Python: Finding symmetries in list of lists - python

I'm having a problem with 'symmetries' and I hope you can help.
I have a list which looks like
list = [[1,2,3,4,5,6],[2,4,6,8,10,12],[1,4,5,2,3,6],[1,2,3,4,9,3]]
and I want to identify symmetries of each element in this list. In this example if I look at the first element (= i) in the list and switch i[1:3] with i[3:5], then I want to search the rest of the list for matches. We can see that the list[3] matches i after the switch.
Can you help me write a fast solution for this? For example:
I have a function to switch elements which looks like:
def switch(i):
i[1:3], i[3:5] = i[3:5],i[1:3]
return i
and then I have a loop which looks like
no_sym = []
for i in list:
sym = [x for x in list if x not in no_sym and not no_sym.append(switch(i))]
continue
but this is not working for me.
Help!

You should not have append in this line:
sym = [x for x in list if x not in no_sym and not no_sym.append(switch(i))]
foo.append(bar) returns None, and so the code is equivalent to [x for x in list if x not in no_sym and not None], which allows every item not in no_sym to make it into sym.
Also, your swtich function actually modifies its arguments, which is probably no what you want. Check:
>>> ls = [[1,2,3,4,5,6], [2,4,6,8,10,12], [1,4,5,2,3,6], [1,2,3,4,9,3]]
>>> switch(ls[0]) == ls[2] # seems harmless
True
>>> switch(ls[0]) == ls[2] # but ls[0] has been modified, so the next test fails
False
To avoid this, switch should make a copy of the argument list:
def switch(ls):
copy_ls = ls[:]
copy_ls[1:3], copy_ls[3:5] = copy_ls[3:5], copy_ls[1:3]
return copy_ls
Now if you want every item and its "symmetrical" brother as a tuple in sym, this will work:
>>> ls = [[1,2,3,4,5,6], [2,4,6,8,10,12], [1,4,5,2,3,6], [1,2,3,4,9,3]]
>>> sym = [(x, switch(x)) for x in ls if switch(x) in ls[ls.index(x)+1:]]
>>> sym
[([1, 2, 3, 4, 5, 6], [1, 4, 5, 2, 3, 6])]
Also you should probably not use list as a variable name because it would shadow a builtin.

I think you not write the switch right.And I exactly do not understand why
you use (not no_sym.append(switch(i))).

In your example, it seems that you assume the index starts with 1. Actually, the index starts with 0. Therefore, your switch function should look like
def switch(i):
i[1:3], i[3:5] = i[3:5], i[1:3]
return i
Also, you need to provide more concrete definition of your 'symmetries'. Is your definition is something like 'tuples a and b are symmetry if len(a) = len(b) and either a[i] == b[i] && a[-(i+1)] == b[-(i+1)] or a[i] == b[-(i+1)] && a[-(i+1)]==b[i] for i >=0 and i

Here is what you want. I'm not sure if I understood what did you mean by "symmetry"
_list = [[1,2,3,4,5,6],[2,4,6,8,10,12],[1,4,5,2,3,6],[1,2,3,4,9,3]]
def switch(i):
result = i[:]
result[1:3], result[3:5] = result[3:5], result[1:3]
return result
sym = [(x, switch(x)) for x in _list if switch(x) in _list]
print sym
[([1, 2, 3, 4, 5, 6], [1, 4, 5, 2, 3, 6]), ([1, 4, 5, 2, 3, 6], [1, 2, 3, 4, 5, 6])]

