Python 的 int.bit_length() 函数的时间复杂度是多少呢? - V2EX
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littleMaple

Python 的 int.bit_length() 函数的时间复杂度是多少呢?

  •  
  •   littleMaple
    MapleCCC Feb 12, 2021 2662 views
    This topic created in 1900 days ago, the information mentioned may be changed or developed.

    假设某整数 x 的二进制最高有效位位数为 n,那么 x.bit_length() 的时间复杂度是 O(n) 还是 O(1) 呢?

    6 replies    2021-02-13 04:22:19 +08:00
    mogg
        1
    mogg  
       Feb 12, 2021
    log n 啊……
    mogg
        2
    mogg  
       Feb 12, 2021   1
    对不起看错了,常规算法是 O(log x ) or O(n)
    固定位数有优化到 O(log 32/64……)的算法(记得 csapp 上有)
    Python 的具体实现得看看源码(
    lxy42
        3
    lxy42  
       Feb 12, 2021   1
    正好在看 Python 源码, [int_bit_length_impl]( https://github.com/python/cpython/blob/master/Objects/longobject.c#L5256).

    从源码来看是 O(1).
    littleMaple
        4
    littleMaple  
    OP
       Feb 12, 2021
    @lxy42 #3 感谢解惑!
    littleMaple
        5
    littleMaple  
    OP
       Feb 12, 2021
    @mogg #2 感谢回复!我这就去看 CSAPP,之前一直放着.
    msg7086
        6
    msg7086  
       Feb 13, 2021 via Android   1
    本质上应该是 lzcnt 吧,让 CPU 算的话是常数时间。
    徒手算的话应该也能优化到常数时间。
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