divide and Conquer algorithm
+def find_min(nums: list[int | float], left: int, right: int) -> int | float:
+    """
+    find min value in list
+    :param nums: contains elements
+    :param left: index of first element
+    :param right: index of last element
+    :return: min in nums
+
+    >>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
+    ...     find_min(nums, 0, len(nums) - 1) == min(nums)
+    True
+    True
+    True
+    True
+    >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    >>> find_min(nums, 0, len(nums) - 1) == min(nums)
+    True
+    >>> find_min([], 0, 0)
+    Traceback (most recent call last):
+        ...
+    ValueError: find_min() arg is an empty sequence
+    >>> find_min(nums, 0, len(nums)) == min(nums)
+    Traceback (most recent call last):
+        ...
+    IndexError: list index out of range
+    >>> find_min(nums, -len(nums), -1) == min(nums)
+    True
+    >>> find_min(nums, -len(nums) - 1, -1) == min(nums)
+    Traceback (most recent call last):
+        ...
+    IndexError: list index out of range
+    """
+    if len(nums) == 0:
+        raise ValueError("find_min() arg is an empty sequence")
+    if (
+        left >= len(nums)
+        or left < -len(nums)
+        or right >= len(nums)
+        or right < -len(nums)
+    ):
+        raise IndexError("list index out of range")
+    if left == right:
+        return nums[left]
+    mid = (left + right) >> 1  # the middle
+    left_min = find_min(nums, left, mid)  # find min in range[left, mid]
+    right_min = find_min(nums, mid + 1, right)  # find min in range[mid + 1, right]
+
+    return left_min if left_min <= right_min else right_min
+
+
 if __name__ == "__main__":
     import doctest
 

maths/find_min.py

@@ -1,4 +1,11 @@
-import math
+"""
+Gamma function is a very useful tool in math and physics.
+It helps calculating complex integral in a convenient way.
+for more info: https://en.wikipedia.org/wiki/Gamma_function
+Python's Standard Library gamma() function overflows around gamma(171.624).
+"""
+
+from math import pi, sqrt, exp
 
 from numpy import inf
 from scipy.integrate import quad
@@ -39,10 +46,75 @@ def gamma(num: float) -> float:
 
 
 def integrand(x: float, z: float) -> float:
-    return math.pow(x, z - 1) * math.exp(-x)
+    return pow(x, z - 1) * exp(-x)
+
+
+def gamma_recursive(num: float) -> float:
+    """
+    Calculates the value of Gamma function of num
+    where num is either an integer (1, 2, 3..) or a half-integer (0.5, 1.5, 2.5 ...).
+    Implemented using recursion
+    Examples:
+    >>> from math import isclose, gamma as math_gamma
+    >>> gamma(0.5)
+    1.7724538509055159
+    >>> gamma(2)
+    1.0
+    >>> gamma(3.5)
+    3.3233509704478426
+    >>> gamma(171.5)
+    9.483367566824795e+307
+    >>> all(isclose(gamma(num), math_gamma(num)) for num in (0.5, 2, 3.5, 171.5))
+    True
+    >>> gamma(0)
+    Traceback (most recent call last):
+        ...
+    ValueError: math domain error
+    >>> gamma(-1.1)
+    Traceback (most recent call last):
+        ...
+    ValueError: math domain error
+    >>> gamma(-4)
+    Traceback (most recent call last):
+        ...
+    ValueError: math domain error
+    >>> gamma(172)
+    Traceback (most recent call last):
+        ...
+    OverflowError: math range error
+    >>> gamma(1.1)
+    Traceback (most recent call last):
+        ...
+    NotImplementedError: num must be an integer or a half-integer
+    """
+    if num <= 0:
+        raise ValueError("math domain error")
+    if num > 171.5:
+        raise OverflowError("math range error")
+    elif num - int(num) not in (0, 0.5):
+        raise NotImplementedError("num must be an integer or a half-integer")
+    elif num == 0.5:
+        return sqrt(pi)
+    else:
+        return 1.0 if num == 1 else (num - 1) * gamma(num - 1)
+
 
+def test_gamma() -> None:
+    """
+    >>> test_gamma()
+    """
+    assert gamma(0.5) == sqrt(pi)
+    assert gamma(1) == 1.0
+    assert gamma(2) == 1.0
+    
 
 if __name__ == "__main__":
     from doctest import testmod
 
     testmod()
+
+    num = 1.0
+    while num:
+        num = float(input("Gamma of: "))
+        print(f"gamma({num}) = {gamma(num)}")
+        print("\nEnter 0 to exit...")