kadanes_algorithm for finding the maximum sum subarray with a twist

Author: mahletseyoum101

circular_kadne.py

@@ -0,0 +1,32 @@
+def kadanes_algorithm(arr):
+    """Standard Kadane's Algorithm for maximum sum subarray."""
+    max_ending_here = max_so_far = arr[0]
+    
+    for num in arr[1:]:
+        max_ending_here = max(num, max_ending_here + num)
+        max_so_far = max(max_so_far, max_ending_here)
+    
+    return max_so_far
+
+def max_circular_subarray(arr):
+    """Kadane's Algorithm variation for circular arrays."""
+    max_kadane = kadanes_algorithm(arr)
+    
+    # Compute total array sum
+    total_sum = sum(arr)
+    
+    # Invert the array elements
+    inverted_arr = [-x for x in arr]
+    
+    # Find the maximum sum of the inverted array (minimum subarray sum)
+    max_inverted_kadane = kadanes_algorithm(inverted_arr)
+    
+    # The maximum circular sum is total_sum + max_inverted_kadane
+    # If max_inverted_kadane is equal to total_sum, it means all elements are negative
+    max_circular = total_sum + max_inverted_kadane if max_inverted_kadane != -total_sum else max_kadane
+    
+    return max(max_kadane, max_circular)
+
+# Example usage
+arr = [1, -2, 4, -3]
+print("Maximum sum subarray (circular):", max_circular_subarray(arr))