Question:

Place the following functions below in order of their efficiency. They all take in a list of numbers between 0 and 1. The list can be quite long. An example input list would be [random.random() for i in range(100000)]. How would you prove that your answer is correct?


def f1(lIn):
    l1 = sorted(lIn)
    l2 = [i for i in l1 if i<0.5]
    return [i*i for i in l2]

def f2(lIn):
    l1 = [i for i in lIn if i<0.5]
    l2 = sorted(l1)
    return [i*i for i in l2]

def f3(lIn):
    l1 = [i*i for i in lIn]
    l2 = sorted(l1)
    return [i for i in l1 if i<(0.5*0.5)]

Answer:

Most to least efficient: f2f1f3. To prove that this is the case, you would want to profile your code. Python has a lovely profiling package that should do the trick.

import cProfile
lIn = [random.random() for i in range(100000)]
cProfile.run('f1(lIn)')
cProfile.run('f2(lIn)')
cProfile.run('f3(lIn)')

For completion's sake, here is what the above profile outputs:

>>> cProfile.run('f1(lIn)')
         4 function calls in 0.045 seconds

   Ordered by: standard name

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.009    0.009    0.044    0.044 :1(f1)
        1    0.001    0.001    0.045    0.045 :1()
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}
        1    0.035    0.035    0.035    0.035 {sorted}


>>> cProfile.run('f2(lIn)')
         4 function calls in 0.024 seconds

   Ordered by: standard name

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.008    0.008    0.023    0.023 :1(f2)
        1    0.001    0.001    0.024    0.024 :1()
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}
        1    0.016    0.016    0.016    0.016 {sorted}


>>> cProfile.run('f3(lIn)')
         4 function calls in 0.055 seconds

   Ordered by: standard name

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.016    0.016    0.054    0.054 :1(f3)
        1    0.001    0.001    0.055    0.055 :1()
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}
        1    0.038    0.038    0.038    0.038 {sorted}

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