Generating a simple mathematical sequence in Python - python

I'm new to Python and coming from a PHP background.. I'm impressed. Is there a way of getting a list of numbers from this sequence:
i^2, i^2 + i, i^2 + 2i, ..., n
i.e. if i=2 and n=30:
4, 6, 8, ..., 30
Okay, this is a really simple sequence but is what's a more general way to do this sort of thing functionally?
Maybe there's some nice functional programming way of doing this? In PHP I think I would make some function some variables and interaction but Python might be able to do it more elegantly?
Many thanks.

You can do this with range:
In [186]: i = 2; n = 30; range(i**2, n+1, i)
Out[186]: [4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]

Python has a cool feature called List Comprehension. You can use it to do something like this:
[i*i+2*n for n in range(30) if (i*i+2*n)<=30]

Related

How to do i print some numbers using .sample() from the random built in module in python

I working on a problem where I'm supposed to generate ten random but unique numbers that range from 1 to 15 inclusive. The thing is, I'm supposed to write everything in one line and to also get this output:
[2, 4, 6, 7, 8, 9, 11, 12, 13, 15]
Below I have some code I wrote but, it's not getting the output I want. What am I doing wrong and can I perhaps see a solution with a break so I know how to do this going down the road?
import random
print(sorted(random.sample(range(1,16),15)))
Output:
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
The output I want is:
[2,4,6,7,8,9,11,12,13,15]
How do I get this in one line of code?
>>> help(random.sample)
sample(population, k): method of random.Random instance
Chooses k unique random elements from a population sequence or set.
I'm supposed to write everything in one line and to also get this output:
[2, 4, 6, 7, 8, 9, 11, 12, 13, 15]
>>> sorted(__import__('random').Random(4225).sample(range(1, 16), 10))
[2, 4, 6, 7, 8, 9, 11, 12, 13, 15]
If you want to generate ten numbers in range 1-15, change
print(sorted(random.sample(range(1,16),15)))
to
print(sorted(random.sample(range(1,16),10)))
# From the documentation :
# random.sample(population, k)
import random
population = range(16)
how_may_sample = 10
random.sample(population, how_many_sample)
# Now in one line
random.sample(range(16), 10)

Usefulness of one-line statements in Python [closed]

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Is using one line loops, even nested loops always a good practice in Python? I see a lot of people just love "one-liners", but to me they're hard to read sometimes, especially if we're talking about nested loops.
Moreover most of nested loops I've seen so far exceed the recommended 79 characters per line.
So I'd like to know if "one-liners" offer anything extra apart being compact? Do they use less memory maybe?
Yes, they may be easily faster, since more code may be run in C (in explicit loop all of immediate steps has to be available to interpreter, in one-liner list comprehension it does not have to). There is also overhead of .append method call, method look-up etc. In list comprehension all of that is avoided:
import timeit
def f1():
result = []
for x in range(100):
for y in range(100):
result.append(x * y)
return result
def f2():
return [x * y for y in range(100) for x in range(100)]
print('loop: ', timeit.timeit(f1, number=1000))
print('oneliner:', timeit.timeit(f2, number=1000))
Results (Python 3):
loop: 1.2545137699926272
oneliner: 0.6745600730064325
Depends on the one-liner, some can be much more efficient and very readable.
Take the case of list comprehension. Lets say you want to take all numbers from 1 to 10 and output a list of their product multiplied by 2.
Input: [1,2,3,...,9,10]
Output: [2,4,6,...,18,20]
You can do it in a for loop like so:
output = []
for i in range(1, 11):
output.append(i*2)
Or you can just use list comprehension:
[i*2 for i in range(1,11)]
You'll see the list comprehension is MUCH faster, and also quite readable.
The same can be said for dict comprehension, set comprehension and generator expressions. Also the use of map() and filter() are highly encouraged as long as it's understandable.
For discussion... they all do the same.
'a' a list comprehension... the smoking one-liner...
'b' same thing, but you can provide annotation within a list comprehension... it is still technically a one-liner
'c' the conventional approach.
If speed is a concern, I am less worried about the speed unless, I perform the same task day in day out and it takes a really long time to perform. Comparing speed when you are talking micro or nanoseconds may be of academic interest, but it will not impact the vast majority of users.
I always vote for clarity of expression over compactness of code.
a = [i**2 for i in range(20) if i > 5 and i < 10]
b = [i**2 # do this
for i in range(20) # using these
if (i > 5) and # where this and
(i < 10) # this is good
]
c = []
for i in range(20):
if (i > 5) and (i < 10):
c.append(i**2)
EDIT
The example given of producing the product of a range of numbers, is a good indicator, that the oneliner need not be the issue, but the method used to obtain the result. I will illustrate with determining the product using only 10 values... try it with 100 if you like. I will do it in full format, but could reduce everything to a oneliner if need (import excluded).
>>> import numpy as np
>>> a = np.arange(10)
>>> b = np.arange(10).reshape(10,1)
>>> a
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> b
array([[0],
[1],
[2],
[3],
[4],
[5],
[6],
[7],
[8],
[9]])
>>> a*b
array([[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18],
[ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27],
[ 0, 4, 8, 12, 16, 20, 24, 28, 32, 36],
[ 0, 5, 10, 15, 20, 25, 30, 35, 40, 45],
[ 0, 6, 12, 18, 24, 30, 36, 42, 48, 54],
[ 0, 7, 14, 21, 28, 35, 42, 49, 56, 63],
[ 0, 8, 16, 24, 32, 40, 48, 56, 64, 72],
[ 0, 9, 18, 27, 36, 45, 54, 63, 72, 81]])
or as a one-liner
>>> out = np.arange(10) * np.arange(10).reshape(10,1)
and of course there are built-in functions to do this without the full expression I have shown.
The point being made, speed isn't everything. Clarity of code AND choosing the right tools to do the job should be considered first.
Yes. This is good practice.
Usually experienced programmers use anonymous functions (see, lambda: http://www.secnetix.de/olli/Python/lambda_functions.hawk) in one-line loops and it gives better performance.