Related

How to calculate a cumulative product of a list using list comprehension

I'm trying my hand at converting the following loop to a comprehension.
Problem is given an input_list = [1, 2, 3, 4, 5]
return a list with each element as multiple of all elements till that index starting from left to right.
Hence return list would be [1, 2, 6, 24, 120].
The normal loop I have (and it's working):
l2r = list()
for i in range(lst_len):
if i == 0:
l2r.append(lst_num[i])
else:
l2r.append(lst_num[i] * l2r[i-1])
Python 3.8+ solution:
:= Assignment Expressions
lst = [1, 2, 3, 4, 5]
curr = 1
out = [(curr:=curr*v) for v in lst]
print(out)
Prints:
[1, 2, 6, 24, 120]
Other solution (with itertools.accumulate):
from itertools import accumulate
out = [*accumulate(lst, lambda a, b: a*b)]
print(out)
Well, you could do it like this(a):
import math
orig = [1, 2, 3, 4, 5]
print([math.prod(orig[:pos]) for pos in range(1, len(orig) + 1)])
This generates what you wanted:
[1, 2, 6, 24, 120]
and basically works by running a counter from 1 to the size of the list, at each point working out the product of all terms before that position:
pos values prod
=== ========= ====
1 1 1
2 1,2 2
3 1,2,3 6
4 1,2,3,4 24
5 1,2,3,4,5 120
(a) Just keep in mind that's less efficient at runtime since it calculates the full product for every single element (rather than caching the most recently obtained product). You can avoid that while still making your code more compact (often the reason for using list comprehensions), with something like:
def listToListOfProds(orig):
curr = 1
newList = []
for item in orig:
curr *= item
newList.append(curr)
return newList
print(listToListOfProds([1, 2, 3, 4, 5]))
That's obviously not a list comprehension but still has the advantages in that it doesn't clutter up your code where you need to calculate it.
People seem to often discount the function solution in Python, simply because the language is so expressive and allows things like list comprehensions to do a lot of work in minimal source code.
But, other than the function itself, this solution has the same advantages of a one-line list comprehension in that it, well, takes up one line :-)
In addition, you're free to change the function whenever you want (if you find a better way in a later Python version, for example), without having to change all the different places in the code that call it.
This should not be made into a list comprehension if one iteration depends on the state of an earlier one!
If the goal is a one-liner, then there are lots of solutions with #AndrejKesely's itertools.accumulate() being an excellent one (+1). Here's mine that abuses functools.reduce():
from functools import reduce
lst = [1, 2, 3, 4, 5]
print(reduce(lambda x, y: x + [x[-1] * y], lst, [lst.pop(0)]))
But as far as list comprehensions go, #AndrejKesely's assignment-expression-based solution is the wrong thing to do (-1). Here's a more self contained comprehension that doesn't leak into the surrounding scope:
lst = [1, 2, 3, 4, 5]
seq = [a.append(a[-1] * b) or a.pop(0) for a in [[lst.pop(0)]] for b in [*lst, 1]]
print(seq)
But it's still the wrong thing to do! This is based on a similar problem that also got upvoted for the wrong reasons.
A recursive function could help.
input_list = [ 1, 2, 3, 4, 5]
def cumprod(ls, i=None):
i = len(ls)-1 if i is None else i
if i == 0:
return 1
return ls[i] * cumprod(ls, i-1)
output_list = [cumprod(input_list, i) for i in range(len(input_list))]
output_list has value [1, 2, 6, 24, 120]
This method can be compressed in python3.8 using the walrus operator
input_list = [ 1, 2, 3, 4, 5]
def cumprod_inline(ls, i=None):
return 1 if (i := len(ls)-1 if i is None else i) == 0 else ls[i] * cumprod_inline(ls, i-1)
output_list = [cumprod_inline(input_list, i) for i in range(len(input_list))]
output_list has value [1, 2, 6, 24, 120]
Because you plan to use this in list comprehension, there's no need to provide a default for the i argument. This removes the need to check if i is None.
input_list = [ 1, 2, 3, 4, 5]
def cumprod_inline_nodefault(ls, i):
return 1 if i == 0 else ls[i] * cumprod_inline_nodefault(ls, i-1)
output_list = [cumprod_inline_nodefault(input_list, i) for i in range(len(input_list))]
output_list has value [1, 2, 6, 24, 120]
Finally, if you really wanted to keep it to a single , self-contained list comprehension line, you can follow the approach note here to use recursive lambda calls
input_list = [ 1, 2, 3, 4, 5]
output_list = [(lambda func, x, y: func(func,x,y))(lambda func, ls, i: 1 if i == 0 else ls[i] * func(func, ls, i-1),input_list,i) for i in range(len(input_list))]
output_list has value [1, 2, 6, 24, 120]
It's entirely over-engineered, and barely legible, but hey! it works and its just for fun.
For your list, it might not be intentional that the numbers are consecutive, starting from 1. But for cases that that pattern is intentional, you can use the built in method, factorial():
from math import factorial
input_list = [1, 2, 3, 4, 5]
l2r = [factorial(i) for i in input_list]
print(l2r)
Output:
[1, 2, 6, 24, 120]
The package numpy has a number of fast implementations of list comprehensions built into it. To obtain, for example, a cumulative product:
>>> import numpy as np
>>> np.cumprod([1, 2, 3, 4, 5])
array([ 1, 2, 6, 24, 120])
The above returns a numpy array. If you are not familiar with numpy, you may prefer to obtain just a normal python list:
>>> list(np.cumprod([1, 2, 3, 4, 5]))
[1, 2, 6, 24, 120]
using itertools and operators:
from itertools import accumulate
import operator as op
ip_lst = [1,2,3,4,5]
print(list(accumulate(ip_lst, func=op.mul)))

