Pythonic way of getting hierarchy of elements in numeric list - python

I have a numeric list a and I want to output a list with the hierarchical position of every element in a (0 for the highest value, 1 for the second-highest, etc).
I want to know if this is the most Pythonic and efficient way to do this. Perhaps there is a better way?
a = [3,5,6,25,-3,100]
b = sorted(a)
b = b[::-1]
[b.index(i) for i in a]

#ThierryLathuille's answer works only if there are no duplicates in the input list since the answer relies on a dict with the list values as keys. If there can be duplicates in the list, you should sort the items in the input list with their indices generated by enumerate, and map those indices to their sorted positions instead:
from operator import itemgetter
mapping = dict(zip(map(itemgetter(0), sorted(enumerate(a), key=itemgetter(1), reverse=True)), range(len(a))))
mapping becomes:
{5: 0, 3: 1, 2: 2, 1: 3, 0: 4, 4: 5}
so that you can then iterate an index over the length of the list to obtain the sorted positions in order:
[mapping[i] for i in range(len(a))]
which returns:
[4, 3, 2, 1, 5, 0]

You could also you numpy.argsort(-a) (-a because argsort assumes ascending order). It could have better performance for large arrays (though there's no official analysis that I know of).

One problem with your solution is the repeated use of index, that will make your final comprehension O(n**2), as index has to go over the sorted list each time.
It would be more efficient to build a dict with the rank of each value in the sorted list:
a = [3,5,6,25,-3,100]
ranks = {val:idx for idx, val in enumerate(sorted(a, reverse=True))}
# {100: 0, 25: 1, 6: 2, 5: 3, 3: 4, -3: 5}
out = [ranks[val] for val in a]
print(out)
# [4, 3, 2, 1, 5, 0]
in order to have a final step in O(n).

First, zip the list with a with range(len(a)) to create a list of tuples (of element and their positions), sort this list in reverse order, zip this with range(len(a)) to mark the positions of each element after the sort, now unsort this list (by sorting this based on the original position of each element), and finally grab the position of each element when it was sorted
>>> a = [3,5,6,25,-3,100]
>>> [i for _,i in sorted(zip(sorted(zip(a, range(len(a))), reverse=True), range(len(a))), key=lambda t:t[0][1])]
[4, 3, 2, 1, 5, 0]

Related

How to print non repeating elements with original list

given a list of integers nums, return a list of all the element but the repeating number should not be printed more than twice
example
input: nums = [1,1,2,3,3,4,4,4,5]
output: [1,1,2,3,3,4,4,5]
A more flexible implementation using itertools:
from itertools import islice, groupby, chain
nums = [1,1,2,3,3,4,4,4,5]
output = (islice(g, 2) for _, g in groupby(nums))
output = list(chain.from_iterable(output))
print(output) # [1, 1, 2, 3, 3, 4, 4, 5]
You can replace 2 in islice(g, 2) to tune the max repeats you want.
The easiest and I guess most straight forward way to use unique collections is with a set:
list(set(nums)) -> [1, 2, 3, 4, 5]
The downside of this approuch is that sets are unordered. And we cannot really depend on how the list will be sorted after the conversion.
If order is important in your case you can do this:
list(dict.fromkeys(nums))
[1, 2, 3, 4, 5]
dicts are ordered since python3 came out, and their keys are unique. So with this small trick we get a list of the unique keys of a dictionary, but still maitain the original order!

Is there a function to convert a int list to a list that shows the smallest-to-largest order of the list? [duplicate]

This question already has answers here:
Sorting list based on values from another list
(20 answers)
Closed 3 years ago.
I need a function that turns a list like
[10,5,2,3,7]
to a list like
[4,2,0,1,3]
Basically a list [0,1,2,3,4...] but arranged in the order that the original list has, smallest to biggest.
I have no idea where to even start on a function like this. I have Python 3.5.2.
hiro protagonist's answer was close, but he indexed the wrong list.
>>> data = [10,5,2,3,7]
>>> sorted_list = sorted(data)
>>> [sorted_list.index(item) for item in data]
[4, 2, 0, 1, 3]
This wouldn't account for cases where you want to account for multiple occurrences and whatnot, but I'm not sure if that's required in your case.
Try this:
>>> d = [10, 5, 2, 3, 7]
>>> [sorted(d).index(i) for i in d]
[4, 2, 0, 1, 3]
This solution would work; however, there is probably a solution that is more space efficient. This solution does allow for repeat elements though.
l1 = [10, 5, 2, 3, 7] # Your list
l2 = sorted(l1) # Get the sorted version of our list.
# A dictionary containing each element and a list of the indices where they are found
element_indices = {}
for index, element in enumerate(l2):
if element not in element_indices:
element_indices[element] = [index] # Store the index for each element when it is sorted
else: # We have seen this element before
element_indices[element].append(index)
l2 = [element_indices[value].pop() for value in l1] # Change each element to its sorted equivalent index
print(l2) # [4, 2, 0, 1, 3]

Converting a list of "pairs" into a dictionary of dictionaries?

