adding a split_workload algorithm

sorts/split_workload.py

@@ -0,0 +1,72 @@
+def split_list(
+    timings: list[int | float | str],
+) -> tuple[list[int | float], list[int | float], int | float] | None:
+    """
+
+    This algorithm is a brute-force search over (nearly) all 2^n
+    possible partitions and was created for educational purposes.
+    the asymptotic runtime of this code is: O(n * 2^n)
+
+    this is a case of the partition problem.
+    it accepts a multiset ( list ) of integers,
+    distributes them, and returns a tuple, containing two lists,
+    with minimal difference between their sums
+
+    >>> split_list([27, 21, 92, 87, 1, 32])
+    ([27, 21, 87], [92, 1, 32], 10)
+    >>> split_list([52, 385, 9956, 25, 2367, 1111, 17, 925])
+    ([9956], [52, 385, 25, 2367, 1111, 17, 925], 5074)
+    >>> split_list([12, 10, 11, 9])
+    ([10, 11], [12, 9], 0)
+    >>> split_list([-1551, 2712, 2325, 2623])
+    ([1551, 2712], [2325, 2623], 685)
+    >>> split_list(["12.5", "10", "11", "9"])
+    ([10, 11], [12.5, 9], 0.5)
+    >>> split_list(["twelve", "ten", "eleven", "nine"])
+    Traceback (most recent call last):
+    ValueError: Timings must be a list of numbers
+
+    """
+    valid_timings: list[int | float] = []
+    for current_element in timings:
+        if (
+            isinstance(current_element, str)
+            and current_element.replace(".", "", 1).isdigit()
+        ):
+            is_current_elem_int = float(current_element).is_integer()
+            if not is_current_elem_int:
+                valid_timings.append(abs(float(current_element)))
+            else:
+                valid_timings.append(abs(int(float(current_element))))
+        elif isinstance(current_element, (int, float)):
+            valid_timings.append(abs(current_element))
+        else:
+            print(type(current_element))
+            raise ValueError("Timings must be a list of numbers")
+
+    if len(valid_timings) == 0:
+        return ([], [], 0)
+    elif len(valid_timings) == 1:
+        return ([valid_timings[0]], [], valid_timings[0])
+
+    result = None
+    n = len(valid_timings)
+    smallest_diff = float("inf")
+    for i in range(1, 2**n - 1):
+        indices = [j for j in range(n) if i & (1 << j) != 0]
+        distributed_timings_1 = [valid_timings[j] for j in indices]
+        distributed_timings_2 = [valid_timings[j] for j in range(n) if j not in indices]
+        diff = abs(sum(distributed_timings_1) - sum(distributed_timings_2))
+
+        if diff < smallest_diff:
+            smallest_diff = diff
+            result = (
+                distributed_timings_1,
+                distributed_timings_2,
+                smallest_diff,
+            )
+    return result
+
+
+if __name__ == "__main__":
+    __import__("doctest").testmod()