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72 lines
2.1 KiB
Python
72 lines
2.1 KiB
Python
"""
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smallest_range function takes a list of sorted integer lists and finds the smallest
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range that includes at least one number from each list, using a min heap for efficiency.
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"""
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from heapq import heappop, heappush
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from sys import maxsize
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def smallest_range(nums: list[list[int]]) -> list[int]:
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"""
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Find the smallest range from each list in nums.
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Uses min heap for efficiency. The range includes at least one number from each list.
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Args:
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nums: List of k sorted integer lists.
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Returns:
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list: Smallest range as a two-element list.
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Examples:
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>>> smallest_range([[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]])
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[20, 24]
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>>> smallest_range([[1, 2, 3], [1, 2, 3], [1, 2, 3]])
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[1, 1]
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>>> smallest_range(((1, 2, 3), (1, 2, 3), (1, 2, 3)))
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[1, 1]
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>>> smallest_range(((-3, -2, -1), (0, 0, 0), (1, 2, 3)))
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[-1, 1]
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>>> smallest_range([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
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[3, 7]
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>>> smallest_range([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
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[0, 0]
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>>> smallest_range([[], [], []])
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Traceback (most recent call last):
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...
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IndexError: list index out of range
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"""
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min_heap: list[tuple[int, int, int]] = []
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current_max = -maxsize - 1
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for i, items in enumerate(nums):
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heappush(min_heap, (items[0], i, 0))
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current_max = max(current_max, items[0])
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# Initialize smallest_range with large integer values
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smallest_range = [-maxsize - 1, maxsize]
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while min_heap:
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current_min, list_index, element_index = heappop(min_heap)
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if current_max - current_min < smallest_range[1] - smallest_range[0]:
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smallest_range = [current_min, current_max]
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if element_index == len(nums[list_index]) - 1:
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break
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next_element = nums[list_index][element_index + 1]
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heappush(min_heap, (next_element, list_index, element_index + 1))
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current_max = max(current_max, next_element)
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return smallest_range
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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print(f"{smallest_range([[1, 2, 3], [1, 2, 3], [1, 2, 3]])}") # Output: [1, 1]
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