This question was previously asked here with an egregious typo: Counting "unique pairs" of numbers into a python dictionary?
This is an algorithmic problem, and I don't know of the most efficient solution. My idea would be to somehow cache values in a list and enumerate pairs...but that would be so slow. I'm guessing there's something useful from itertools.
Let's say I have a list of integers whereby are never repeats:
list1 = [2, 3]
In this case, there is a unique pair 2-3 and 3-2, so the dictionary should be:
{2:{3: 1}, 3:{2: 1}}
That is, there is 1 pair of 2-3 and 1 pair of 3-2.
For larger lists, the pairing is the same, e.g.
list2 = [2, 3, 4]
has the dicitonary
{2:{3:1, 4:1}, 3:{2:1, 4:1}, 4:{3:1, 2:1}}
(1) Once the size of the lists become far larger, how would one algorithmically find the "unique pairs" in this format using python data structures?
(2) I mentioned that the lists cannot have repeat integers, e.g.
[2, 2, 3]
is impossible, as there are two 2s.
However, one may have a list of lists:
list3 = [[2, 3], [2, 3, 4]]
whereby the dictionary must be
{2:{3:2, 4:1}, 3:{2:2, 4:1}, 4:{2:1, 3:1}}
as there are two pairs of 2-3 and 3-2. How would one "update" the dictionary given multiple lists within a list?
EDIT: My ultimate use case is, I want to iterate through hundreds of lists of integers, and create a single dictionary with the "counts" of pairs. Does this make sense? There might be another data structure which is more useful.
For the nested list example, you can do the following, making use of itertools.permutations and dict.setdefault:
from itertools import permutations
list3 = [[2, 3], [2, 3, 4]]
d = {}
for l in list3:
for a, b in permutations(l, 2):
d[a][b] = d.setdefault(a, {}).setdefault(b, 0) + 1
# {2: {3: 2, 4: 1}, 3: {2: 2, 4: 1}, 4: {2: 1, 3: 1}}
For flat lists l, use only the inner loop and omit the outer one
For this example I'll just use a list with straight numbers and no nested list:
values = [3, 2, 4]
result = dict.from_keys(values)
for key, value in result.items():
value = {}
for num in values:
if num != key:
value[num] = 1
This creates a dict with each number as a key. Now in each key, make the value a nested dict who's contents are num: 1 for each number in the original values list if it isn't the name of the key that we're in
use defaultdict with permutations
from collections import defaultdict
from itertools import permutations
d = defaultdict(dict)
for i in [x for x in permutations([4,2,3])]:
d[i[0]] = {k: 1 for k in i[1:]}
output is
In [22]: d
Out[22]: defaultdict(dict, {2: {3: 1, 4: 1}, 4: {2: 1, 3: 1}, 3: {2: 1, 4: 1}})
for inherit list of lists https://stackoverflow.com/a/52206554/8060120

list match in python: get indices of a sub-list in a larger list

For two lists,
a = [1, 2, 9, 3, 8, ...] (no duplicate values in a, but a is very big)
b = [1, 9, 1,...] (set(b) is a subset of set(a), 1<<len(b)<<len(a))
indices = get_indices_of_a(a, b)
how to let get_indices_of_a return indices = [0, 2, 0,...] with array(a)[indices] = b? Is there a faster method than using a.index, which is taking too long?
Making b a set is a fast method of matching lists and returning indices (see compare two lists in python and return indices of matched values ), but it will lose the index of the second 1 as well as the sequence of the indices in this case.
A fast method (when a is a large list) would be using a dict to map values in a to indices:
>>> index_dict = dict((value, idx) for idx,value in enumerate(a))
>>> [index_dict[x] for x in b]
[0, 2, 0]
This will take linear time in the average case, compared to using a.index which would take quadratic time.
Presuming we are working with smaller lists, this is as easy as:
>>> a = [1, 2, 9, 3, 8]
>>> b = [1, 9, 1]
>>> [a.index(item) for item in b]
[0, 2, 0]
On larger lists, this will become quite expensive.
(If there are duplicates, the first occurrence will always be the one referenced in the resulting list, if not set(b) <= set(a), you will get a ValueError).

