feat: Add Kadane's Algorithm

dynamic_programming/kadanes_algorithm.py

@@ -0,0 +1,35 @@
+"""
+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()