Function that compares 1st and last element, 2nd and 2nd last element, and so on

I want to write a function that compares the first element of this list with the last element of this list, the second element of this list with the second last element of this list, and so on. If the compared elements are the same, I want to add the element to a new list. Finally, I'd like to print this new list.
For example,
>>> f([1,5,7,7,8,1])
[1,7]
>>> f([3,1,4,1,5]
[1,4]
>>> f([2,3,5,7,1,3,5])
[3,7]
I was thinking to take the first (i) and last (k) element, compare them, then raise i but lower k, then repeat the process. When i and k 'overlap', stop, and print the list. I've tried to visualise my thoughts in the following code:
def f(x):
newlist=[]
k=len(x)-1
i=0
for j in x:
if x[i]==x[k]:
if i<k:
newlist.append(x[i])
i=i+1
k=k-1
print(newlist)
Please let me know if there are any errors in my code, or if there is a more suitable way to address the problem.
As I am new to Python, I am not very good with understanding complicated terminology/features of Python. As such, it would be encouraged if you took this into account in your answer.
You could use a conditional list comprehension with enumerate, comparing the element x at index i to the element at index -1-i (-1 being the last index of the list):
>>> lst = [1,5,7,7,8,1]
>>> [x for i, x in enumerate(lst[:(len(lst)+1)//2]) if lst[-1-i] == x]
[1, 7]
>>> lst = [3,1,4,1,5]
>>> [x for i, x in enumerate(lst[:(len(lst)+1)//2]) if lst[-1-i] == x]
[1, 4]
Or, as already suggested in other answers, use zip. However, it is enough to slice the first argument; the second one can just be the reversed list, as zip will stop once one of the argument lists is finished, making the code a bit shorter.
>>> [x for x, y in zip(lst[:(len(lst)+1)//2], reversed(lst)) if x == y]
In both approaches, (len(lst)+1)//2 is equivalent to int(math.ceil(len(lst)/2)).
maybe you want something like for even length of list:
>>> r=[l[i] for i in range(len(l)/2) if l[i]==l[-(i+1)]]
>>> r
[3]
>>> l=[1,5,7,7,8,1]
>>> r=[l[i] for i in range(len(l)/2) if l[i]==l[-(i+1)]]
>>> r
[1, 7]
And for odd length of list :
>>> l=[3,1,4,1,5]
>>> r=[l[i] for i in range(len(l)/2+1) if l[i]==l[-(i+1)]]
>>> r
[1, 4]
so you can create a function :
def myfunc(mylist):
if (len(mylist) % 2 == 0):
return [l[i] for i in range(len(l)/2) if l[i]==l[-(i+1)]]
else:
return [l[i] for i in range(len(l)/2+1) if l[i]==l[-(i+1)]]
and use it this way :
>>> l=[1,5,7,7,8,1]
>>> myfunc(l)
[1, 7]
>>> l=[3,1,4,1,5]
>>> myfunc(l)
[1, 4]
What you can do is zip over the first half and the second half reversed and use list comprehensions to build a list of the same ones:
[element_1 for element_1, element_2 in zip(l[:len(l)//2], reversed(l[(len(l)+1)//2:])) if element_1 == element_2]
What happens is that you take the first half and iterate over those as element_1, the second half reversed as element_2 and then only add them if they are the same:
l = [1, 2, 3, 3, 2, 4]
l[:len(l)//2] == [1, 2, 3]
reversed(l[(len(l)+1)//2:])) == [4, 2, 3]
1 != 4, 2 == 2, 3 == 3, result == [2, 3]
If you also want to include the middle element in the case of an odd list, we can just extend our lists to both include the middle element, which will always evaluate as the same:
[element_1 for element_1, element_2 in zip(l[:(len(l) + 1)//2], reversed(l[len(l)//2:])) if element_1 == element_2]
l = [3, 1, 4, 1, 5]
l[:len(l)//2] == [3, 1, 4]
reversed(l[(len(l)+1)//2:])) == [5, 1, 4]
3 != 5, 1 == 1, 4 == 4, result == [1, 4]
Here is my solution:
[el1 for (el1, el2) in zip(L[:len(L)//2+1], L[len(L)//2:][::-1]) if el1==el2]
There is a lot going on, so let me explain step by step:
L[:len(L)//2+1] is the first half of the list plus an extra element (which is useful for lists of odd lengths)
L[len(L)//2:][::-1] is the second half of the list, reversed ([::-1])
zip creates a list of pairs from two lists. it stops at the end of the shortest list. We use this in the case the length of the list is even, so the extra term in the first half is neglected
List comprehension essentially equivalent to a for loop, but useful to create a list "on the fly". It will return an element only if the if condition is true, otherwise it will pass.
You can easily modify the solution above if you are interested in the indexes (of the first half) where the match occurs:
[idx for idx, (el1, el2) in enumerate(zip(L[:len(L)//2+1], L[len(L)//2:][::-1])) if el1==el2]
You can use the following which leverages from zip_longest:
from itertools import zip_longest
def compare(lst):
size = len(lst) // 2
return [y for x, y in zip_longest(lst[:size], lst[-1:size-1:-1], fillvalue=None) if x == y or x is None]
print(compare([1, 5, 7, 7, 8, 1])) # [1, 7]
print(compare([3, 1, 4, 1, 5])) # [1, 4]
print(compare([2, 3, 5, 7, 1, 3, 5])) # [3, 7]
On zip_longest:
Normally, zip stops zipping when one of its iterators run out. zip_longest does not have that limitation and it simply keeps on zipping by adding dummy values.
Example:
list(zip([1, 2, 3], ['a'])) # [(1, 'a')]
list(zip_longest([1, 2, 3], ['a'], fillvalue='z')) # [(1, 'a'), (2, 'z'), (3, 'z')]

