Add Kadane's algorithm for maximum subarray sum

dynamic_programming/kadanes_algorithm.py

@@ -0,0 +1,55 @@
+"""
+Kadane's Algorithm: Given an array of integers, find the contiguous subarray
+with the largest sum.
+
+Example:
+    [-2, 1, -3, 4, -1, 2, 1, -5, 4] --> 6 (subarray [4, -1, 2, 1])
+
+Reference: https://en.wikipedia.org/wiki/Maximum_subarray_problem
+"""
+
+
+def kadanes_algorithm(arr: list[int]) -> int:
+    """
+    Finds the maximum sum of a contiguous subarray using Kadane's Algorithm.
+
+    Parameters
+    ----------
+    arr: list[int], the input list of integers
+
+    Returns
+    -------
+    int: the maximum subarray sum
+
+    >>> kadanes_algorithm([-2, 1, -3, 4, -1, 2, 1, -5, 4])
+    6
+    >>> kadanes_algorithm([1])
+    1
+    >>> kadanes_algorithm([-1, -2, -3])
+    -1
+    >>> kadanes_algorithm([5, 4, -1, 7, 8])
+    23
+    >>> kadanes_algorithm([0, 0, 0])
+    0
+    >>> kadanes_algorithm([-2, -3, 4, -1, -2, 1, 5, -3])
+    7
+    """
+    if not arr:
+        raise ValueError("Array cannot 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()
+
+    arr = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
+    print(f"Maximum subarray sum: {kadanes_algorithm(arr)}")