减少基本图形公式的复杂度/计算时间 [英] Reducing the complexity/computation time for a basic graph formula
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问题描述
我尝试使用基本公式(是从另一个SO问题中得到的),用于计算 n
个顶点的不同边集的最大数量:
I tried to use the basic formula (got it from another SO question),
for calculating the max number of different edge sets, for n
vertices:
2**(n*(n-1)/2)
但是它仅对小范围的数字有用-然后变得太复杂了.
but it's good only for small range of numbers - then it gets too complex.
有没有办法改善这个公式/降低复杂性?
Is there a way to improve this formula/reduce the complexity?
推荐答案
这是一种大大加快此速度的简便方法: 2 ** x
始终等于 1<<x
,只要 x
是非负整数;但后者要快上百倍,因为它只是移位位,而不是进行算术运算
Here's an easy way to speed this up quite considerably: 2 ** x
is always equal to 1 << x
, so long as x
is a non-negative integer; but the latter is hundreds of times faster, because it's just shifting bits rather than doing arithmetic.
>>> def slow(n):
... return 2 ** (n * (n-1) // 2)
...
>>> def fast(n):
... return 1 << (n * (n-1) // 2)
...
>>> from timeit import timeit
>>> timeit(lambda: slow(1000), number=1000)
1.5656050549987413
>>> timeit(lambda: fast(1000), number=1000)
0.005352460000722203
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