Using list comprehensions to make a funcion more pythonic

I'm doing some Google Python Class exercises and I'm trying to find a pythonic solution to the following problem.
D. Given a list of numbers, return a list where all adjacent ==
elements have been reduced to a single element, so [1, 2, 2, 3]
returns [1, 2, 3]. You may create a new list or modify the passed in
list.
My try, which is working perfectly is the following:
def remove_adjacent(nums):
result = []
for num in nums:
if len(result) == 0 or num != result[-1]:
result.append(num)
return result
For example, with remove_adjacent([2, 2, 3, 3, 3]) the output is [2, 3]. Everything's ok.
I'm trying to use list comprehensions in order to archieve this in a more pythonic way, so my try is the following:
def remove_adjacent(nums):
result = []
result = [num for num in nums if (len(result)==0 or num!=result[-1])]
return result
This, with the same input [2, 2, 3, 3, 3], the output is [2, 2, 3, 3, 3] (the same). Meeeh! Wrong.
What I'm doing wrong with the list comprehensions? Am I trying to do something which is impossible to do with list comprehensions? I know it's a bit weird to initialize the list (result = []), so maybe it's not posible to do it using list comprehensions in this case.
Am I trying to do something which is impossible to do with list comprehensions?
Yep. A list comprehension can't refer to itself by name, because the variable doesn't get bound at all until the comprehension is completely done evaluating. That's why you get a NameError if you don't have result = [] in your second code block.
If it's not cheating to use standard modules, consider using groupby to group together similar values in your list:
>>> import itertools
>>> seq = [1, 2, 2, 3]
>>> [k for k,v in itertools.groupby(seq)]
[1, 2, 3]
>>> seq = [2,2,3,3,3]
>>> [k for k,v in itertools.groupby(seq)]
[2, 3]
For the sake of learning, I'd suggest using core reduce function:
def remove_adjacent(lst):
return reduce(lambda x, y: x+[y] if not x or x[-1] != y else x, lst, [])

creating a sublist from a list in python

please help me, i want to write a function that takes a list as an argument and returns a new list of elements that appear more than once from the original list. I tried writing it this way but it doesn't give me the answer
def list(n):
l = [ ]
for s in n:
if n.count(s) > 1:
l.append(s)
return l
return None
You're close. You need to remove the return statement from the for loop. As it is, you return unconditionally after the first element.
def list(n):
l = []
for s in n:
if n.count(s) > 1:
l.append(s)
return l
Second, I highly recommend that you don't use list as the name of this function as then you shadow the builtin list function which is very useful.
You can use filter() function to do that.
This is not the most fast for CPU but laconic and pythonic enough.
my_list = [1, 2, 2, 3, 4, 4, 5, 5, 6, 7]
print filter(lambda x: my_list.count(x) > 1, my_list)
DEMO #1
Also you can use a list comprehension as 6502 mentioned:
my_list = [1, 2, 2, 3, 4, 4, 5, 5, 6, 7]
print [x for x in my_list if my_list.count(x) > 1]
DEMO #2
def list_duplicates(seq):
seen = set()
seen_add = seen.add
#adds all elements it doesn't know yet to seen and all other to seen_twice
seen_twice = set( x for x in seq if x in seen or seen_add(x) )
# turn the set into a list (as requested)
return list( seen_twice )
a = [1,2,3,2,1,5,6,5,5,5]
list_duplicates(a)
This will print
[1,2,5]
I think solution of Eugene Naydenov is good, but I some enhance it:
In [1]: my_list = [1, 2, 2, 3, 4, 4, 5, 5, 6, 7];
In [2]: set_list = lambda(lst) : list(set(i for i in filter(lambda x: my_list.count(x) > 1, lst))) #set_list is function
In [3]: set_list(my_list)
Out[3]: [2, 4, 5]

