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.
Related
I am trying to solve a assignment where are 13 lights and starting from 1, light is turned off at every 5th light, when the count reaches 13, start from 1st item again. The function should return the order of lights turned off. In this case, for a list of 13 items, the return list would be [5, 10, 2, 8, 1, 9, 4, 13, 12, 3, 7, 11, 6]. Also, turned off lights would not count again.
So the way I was going to approach this problem was to have a list named turnedon, which is [1,2,3,4,5,6,7,8,9,10,11,12,13] and an empty list called orderoff and append to this list whenever a light gets turned off in the turnedon list. So while the turnedon is not empty, iterate through the turnedon list and append the light getting turned off and remove that turnedoff light from the turnedon list, if that makes sense. I cannot figure out what should go into the while loop though. Any idea would be really appreciated.
def orderoff():
n=13
turnedon=[]
for n in range(1,n+1):
turnedon.append(n)
orderoff=[]
while turneon !=[]:
This problem is equivalent to the well-known Josephus problem, in which n prisoners stand in a circle, and they are killed in a sequence where each time, the next person to be killed is k steps around the circle from the previous person; the steps are only counted over the remaining prisoners. A sample solution in Python can be found on the Rosetta code website, which I've adapted slightly below:
def josephus(n, k):
p = list(range(1, n+1))
i = 0
seq = []
while p:
i = (i+k-1) % len(p)
seq.append(p.pop(i))
return seq
Example:
>>> josephus(13, 5)
[5, 10, 2, 8, 1, 9, 4, 13, 12, 3, 7, 11, 6]
This works, but the results are different from yours:
>>> pos = 0
>>> result = []
>>> while len(result) < 13 :
... pos += 5
... pos %= 13
... if pos not in result :
... result.append(pos)
...
>>> result = [i+1 for i in result] # make it 1-based, not 0-based
>>> result
[6, 11, 3, 8, 13, 5, 10, 2, 7, 12, 4, 9, 1]
>>>
I think a more optimal solution would be to use a loop, add the displacement each time, and use modules to keep the number in range
def orderoff(lights_num,step):
turnd_off=[]
num =0
for i in range(max):
num =((num+step-1)%lights_num)+1
turnd_off.append(num)
return turnd_off
print(orderoff(13))
I am using the itertools library module in python.
I am interested the different ways to choose 15 of the first 26000 positive integers. The function itertools.combinations(range(1,26000), 15) enumerates all of these possible subsets, in a lexicographical ordering.
The binomial coefficient 26000 choose 15 is a very large number, on the order of 10^54. However, python has no problem running the code y = itertools.combinations(range(1,26000), 15) as shown in the sixth line below.
If I try to do y[3] to find just the 3rd entry, I get a TypeError. This means I need to convert it into a list first. The problem is that trying to convert it into a list gives a MemoryError. All of this is shown in the screenshot above.
Converting it into a list does work for smaller combinations, like 6 choose 3, shown below.
My question is:
Is there a way to access specific elements in itertools.combinations() without converting it into a list?
I want to be able to access, say, the first 10000 of these ~10^54 enumerated 15-element subsets.
Any help is appreciated. Thank you!
You can use a generator expression:
comb = itertools.combinations(range(1,26000), 15)
comb1000 = (next(comb) for i in range(1000))
To jump directly to the nth combination, here is an itertools recipe:
def nth_combination(iterable, r, index):
"""Equivalent to list(combinations(iterable, r))[index]"""
pool = tuple(iterable)
n = len(pool)
if r < 0 or r > n:
raise ValueError
c = 1
k = min(r, n-r)
for i in range(1, k+1):
c = c * (n - k + i) // i
if index < 0:
index += c
if index < 0 or index >= c:
raise IndexError
result = []
while r:
c, n, r = c*r//n, n-1, r-1
while index >= c:
index -= c
c, n = c*(n-r)//n, n-1
result.append(pool[-1-n])
return tuple(result)
It's also available in more_itertools.nth_combination
>>> import more_itertools # pip install more-itertools
>>> more_itertools.nth_combination(range(1,26000), 15, 123456)
(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 19541)
To instantly "fast-forward" a combinations instance to this position and continue iterating, you can set the state to the previously yielded state (note: 0-based state vector) and continue from there:
>>> comb = itertools.combinations(range(1,26000), 15)
>>> comb.__setstate__((0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 19540))
>>> next(comb)
(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 19542)
If you want to access the first few elements, it's pretty straightforward with islice:
import itertools
print(list(itertools.islice(itertools.combinations(range(1,26000), 15), 1000)))
Note that islice internally iterates the combinations up to the specified point, so it can't magically give you the middle elements without iterating all the way there. You'd have to go down the route of computing the elements you want combinatorially in that case.
