Enhancement/issue 8427

dynamic_programming/max_sub_array_sum.py

@@ -0,0 +1,43 @@
+def max_sub_array_sum(arr: list[int], size: int) -> int:
+    """
+    Finds the maximum sum of a subarray within the given array using Kadane's algorithm.
+
+    Args:
+        arr (list): The input array of numbers.
+        size (int): The size of the array.
+
+    Returns:
+        int: The maximum sum of a subarray within the array.
+
+    Example:
+        >>> arr = [-2, -3, 4, -1, -2, 5, -3]
+        >>> max_sub_array_sum(arr, len(arr))
+        6
+        In this example, the input array is [-2, -3, 4, -1, -2, 5, -3].
+        The maximum sum of a subarray within this array is 6,
+        which corresponds to the subarray [4, -1, -2, 5].
+
+        >>> arr = [-3, -4, 5, -1, 2, -4, 6, -1]
+        >>> max_sub_array_sum(arr, len(arr))
+        8
+
+    References:
+    https://en.wikipedia.org/wiki/Maximum_subarray_problem
+    """
+    max_till_now = arr[0]
+    max_ending = 0
+
+    for i in range(size):
+        max_ending = max_ending + arr[i]
+        if max_ending < 0:
+            max_ending = 0
+        elif max_till_now < max_ending:
+            max_till_now = max_ending
+
+    return max_till_now
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

other/sliding_window.py

@@ -0,0 +1,36 @@
+def sliding_window(elements: list[int], window_size: int) -> list[list[int]]:
+    """
+    Generate sliding windows of a specified size over a list of elements.
+
+    Args:
+        elements (list): The input list of elements.
+        window_size (int): The size of the sliding window.
+
+    Returns:
+        list: A list of sliding windows.
+
+    Example:
+        >>> lst = [1, 2, 3, 4, 5, 6, 7, 8]
+        >>> result = sliding_window(lst, 3)
+        >>> print(result)
+        [[1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, 6], [5, 6, 7], [6, 7, 8]]
+
+    References:
+    https://stackoverflow.com/questions/8269916/what-is-sliding-window-algorithm-examples
+    """
+
+    if len(elements) <= window_size:
+        return [elements]
+
+    windows = []
+    for i in range(len(elements) - window_size + 1):
+        window = elements[i : i + window_size]
+        windows.append(window)
+
+    return windows
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

other/sliding_window_generators.py

@@ -0,0 +1,37 @@
+from collections.abc import Generator
+
+
+def sliding_window(
+    elements: list[int], window_size: int
+) -> Generator[list[int], None, None]:
+    """
+    Generate sliding windows of size window_size from the given elements.
+
+    Args:
+        elements (list): The input list of elements.
+        window_size (int): The size of the sliding window.
+
+    Returns:
+        generator: A generator that yields sublists of size window_size.
+
+    Example:
+        >>> lst = [1, 2, 3, 4, 5, 6, 7, 8]
+        >>> sw_gen = sliding_window(lst, 3)
+        >>> print(next(sw_gen))
+        [1, 2, 3]
+        >>> print(next(sw_gen))
+        [2, 3, 4]
+
+    References:
+    https://stackoverflow.com/questions/8269916/what-is-sliding-window-algorithm-examples
+    """
+    if len(elements) <= window_size:
+        yield elements
+    for i in range(len(elements) - window_size + 1):
+        yield elements[i : i + window_size]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()