concatenate an arbitrary number of lists in a function in Python

I hope to write the join_lists function to take an arbitrary number of lists and concatenate them. For example, if the inputs are
m = [1, 2, 3]
n = [4, 5, 6]
o = [7, 8, 9]
then we I call print join_lists(m, n, o), it will return [1, 2, 3, 4, 5, 6, 7, 8, 9]. I realize I should use *args as the argument in join_lists, but not sure how to concatenate an arbitrary number of lists. Thanks.
Although you can use something which invokes __add__ sequentially, that is very much the wrong thing (for starters you end up creating as many new lists as there are lists in your input, which ends up having quadratic complexity).
The standard tool is itertools.chain:
def concatenate(*lists):
return itertools.chain(*lists)
or
def concatenate(*lists):
return itertools.chain.from_iterable(lists)
This will return a generator which yields each element of the lists in sequence. If you need it as a list, use list: list(itertools.chain.from_iterable(lists))
If you insist on doing this "by hand", then use extend:
def concatenate(*lists):
newlist = []
for l in lists: newlist.extend(l)
return newlist
Actually, don't use extend like that - it's still inefficient, because it has to keep extending the original list. The "right" way (it's still really the wrong way):
def concatenate(*lists):
lengths = map(len,lists)
newlen = sum(lengths)
newlist = [None]*newlen
start = 0
end = 0
for l,n in zip(lists,lengths):
end+=n
newlist[start:end] = list
start+=n
return newlist
http://ideone.com/Mi3UyL
You'll note that this still ends up doing as many copy operations as there are total slots in the lists. So, this isn't any better than using list(chain.from_iterable(lists)), and is probably worse, because list can make use of optimisations at the C level.
Finally, here's a version using extend (suboptimal) in one line, using reduce:
concatenate = lambda *lists: reduce((lambda a,b: a.extend(b) or a),lists,[])
One way would be this (using reduce) because I currently feel functional:
import operator
from functools import reduce
def concatenate(*lists):
return reduce(operator.add, lists)
However, a better functional method is given in Marcin's answer:
from itertools import chain
def concatenate(*lists):
return chain(*lists)
although you might as well use itertools.chain(*iterable_of_lists) directly.
A procedural way:
def concatenate(*lists):
new_list = []
for i in lists:
new_list.extend(i)
return new_list
A golfed version: j=lambda*x:sum(x,[]) (do not actually use this).
You can use sum() with an empty list as the start argument:
def join_lists(*lists):
return sum(lists, [])
For example:
>>> join_lists([1, 2, 3], [4, 5, 6])
[1, 2, 3, 4, 5, 6]
Another way:
>>> m = [1, 2, 3]
>>> n = [4, 5, 6]
>>> o = [7, 8, 9]
>>> p = []
>>> for (i, j, k) in (m, n, o):
... p.append(i)
... p.append(j)
... p.append(k)
...
>>> p
[1, 2, 3, 4, 5, 6, 7, 8, 9]
>>>
This seems to work just fine:
def join_lists(*args):
output = []
for lst in args:
output += lst
return output
It returns a new list with all the items of the previous lists. Is using + not appropriate for this kind of list processing?
Or you could be logical instead, making a variable (here 'z') equal to the first list passed to the 'join_lists' function
then assigning the items in the list (not the list itself) to a new list to which you'll then be able add the elements of the other lists:
m = [1, 2, 3]
n = [4, 5, 6]
o = [7, 8, 9]
def join_lists(*x):
z = [x[0]]
for i in range(len(z)):
new_list = z[i]
for item in x:
if item != z:
new_list += (item)
return new_list
then
print (join_lists(m, n ,o)
would output:
[1, 2, 3, 4, 5, 6, 7, 8, 9]

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