I have an assignment to add a value to a sorted list using list comprehension. I'm not allowed to import modules, only list comprehension, preferably a one liner. I'm not allowed to create functions and use them aswell.
I'm completely in the dark with this problem. Hopefully someone can help :)
Edit: I don't need to mutate the current list. In fact, I'm trying my solution right now with .pop, I need to create a new list with the element properly added, but I still can't figure out much.
try:
sorted_a.insert(next(i for i,lhs,rhs in enumerate(zip(sorted_a,sorted_a[1:])) if lhs <= value <= rhs),value)
except StopIteration:
sorted_a.append(value)
I guess ....
with your new problem statement
[x for x in sorted_a if x <= value] + [value,] + [y for y in sorted_a if y >= value]
you could certainly improve the big-O complexity
For bisecting the list, you may use bisect.bisect (for other readers referencing the answer in future) as:
>>> from bisect import bisect
>>> my_list = [2, 4, 6, 9, 10, 15, 18, 20]
>>> num = 12
>>> index = bisect(my_list, num)
>>> my_list[:index]+[num] + my_list[index:]
[2, 4, 6, 9, 10, 12, 15, 18, 20]
But since you can not import libraries, you may use sum and zip with list comprehension expression as:
>>> my_list = [2, 4, 6, 9, 10, 15, 18, 20]
>>> num = 12
>>> sum([[i, num] if i<num<j else [i] for i, j in zip(my_list,my_list[1:])], [])
[2, 4, 6, 9, 10, 12, 15, 18]
Suppose I have a list:
a = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
I want to write a program that prints out all the elements of the list that are less than 10.
Actually its pretty simple I got this program but, I need to do it in a single line and I've no idea how to do that. Need some help with this.
print [x for x in a if x < 10]
Take a further look at lambda functions, I feel this is what you are looking for.
So in order to print something out of a list that is less than 10 In the same line, first you need to create a list:
numbers = []
loop through every single element of the list
for i in a:
And then you need a If statement to check if the element is less than 10
if i < 10:
Append the number to the list
numbers.append(str(i))
Join the results together:
result = " ".join(numbers)
And lastly printing it out
print(result)
And if you combine everything together, this is what you should get:
a = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
numbers = []
for i in a:
if i < 10:
numbers.append(str(i))
result = " ".join(numbers)
print(result)
The result should be:
1 1 2 3 5 8
Hey im new to python. How do you get a portion of a list by the relative value of its sorting key.
example...
list = [11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10]
list.sort()
newList = list.split("all numbers that are over 13")
assert newList == [14,15,16]
>>> l = [11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10]
>>> sorted(x for x in l if x > 13)
[14, 15, 16]
or with filter (would be a little bit slower if you have big list, because of lambda)
>>> sorted(filter(lambda x: x > 13, l))
[14, 15, 16]
Use [item for item in newList if item > 13].
There is a decent chance this could be replaced with the generator expression (item for item in newList if item > 13), which filters lazily rather than storing the whole list in memory.
You might also be interested in changing the code just a bit to something like
all_numbers = [11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
filtered_sorted_numbers = sorted(number for number in all_numbers if number > 13)
which performs the sorting—a worst case O(n log n) operation—on only the filtered values.