feat: Add LCM function

dynamic_programming/kadanes_algorithm.py

@@ -0,0 +1,36 @@
+"""
+Kadane's Algorithm
+Find the maximum sum of a contiguous subarray.
+
+Time Complexity: O(n)
+Space Complexity: O(1)
+"""
+
+from typing import List
+
+
+def max_subarray_sum(arr: List[int]) -> int:
+    """
+    Find the maximum sum of a contiguous subarray.
+
+    >>> max_subarray_sum([-2, 1, -3, 4, -1, 2, 1, -5, 4])
+    6
+    >>> max_subarray_sum([1])
+    1
+    >>> max_subarray_sum([5, 4, -1, 7, 8])
+    23
+    """
+    if not arr:
+        raise ValueError("Array must not be empty")
+
+    max_sum = current_sum = arr[0]
+    for num in arr[1:]:
+        current_sum = max(num, current_sum + num)
+        max_sum = max(max_sum, current_sum)
+    return max_sum
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

maths/abs_max.py

@@ -0,0 +1,21 @@
+"""Find the absolute maximum element in a list."""
+
+
+def abs_max(arr: list[int]) -> int:
+    """
+    Find the element with maximum absolute value.
+
+    >>> abs_max([-10, 20, -30, 40])
+    -30
+    >>> abs_max([1, 2, 3])
+    3
+    """
+    if not arr:
+        raise ValueError("List is empty")
+    return max(arr, key=abs)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

maths/average.py

@@ -0,0 +1,21 @@
+"""Compute average of a list of numbers."""
+
+
+def average(numbers: list[float]) -> float:
+    """
+    Compute the arithmetic mean.
+
+    >>> average([1, 2, 3, 4, 5])
+    3.0
+    >>> average([10, 20])
+    15.0
+    """
+    if not numbers:
+        raise ValueError("List is empty")
+    return sum(numbers) / len(numbers)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

maths/gcd.py

@@ -0,0 +1,20 @@
+"""Greatest Common Divisor using Euclidean algorithm."""
+
+
+def gcd(a: int, b: int) -> int:
+    """
+    Find GCD of two numbers.
+
+    >>> gcd(12, 8)
+    4
+    >>> gcd(54, 24)
+    6
+    """
+    while b:
+        a, b = b, a % b
+    return a
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()

maths/lcm.py

@@ -0,0 +1,19 @@
+"""Least Common Multiple using GCD."""
+
+
+def lcm(a: int, b: int) -> int:
+    """
+    Find LCM of two numbers.
+
+    >>> lcm(4, 6)
+    12
+    >>> lcm(3, 7)
+    21
+    """
+    from math import gcd
+    return abs(a * b) // gcd(a, b)
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()