Added Kadane's Algorithm implementation

.pre-commit-config.yaml

@@ -32,6 +32,7 @@ repos:
     rev: "v2.5.0"
     hooks:
       - id: pyproject-fmt
+        language_version: python3.12
 
   - repo: local
     hooks:

data_structures/arrays/kadanes_algorithm.py

@@ -0,0 +1,56 @@
+class KadaneAlgorithm:
+    """
+    Kadane's Algorithm to find the maximum sum
+    of a contiguous subarray in a given array.
+
+    Time Complexity: O(n)
+    Space Complexity: O(1)
+
+    The function works efficiently with both positive and negative integers.
+
+    Usage:
+    >>> kadane = KadaneAlgorithm()
+    >>> kadane.max_subarray_sum([1, 2, 3, -2, 5])
+    9
+    >>> kadane.max_subarray_sum([-1, -2, -3, -4])
+    -1
+    >>> kadane.max_subarray_sum([1, 2, 3, 4])
+    10
+    >>> kadane.max_subarray_sum([10, -10, 20, -5, 10])
+    25
+    """
+
+    def __init__(self):
+        pass
+
+    def max_subarray_sum(self, arr: list[int]) -> int:
+        """
+        This function finds the maximum sum of a
+        contiguous subarray using Kadane's Algorithm.
+
+        :param arr: List of integers.
+        :return: Maximum sum of a contiguous subarray.
+
+        Raises:
+            ValueError: If the input array is empty.
+
+        >>> kadane = KadaneAlgorithm()
+        >>> kadane.max_subarray_sum([1, 2, 3, -2, 5])
+        9
+        >>> kadane.max_subarray_sum([-1, -2, -3, -4])
+        -1
+        >>> kadane.max_subarray_sum([1, 2, 3, 4])
+        10
+        >>> kadane.max_subarray_sum([10, -10, 20, -5, 10])
+        25
+        """
+        if not arr:
+            raise ValueError("Input 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

pyproject.toml

@@ -49,6 +49,30 @@ euler-validate = [
 [tool.ruff]
 target-version = "py313"
 
+[tool.codespell]
+ignore-words-list = "3rt,ans,bitap,crate,damon,fo,followings,hist,iff,kwanza,manuel,mater,secant,som,sur,tim,toi,zar"
+skip = "./.*,*.json,*.lock,ciphers/prehistoric_men.txt,project_euler/problem_022/p022_names.txt,pyproject.toml,strings/dictionary.txt,strings/words.txt"
+
+[tool.pytest.ini_options]
+markers = [
+  "mat_ops: mark a test as utilizing matrix operations.",
+]
+addopts = [
+  "--durations=10",
+  "--doctest-modules",
+  "--showlocals",
+]
+
+[tool.coverage.report]
+omit = [
+  ".env/*",
+  "project_euler/*",
+]
+sort = "Cover"
+
+[tool.mypy]
+python_version = "3.12"
+
 output-format = "full"
 lint.select = [
   # https://beta.ruff.rs/docs/rules
@@ -158,27 +182,6 @@ lint.pylint.max-branches = 20 # default: 12
 lint.pylint.max-returns = 8 # default: 6
 lint.pylint.max-statements = 88 # default: 50
 
-[tool.codespell]
-ignore-words-list = "3rt,ans,bitap,crate,damon,fo,followings,hist,iff,kwanza,manuel,mater,secant,som,sur,tim,toi,zar"
-skip = "./.*,*.json,*.lock,ciphers/prehistoric_men.txt,project_euler/problem_022/p022_names.txt,pyproject.toml,strings/dictionary.txt,strings/words.txt"
-
-[tool.pytest.ini_options]
-markers = [
-  "mat_ops: mark a test as utilizing matrix operations.",
-]
-addopts = [
-  "--durations=10",
-  "--doctest-modules",
-  "--showlocals",
-]
-
-[tool.coverage.report]
-omit = [
-  ".env/*",
-  "project_euler/*",
-]
-sort = "Cover"
-
 [tool.sphinx-pyproject]
 copyright = "2014, TheAlgorithms"
 autoapi_dirs = [