From efa5b8ef3f1fd2b9cf8ec7cd1e7e1850d86aa0d5 Mon Sep 17 00:00:00 2001
From: Saurav <sauravgc33@gmail.com>
Date: Thu, 9 Apr 2026 16:40:03 +0545
Subject: [PATCH 1/3] Add Kadane's algorithm for maximum subarray sum

---
 dynamic_programming/kadanes_algorithm.py | 53 ++++++++++++++++++++++++
 1 file changed, 53 insertions(+)
 create mode 100644 dynamic_programming/kadanes_algorithm.py

diff --git a/dynamic_programming/kadanes_algorithm.py b/dynamic_programming/kadanes_algorithm.py
new file mode 100644
index 000000000000..2360e1029da1
--- /dev/null
+++ b/dynamic_programming/kadanes_algorithm.py
@@ -0,0 +1,53 @@
+"""
+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])
+"""
+
+
+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)}")

From 65730becbd7ce1fd7cab1c01c2d9cd61fa17dbde Mon Sep 17 00:00:00 2001
From: Saurav <sauravgc33@gmail.com>
Date: Thu, 9 Apr 2026 16:46:34 +0545
Subject: [PATCH 2/3] Add Wikipedia reference to Kadane's algorithm

---
 dynamic_programming/kadanes_algorithm.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/dynamic_programming/kadanes_algorithm.py b/dynamic_programming/kadanes_algorithm.py
index 2360e1029da1..6c7cac9e983f 100644
--- a/dynamic_programming/kadanes_algorithm.py
+++ b/dynamic_programming/kadanes_algorithm.py
@@ -4,8 +4,9 @@
 
 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:
     """

From 21fad4e97adadbe4a33f6dbeacc1be1ea315f424 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Thu, 9 Apr 2026 11:03:03 +0000
Subject: [PATCH 3/3] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 dynamic_programming/kadanes_algorithm.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/dynamic_programming/kadanes_algorithm.py b/dynamic_programming/kadanes_algorithm.py
index 6c7cac9e983f..5b38ec621715 100644
--- a/dynamic_programming/kadanes_algorithm.py
+++ b/dynamic_programming/kadanes_algorithm.py
@@ -8,6 +8,7 @@
 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.