Generating a list of prime numbers using list comprehension

I'm trying to create a list of all the prime numbers less than or equal to a given number. I did that successfully using for loops. I was trying to achieve the same using list comprehension using python. But my output has some unexpected values.
Here is my code..
pr=[2]
pr+=[i for i in xrange(3,num+1) if not [x for x in pr if i%x==0]]
where num is the number I had taken as input from user.
The output of the above code for
num=20 is this: [2, 3, 5, 7, 9, 11, 13, 15, 17, 19]
I'm puzzled as to why 9 and 15 are there in the output. What am I doing wrong here?
It simply doesn’t work that way. List comprehensions are evaluated separately, so you can imagine it like this:
pr = [2]
tmp = [i for i in xrange(3,num+1) if not [x for x in pr if i%x==0]]
pr += tmp
By the time tmp is evaluated, pr only contains 2, so you only ever check if a number is divisible by 2 (i.e. if it’s even). That’s why you get all uneven numbers.
You simply can’t solve this nicely† using list comprehensions.
† Not nicely, but ugly and in a very hackish way, by abusing that you can call functions inside a list comprehension:
pr = [2]
[pr.append(i) for i in xrange(3,num+1) if not [x for x in pr if i%x==0]]
print(pr) # [2, 3, 5, 7, 11, 13, 17, 19]
This abuses list comprehensions and basically collects a None value for each prime number you add to pr. So it’s essentially like your normal for loop except that we unnecessarily collect None values in a list… so you should rather allow yourself to use a line break and just use a normal loop.
Your list pr doesn't update until after your entire list comprehension is done. This means your list only contains 2, so every number dividable by 2 is not in the list (as you can see). You should update the list whenever you found a new prime number.
This is because the pr += [...] is evaluated approximately as this:
pr = [2]
tmp = [i for i in xrange(3,num+1) if not [x for x in pr if i%x==0]]
pr.extend(tmp)
So while tmp is generated, contents of pr remains the same ([2]).
I would go with function like this:
>>> import itertools
>>> def primes():
... results = []
... for i in itertools.count(2):
... if all(i%x != 0 for x in results):
... results.append(i)
... yield i
...
# And then you can fetch first 10 primes
>>> list(itertools.islice(primes(), 10))
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
# Or get primes smaller than X
>>> list(itertools.takewhile(lambda x: x < 50, primes()))
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
Note, that using all is more efficient than creating array and testing whether it's empty.

