Add kadane's algorithm in dp/ folder

dynamic_programming/kadane_algorithm.py

@@ -0,0 +1,62 @@
+"""
+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()