python – 递归闭包(函数发生器)

我一直在学习函数式编程,我开始思考,组装数学运算符.
计数 – >另外 – >乘法 – >权力 – > …自然地出来了简单和最天真的代码来表达这一点,它的工作原理！问题是我真的不知道为什么它能如此好地运行并且输出如此大的输出.

问题是：
这个功能的复杂性是什么？

代码在python中：

def operator(d):
        if d<=1:
                return lambda x,y:x+y
        else:
                return lambda x,y:reduce(operator(d-1),(x for i in xrange(y)))


#test 
f1 = operator(1)       #f1 is adition
print("f1",f1(50,52))  #50+52

f2 = operator(2)      #f2 is multiplication
print("f2",f2(2,20))  #2*20

f3 = operator(3)      #f3 is power, just look how long output can be
print("f3",f3(4,100)) #4**100 

f4 = operator(4)      #f4 is superpower, this one does not work that well
print("f4",f4(2,6))   #((((2**2)**2)**2)**2)**2

f5 = operator(5)      #f5 do not ask about this one, 
print("f5",f5(2,4))   #

输出(即时)：

('f1', 102)
('f2', 40)
('f3', 1606938044258990275541962092341162602522202993782792835301376L)
('f4', 4294967296L)
('f5', 32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638215525166389437335543602135433229604645318478604952148193555853611059596230656L)

解决方法:

反汇编告诉你这里没有应用任何魔法优化,它实际上只是对genexpr的减少. Python似乎完全可以完成这项任务,即使它让你感到惊讶.

>>> import dis
>>> dis.dis(f3)
  5           0 LOAD_GLOBAL              0 (reduce)
              3 LOAD_GLOBAL              1 (operator)
              6 LOAD_DEREF               1 (d)
              9 LOAD_CONST               1 (1)
             12 BINARY_SUBTRACT     
             13 CALL_FUNCTION            1
             16 LOAD_CLOSURE             0 (x)
             19 BUILD_TUPLE              1
             22 LOAD_CONST               2 (<code object <genexpr> at 0x7f32d325f830, file "<stdin>", line 5>)
             25 MAKE_CLOSURE             0
             28 LOAD_GLOBAL              2 (xrange)
             31 LOAD_FAST                1 (y)
             34 CALL_FUNCTION            1
             37 GET_ITER            
             38 CALL_FUNCTION            1
             41 CALL_FUNCTION            2
             44 RETURN_VALUE

如果您专门查看f5(2,4)调用,它实际上不执行这么多操作：

>>> counter = 0
>>> def adder(x, y):
...   global counter
...   counter += 1
...   return x + y
... 
>>> def op(d):
...   if d <= 1: return adder
...   return lambda x,y:reduce(op(d-1),(x for i in xrange(y)))
...
>>> op(5)(2,4)
32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638215525166389437335543602135433229604645318478604952148193555853611059596230656L
>>> counter
65035
>>> counter = 0
>>> op(3)(4,100)
>>> counter
297

65k的新增功能,更不用说297的取幂,甚至不值得谈到搞笑优化的现代CPU,所以毫无疑问,它会在眨眼之间完成.尝试增加其中一个参数,看看它如何迅速达到快速评估的边界.

顺便说一下,operator是一个内置模块,你不应该像这样命名自己的函数.

标签：python,closures,complexity-theory,functional-programming,recursion
来源： https://codeday.me/bug/20190530/1183998.html