How to get indices of a sorted array in Python

I have a numerical list:
myList = [1, 2, 3, 100, 5]
Now if I sort this list to obtain [1, 2, 3, 5, 100].
What I want is the indices of the elements from the
original list in the sorted order i.e. [0, 1, 2, 4, 3]
--- ala MATLAB's sort function that returns both
values and indices.
If you are using numpy, you have the argsort() function available:
>>> import numpy
>>> numpy.argsort(myList)
array([0, 1, 2, 4, 3])
http://docs.scipy.org/doc/numpy/reference/generated/numpy.argsort.html
This returns the arguments that would sort the array or list.
Something like next:
>>> myList = [1, 2, 3, 100, 5]
>>> [i[0] for i in sorted(enumerate(myList), key=lambda x:x[1])]
[0, 1, 2, 4, 3]
enumerate(myList) gives you a list containing tuples of (index, value):
[(0, 1), (1, 2), (2, 3), (3, 100), (4, 5)]
You sort the list by passing it to sorted and specifying a function to extract the sort key (the second element of each tuple; that's what the lambda is for. Finally, the original index of each sorted element is extracted using the [i[0] for i in ...] list comprehension.
myList = [1, 2, 3, 100, 5]
sorted(range(len(myList)),key=myList.__getitem__)
[0, 1, 2, 4, 3]
I did a quick performance check on these with perfplot (a project of mine) and found that it's hard to recommend anything else but
np.argsort(x)
(note the log scale):
Code to reproduce the plot:
import perfplot
import numpy as np
def sorted_enumerate(seq):
return [i for (v, i) in sorted((v, i) for (i, v) in enumerate(seq))]
def sorted_enumerate_key(seq):
return [x for x, y in sorted(enumerate(seq), key=lambda x: x[1])]
def sorted_range(seq):
return sorted(range(len(seq)), key=seq.__getitem__)
b = perfplot.bench(
setup=np.random.rand,
kernels=[sorted_enumerate, sorted_enumerate_key, sorted_range, np.argsort],
n_range=[2 ** k for k in range(15)],
xlabel="len(x)",
)
b.save("out.png")
The answers with enumerate are nice, but I personally don't like the lambda used to sort by the value. The following just reverses the index and the value, and sorts that. So it'll first sort by value, then by index.
sorted((e,i) for i,e in enumerate(myList))
Updated answer with enumerate and itemgetter:
sorted(enumerate(a), key=lambda x: x[1])
# [(0, 1), (1, 2), (2, 3), (4, 5), (3, 100)]
Zip the lists together: The first element in the tuple will the index, the second is the value (then sort it using the second value of the tuple x[1], x is the tuple)
Or using itemgetter from the operatormodule`:
from operator import itemgetter
sorted(enumerate(a), key=itemgetter(1))
Essentially you need to do an argsort, what implementation you need depends if you want to use external libraries (e.g. NumPy) or if you want to stay pure-Python without dependencies.
The question you need to ask yourself is: Do you want the
indices that would sort the array/list
indices that the elements would have in the sorted array/list
Unfortunately the example in the question doesn't make it clear what is desired because both will give the same result:
>>> arr = np.array([1, 2, 3, 100, 5])
>>> np.argsort(np.argsort(arr))
array([0, 1, 2, 4, 3], dtype=int64)
>>> np.argsort(arr)
array([0, 1, 2, 4, 3], dtype=int64)
Choosing the argsort implementation
If you have NumPy at your disposal you can simply use the function numpy.argsort or method numpy.ndarray.argsort.
An implementation without NumPy was mentioned in some other answers already, so I'll just recap the fastest solution according to the benchmark answer here
def argsort(l):
return sorted(range(len(l)), key=l.__getitem__)
Getting the indices that would sort the array/list
To get the indices that would sort the array/list you can simply call argsort on the array or list. I'm using the NumPy versions here but the Python implementation should give the same results
>>> arr = np.array([3, 1, 2, 4])
>>> np.argsort(arr)
array([1, 2, 0, 3], dtype=int64)
The result contains the indices that are needed to get the sorted array.
Since the sorted array would be [1, 2, 3, 4] the argsorted array contains the indices of these elements in the original.
The smallest value is 1 and it is at index 1 in the original so the first element of the result is 1.
The 2 is at index 2 in the original so the second element of the result is 2.
The 3 is at index 0 in the original so the third element of the result is 0.
The largest value 4 and it is at index 3 in the original so the last element of the result is 3.
Getting the indices that the elements would have in the sorted array/list
In this case you would need to apply argsort twice:
>>> arr = np.array([3, 1, 2, 4])
>>> np.argsort(np.argsort(arr))
array([2, 0, 1, 3], dtype=int64)
In this case :
