Add Kadane's Algorithm implementation (fixes #8756)

scripts/kadanes_algorithm.py

@@ -0,0 +1,90 @@
+"""
+Kadane's Algorithm - Maximum Subarray Sum
+
+This algorithm finds the contiguous subarray within a one-dimensional
+array of numbers which has the largest sum.
+
+Time Complexity: O(n)
+Space Complexity: O(1)
+
+Author: kl2400033266
+Issue: #8756
+"""
+
+def kadanes_algorithm(arr):
+    """
+    Find the maximum sum of a contiguous subarray using Kadane's Algorithm.
+
+    Args:
+        arr: List of integers
+
+    Returns:
+        Maximum sum of contiguous subarray
+    """
+    if not arr:
+        return 0
+
+    max_current = arr[0]
+    max_global = arr[0]
+
+    for i in range(1, len(arr)):
+        max_current = max(arr[i], max_current + arr[i])
+        if max_current > max_global:
+            max_global = max_current
+
+    return max_global
+
+
+def kadanes_with_indices(arr):
+    """
+    Find maximum subarray sum along with start and end indices.
+
+    Args:
+        arr: List of integers
+
+    Returns:
+        Tuple of (max_sum, start_index, end_index)
+    """
+    if not arr:
+        return 0, -1, -1
+
+    max_current = arr[0]
+    max_global = arr[0]
+    start = end = temp_start = 0
+
+    for i in range(1, len(arr)):
+        if arr[i] > max_current + arr[i]:
+            max_current = arr[i]
+            temp_start = i
+        else:
+            max_current = max_current + arr[i]
+
+        if max_current > max_global:
+            max_global = max_current
+            start = temp_start
+            end = i
+
+    return max_global, start, end
+
+
+# Example usage and testing
+if __name__ == "__main__":
+    # Test case 1: Mixed positive and negative numbers
+    arr1 = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
+    print(f"Array: {arr1}")
+    print(f"Maximum Subarray Sum: {kadanes_algorithm(arr1)}")
+
+    max_sum, start, end = kadanes_with_indices(arr1)
+    print(f"Maximum Sum: {max_sum}, Subarray: {arr1[start:end+1]}")
+    print()
+
+    # Test case 2: All negative numbers
+    arr2 = [-5, -3, -1, -4, -2]
+    print(f"Array: {arr2}")
+    print(f"Maximum Subarray Sum: {kadanes_algorithm(arr2)}")
+    print()
+
+    # Test case 3: All positive numbers
+    arr3 = [1, 2, 3, 4, 5]
+    print(f"Array: {arr3}")
+    print(f"Maximum Subarray Sum: {kadanes_algorithm(arr3)}")