Multiple loop control variables in Python for loop

I came across a situation where I need to implement a for loop with more than one loop control variable. Basically this is what I am trying to do
Java:
for (int i=0,j=n; i<n,j>=0; i++, j--)
do my stuff
How do I do this in Python?
for i in range(0,n), j in range(n-1,-1,-1):
do my stuff
But this doesn't work. What would be the right syntax here? Also, is there a more elegant(pythonic) construct for the use-case?
For your specific example, it doesn't look like you really need separate variables in the loop definition itself. You can just iterate over the i values and construct the j values by doing n-i:
for i in range(0, n):
j = n-i
# do stuff
In general, you can't specify multiple values in the for statement if they depend on each other. Instead, use the for to iterate over some "base" value or values from which the others can be derived.
You can specify multiple values in the for loop, but they must be drawn from a single iterable:
for i, j in zip(range(0, n), range(n, 0, -1)):
# do stuff
This takes i from the first range (0 to n-1) and j from the second (n to 1). zip creates a new iterable by componentwise pairing the elements of the iterables you give it.
The thing to remember is that Python for loops are not like loops in Java/C, which have an initialize/check end condition/update structure that repeatedly modifies some persistent loop index variable. Python for loops iterate over a "stream" of values provided by a "source" iterable, grabbing one value at a time from the source. (This is similar to foreach-type constructs in some other languages.) Whatever you want to iterate over, you need to get it into an iterable before you begin the loop. In other words, every Python for loop can be thought of as roughly analogous to something like:
for (i=iterable.getNextValue(); iterable.isNotEmpty(); i=iterable.getNextValue())
You can't have the loop initialization be different from the loop update, and you can't have those be any operation other than "get the next value", and you can't have the end condition be anything other than "is the iterable exhausted". If you want to do anything like that, you have to either do it yourself inside the loop (e.g., by assigning a secondary "loop variable" as in my example, or by checking for a custom loop exit condition and breaking out), or build it into the "source" that you're iterating over.
A lot depends on iterators you want. Here's a couple of options. What they have in common is that for... in... will traverse over lists, tuples, and anything else which supports iteration. So you could loop over a list of known values or a generator which produces an arbitrary series of values. The for... in... is the same regardless.
Here's some standard python tricks:
nested loops
for i in range(10):
for j in range (10):
print i, j
This is simple and clear, but for complex iterations it may get very deeply nested. Here range is a generator, which means it produces an iteration over a series (in this case, 10 numbers - but it could be any arbitrary stream of values))
zip
for multiple iterators you can use zip() which creates an iterable object that produces a value from each of several of iterables at the same time. You can use multple assignment inside the for loop to grab pieces out of the zip
a = [1,2,3,4]
b = ['a','b','c','d']
for number, letter in zip (a, b):
print letter, ":", number
# a : 1
# b : 2
# c : 3
# d : 4
zip will stop when the first member is exhausted:
a = [1,2]
b = ['a','b','c','d']
for number, letter in zip (a, b):
print letter, ":", number
# a : 1
# b : 2
zip also uses generators:
test = zip (range(10), range(10,20))
for item in test: print item
#(0, 10)
#(1, 11)
#(2, 12)
#(3, 13)
#(4, 14)
#(5, 15)
#(6, 16)
#(7, 17)
#(8, 18)
#(9, 19)
itertools
For more complex iterations there's a lot of great tools in the itertools module This is particularly nice for things like getting all of the products or permutations of multiple iterators. It's worth checking out but I think it's more than you need
You can create a list comprehension using more than one loop control variable:
>>> n = 10
>>> stuff = [i*j for i in range(n) for j in range(n-1,-1,-1)]
>>> stuff
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0, 45, 40, 35, 30, 25, 20, 15, 10, 5, 0, 54, 48, 42, 36, 30, 24, 18, 12, 6, 0, 63, 56, 49, 42, 35, 28, 21, 14, 7, 0, 72, 64, 56, 48, 40, 32, 24, 16, 8, 0, 81, 72, 63, 54, 45, 36, 27, 18, 9, 0]

Defining the length of sequence instead of the step size

I am new to python and want a function which produces a list that contains a number of integers i.e. [1,3,5,7....] like you can do with the range function i.e. range(1,21,2).
However instead of setting the upper limit I want to set how long the list should be, so I would state the starting point, the step and the number of integers I want in my list. Does such a function exist?
No, but it's pretty easy to make one:
def myrange(start, step, count):
return range(start, start + (step * count), step)
short demonstration:
>>> myrange(10, 2, 5)
[10, 12, 14, 16, 18]
>>> myrange(10, -2, 5)
[10, 8, 6, 4, 2]
In python 3 it'll return a range object, just like the regular range() function would:
>>> myrange(10, 2, 5)
range(10, 20, 2)
>>> list(myrange(10, 2, 5))
[10, 12, 14, 16, 18]
Martijn Pieter's answer is good for integers. If start orstep may be floats, you could use a list comprehension:
[start+i*step for i in range(count)]

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