From 2b64e1803dbd4f2c28b910ce8f2c4f1bc994ea93 Mon Sep 17 00:00:00 2001
From: Tanish22 <Tanishcse22@gmail.com>
Date: Sun, 12 Oct 2025 08:21:33 +0530
Subject: [PATCH 1/2] Adding kadane's algorithm to dp/ folder

kadane's algorithm is not present in dynamic_programming folder so adding it.
---
 dynamic_programming/kadane_algorithm.py | 61 +++++++++++++++++++++++++
 1 file changed, 61 insertions(+)
 create mode 100644 dynamic_programming/kadane_algorithm.py

diff --git a/dynamic_programming/kadane_algorithm.py b/dynamic_programming/kadane_algorithm.py
new file mode 100644
index 000000000000..39d59dd922e9
--- /dev/null
+++ b/dynamic_programming/kadane_algorithm.py
@@ -0,0 +1,61 @@
+"""
+Kadane's Algorithm implementation in Python.
+
+Finds the maximum sum of a contiguous subarray within
+a one-dimensional array of numbers.
+
+Source:
+https://en.wikipedia.org/wiki/Maximum_subarray_problem
+"""
+
+
+def kadane(arr: list[int]) -> tuple[int, list[int]]:
+    """
+    Returns the maximum sum of a contiguous subarray and the subarray itself.
+
+    Parameters
+    ----------
+    arr : list
+        List of integers (can be positive, negative, or zero).
+
+    Returns
+    -------
+    tuple
+        Maximum subarray sum and the corresponding subarray.
+
+    Examples
+    --------
+    >>> kadane([-2,1,-3,4,-1,2,1,-5,4])
+    (6, [4, -1, 2, 1])
+
+    >>> kadane([1,2,3,4])
+    (10, [1, 2, 3, 4])
+
+    >>> kadane([-1,-2,-3])
+    (-1, [-1])
+    """
+    if not arr:
+        raise ValueError("Input array cannot be empty")
+
+    max_current = max_global = arr[0]
+    start = end = s = 0
+
+    for i in range(1, len(arr)):
+        if arr[i] > max_current + arr[i]:
+            max_current = arr[i]
+            s = i
+        else:
+            max_current += arr[i]
+
+        if max_current > max_global:
+            max_global = max_current
+            start = s
+            end = i
+
+    return max_global, arr[start:end+1]
+
+
+# Doctest runner
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()

From f0af1b275d96902f9025f7307e97550d718ec958 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 12 Oct 2025 02:52:10 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 dynamic_programming/kadane_algorithm.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/dynamic_programming/kadane_algorithm.py b/dynamic_programming/kadane_algorithm.py
index 39d59dd922e9..757e316c1da8 100644
--- a/dynamic_programming/kadane_algorithm.py
+++ b/dynamic_programming/kadane_algorithm.py
@@ -52,10 +52,11 @@ def kadane(arr: list[int]) -> tuple[int, list[int]]:
             start = s
             end = i
 
-    return max_global, arr[start:end+1]
+    return max_global, arr[start : end + 1]
 
 
 # Doctest runner
 if __name__ == "__main__":
     import doctest
+
     doctest.testmod()