Added Kadane's Algorithm for Maximum Subarray Sum

Author: Aniketsy

Diff for: data_structures/arrays/maximum_subarray.py

@@ -1,3 +1,24 @@
+"""
+Kadane's Algorithm is an efficient method to find the maximum
+sum of a contiguous subarray within a one-dimensional array of
+numbers. It maintains two key values as we traverse the array:
+the current maximum sum ending at the current index and the
+global maximum sum found so far.
+"""
+
+# Advantages
+"""
+- Efficiency: Runs in linear time, `O(n)`.
+- Simplicity: Straightforward to implement and understand.
+- Versatility: Easily adaptable to related problems.
+"""
+
+# Time Complexity
+"""
+- Time Complexity: `O(n)` - processes each element once.
+- Space Complexity: `O(1)` - uses a fixed amount of extra space.
+"""
+
 """
 Find the Maximum Subarray Sum using Kadane's Algorithm.
 Reference: https://leetcode.com/problems/maximum-subarray/
@@ -13,7 +34,6 @@
 Example Input:
 nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
 Output: 6
-
 """
 
 def max_subarray_sum(nums: list[int]) -> int:
@@ -37,37 +57,15 @@ def max_subarray_sum(nums: list[int]) -> int:
         -1
     """
     max_current = max_global = nums[0]
-    
+
     for num in nums[1:]:
         max_current = max(num, max_current + num)
         max_global = max(max_global, max_current)
 
     return max_global
 
+
 if __name__ == "__main__":
     import doctest
 
-    doctest.testmod()
-
-
-# Kadane's Algorithm
-
-"""
-Kadane's Algorithm is an efficient method to find the maximum
-sum of a contiguous subarray within a one-dimensional array of
-numbers. It maintains two key values as we traverse the array:
-the current maximum sum ending at the current index and the
-global maximum sum found so far.
-"""
-# Advantages
-"""
-- Efficiency**: Runs in linear time, `O(n)`.
-- Simplicity**: Straightforward to implement and understand.
-- Versatility**: Easily adaptable to related problems.
-"""
-
-### Time Complexity
-"""
-- Time Complexity**: `O(n)` - processes each element once.
-- Space Complexity**: `O(1)` - uses a fixed amount of extra space.
-"""
+    doctest.testmod()