How do i print a sequence of numbers in python?

It might help to implement this with the ability to specify a range:

def generateNumber[low, high]:
    '''returns a list with integers between low and high inclusive
    example: generateNumber[2,10] --> [2,3,4,5,6,7,8,9,10]
    '''
    return range[low, high+1]

This can also be done with the built-in range function:

range[10]   --> [0,1,2,3,4,5,6,7,8,9]   #note the "off by one"
range[11]   --> [0,1,2,3,4,5,6,7,8,9,10]
range[2,11] --> [2,3,4,5,6,7,8,9,10]

More about range: //docs.python.org/2/library/functions.html#range

Subtle differences between Python methods you already know

Throughout undergrad, I would hear the phrase “there are several ways to skin a cat” repeated by lecturers during math, applied math and physics classes. As awry and violent as I found this Mark Twain phrase, it stuck with me [oddly enough] as a light reminder that there is always a multitude of probable routes one can take in achieving a goal. This helps me quite a lot when deciding on which methods to use in coding.

In my early days, all I knew was range[] as a method for generating monotonically increasing [or decreasing] sequences in Python. Then I was introduced to xrange[] and numpy.arange[] which then made me go hmmm, as a newbie, what is the strategy for deciding which functions to use?

1. The built-in method: range[]

The built-in method range[[start, ]stop, [step]] was my first introduction to generating sequences in Python. The optional arguments in the function are shown in square brackets. The range[] method generates an immutable object that is a sequence of numbers. The range[] object can easily be converted into a Python list by enclosing it in the list method, for example, creating a list of values between 10 [start] and 0 [stop] decreasing in increments of 2 [step].

>>list[range[10,0,-2]]
[10, 8, 6, 4, 2]

This method has proven to be very useful in for loops and list comprehensions alike given that it is built-in and efficient. To measure its speed, I wrote this very simple script which gives a large sample of runtimes for executing range[10]. A large distribution of runtimes [rt] provides a fair measure of how quickly a range[] object is created, on average.

rt=[]for _ in range[1000000]:
    t1 =time.time[]
    seq = range[val]
    rt.append[time.time[]-t1]rt_mean = np.mean[rt]*1.e9
rt_std  = np.std[rt]*1.e9print[u'range[] has an average runtime of %.0f \u00B1 %.0f ns'%[rt_mean,rt_std]]

This brief script provides the average runtime and 1σ uncertainty [or standard deviation] in nanoseconds. One could use the magic method %timeit to obtain a similar measure. Running this script gives us:

range[] has an average runtime of 478 ± 739 ns

Seems fast enough but are there quicker alternatives?

2. The Python 2 built-in method: xrange[]

Another such built-in method you may have discovered before switching to Python 3 is xrange[[start, ]stop, [step]]. It outputs a generator object. Like range[] it is useful in loops and can also be converted into a list object. Using a similar test as before, we can measure its average runtime obtaining the result:

xrange[] has an average runtime of 370 ± 682 ns

Given the error margins, the speed of execution for range[] and xrange[] is rather similar. The main difference is in the output — an iterable given by range[] and a generator object output by xrange[]. Comparing the memory use between the two objects gives,

>> print['Memory use of iterable: %d'%[sys.getsizeof[range_seq]] ]
Memory use of iterable: 152>> print['Memory use of generator object: %d'%[sys.getsizeof[xrange_seq]] ]
Memory use of generator object: 40

While there is no difference in efficiency, the xrange[] object is significantly smaller in byte-size. One more sequence builder we can consider is one that exists within the NumPy library.

3. The NumPy method: numpy.arange[]

The method numpy.arange[[start, ]stop, [step, ]dtype=None] from NumPy provides functionality for generating sequences. It generates a NumPy array object [or numpy.ndarray]. Running a similar script to determine the average runtime yields,

numpy.arange[] has an average runtime of 1111 ± 958 ns

Based on this test, numpy.arange[] executes for well over double the runtime that range[] and xrange[] do, on average.

With xrange[] being restricted to Python 2 and numpy.arange[] being a factor of two slower at generating a sequence than both xrange[] and range[], the answer seems quite clear. The method range[] is the mostefficient way to generate a monotonically increasing or decreasing sequence in Python. While this may be true, the objects produced by each method use up memory differently.

The Caveats — output of each method

Indeed, range[] executesfaster than numpy.arange[] and outputs an object that can be converted into an iterable list. On the other hand, numpy.arange[] gives you a numpy.ndarray. Without a doubt, range[] is a better option in for loops. When it comes to operating on the resulting sequence, however, NumPy arrays have a clear advantage in both memory consumption and speed.

Starting with memory, we can find out how much memory is consumed by a Python list object vs NumPy array.

>> print['Memory use of iterable: %d'%[sys.getsizeof[range_seq]] ]
Memory use of iterable: 152>> print['Memory use of numpy.ndarray: %d '%[sys.getsizeof[arange_seq]] ]
Memory use of numpy.ndarray: 80

NumPy arrays simply take up less space in the compiler memory store making them more efficient to operate on. This is something one can test easily comparing the speed of performing basic arithmetic operations on lists and numpy.ndarrays as has been demonstrated in this UCF web courses article.

All in all, discovering the many ways to de-skin a feline, so to speak, in one’s Python journey can provide insight into understanding the importance of speed, functionality and memory use of different data types and methods. Most importantly, writing short tests to compare runtimes can help one discern which methods will increase both the cleanliness and efficiency of code.

Additional References:

[1] ‘Geeks for Geeks’ post. Title: “range[] vs xrange[] in Python”

[2] ‘Geeks for Geeks’ post. Title: “Python | range[] does not return an iterator”

[3] Reddit post on subreddit:r/learnpython. Title:“Difference between range and arange?”

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