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import bisect |
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from typing import List, Sequence, Tuple |
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def search_for_fit(numbers: Sequence[int], capacity: int) -> int: |
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r""" |
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Finds the index of largest number that fits into the knapsack with the given capacity. |
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""" |
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index = bisect.bisect(numbers, capacity) |
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return -1 if index == 0 else (index - 1) |
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def greedy_knapsack(numbers: List[int], capacity: int) -> List[List[int]]: |
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r""" |
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An efficient greedy algorithm with binary search for the knapsack problem. |
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""" |
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numbers.sort() |
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knapsacks = [] |
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while numbers: |
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current_knapsack = [] |
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remaining_capacity = capacity |
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while True: |
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index = search_for_fit(numbers, remaining_capacity) |
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if index == -1: |
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break |
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remaining_capacity -= numbers[index] |
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current_knapsack.append(numbers.pop(index)) |
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knapsacks.append(current_knapsack) |
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return knapsacks |
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def infer_seqlen(source_len: int, target_len: int, cutoff_len: int) -> Tuple[int, int]: |
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r""" |
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Computes the real sequence length after truncation by the cutoff_len. |
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""" |
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if target_len * 2 < cutoff_len: |
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max_target_len = cutoff_len |
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elif source_len * 2 < cutoff_len: |
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max_target_len = cutoff_len - source_len |
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else: |
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max_target_len = int(cutoff_len * (target_len / (source_len + target_len))) |
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new_target_len = min(max_target_len, target_len) |
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max_source_len = max(cutoff_len - new_target_len, 0) |
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new_source_len = min(max_source_len, source_len) |
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return new_source_len, new_target_len |
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