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