the first element of the original is 3, which is the third largest value so it would have index 2 in the sorted array/list so the first element is 2.
the second element of the original is 1, which is the smallest value so it would have index 0 in the sorted array/list so the second element is 0.
the third element of the original is 2, which is the second-smallest value so it would have index 1 in the sorted array/list so the third element is 1.
the fourth element of the original is 4 which is the largest value so it would have index 3 in the sorted array/list so the last element is 3.
If you do not want to use numpy,
sorted(range(len(seq)), key=seq.__getitem__)
is fastest, as demonstrated here.
The other answers are WRONG.
Running argsort once is not the solution.
For example, the following code:
import numpy as np
x = [3,1,2]
np.argsort(x)
yields array([1, 2, 0], dtype=int64) which is not what we want.
The answer should be to run argsort twice:
import numpy as np
x = [3,1,2]
np.argsort(np.argsort(x))
gives array([2, 0, 1], dtype=int64) as expected.
Most easiest way you can use Numpy Packages for that purpose:
import numpy
s = numpy.array([2, 3, 1, 4, 5])
sort_index = numpy.argsort(s)
print(sort_index)
But If you want that you code should use baisc python code:
s = [2, 3, 1, 4, 5]
li=[]
for i in range(len(s)):
li.append([s[i],i])
li.sort()
sort_index = []
for x in li:
sort_index.append(x[1])
print(sort_index)
We will create another array of indexes from 0 to n-1
Then zip this to the original array and then sort it on the basis of the original values
ar = [1,2,3,4,5]
new_ar = list(zip(ar,[i for i in range(len(ar))]))
new_ar.sort()
`
s = [2, 3, 1, 4, 5]
print([sorted(s, reverse=False).index(val) for val in s])
For a list with duplicate elements, it will return the rank without ties, e.g.
s = [2, 2, 1, 4, 5]
print([sorted(s, reverse=False).index(val) for val in s])
returns
[1, 1, 0, 3, 4]
Import numpy as np
FOR INDEX
S=[11,2,44,55,66,0,10,3,33]
r=np.argsort(S)
[output]=array([5, 1, 7, 6, 0, 8, 2, 3, 4])
argsort Returns the indices of S in sorted order
FOR VALUE
np.sort(S)
[output]=array([ 0, 2, 3, 10, 11, 33, 44, 55, 66])
Code:
s = [2, 3, 1, 4, 5]
li = []
for i in range(len(s)):
li.append([s[i], i])
li.sort()
sort_index = []
for x in li:
sort_index.append(x[1])
print(sort_index)
Try this, It worked for me cheers!
firstly convert your list to this:
myList = [1, 2, 3, 100, 5]
add a index to your list's item
myList = [[0, 1], [1, 2], [2, 3], [3, 100], [4, 5]]
next :
sorted(myList, key=lambda k:k[1])
result:
[[0, 1], [1, 2], [2, 3], [4, 5], [3, 100]]
A variant on RustyRob's answer (which is already the most performant pure Python solution) that may be superior when the collection you're sorting either:
Isn't a sequence (e.g. it's a set, and there's a legitimate reason to want the indices corresponding to how far an iterator must be advanced to reach the item), or
Is a sequence without O(1) indexing (among Python's included batteries, collections.deque is a notable example of this)
Case #1 is unlikely to be useful, but case #2 is more likely to be meaningful. In either case, you have two choices:
Convert to a list/tuple and use the converted version, or
Use a trick to assign keys based on iteration order
This answer provides the solution to #2. Note that it's not guaranteed to work by the language standard; the language says each key will be computed once, but not the order they will be computed in. On every version of CPython, the reference interpreter, to date, it's precomputed in order from beginning to end, so this works, but be aware it's not guaranteed. In any event, the code is:
sizediterable = ...
sorted_indices = sorted(range(len(sizediterable)), key=lambda _, it=iter(sizediterable): next(it))
All that does is provide a key function that ignores the value it's given (an index) and instead provides the next item from an iterator preconstructed from the original container (cached as a defaulted argument to allow it to function as a one-liner). As a result, for something like a large collections.deque, where using its .__getitem__ involves O(n) work (and therefore computing all the keys would involve O(n²) work), sequential iteration remains O(1), so generating the keys remains just O(n).
If you need something guaranteed to work by the language standard, using built-in types, Roman's solution will have the same algorithmic efficiency as this solution (as neither of them rely on the algorithmic efficiency of indexing the original container).
To be clear, for the suggested use case with collections.deque, the deque would have to be quite large for this to matter; deques have a fairly large constant divisor for indexing, so only truly huge ones would have an issue. Of course, by the same token, the cost of sorting is pretty minimal if the inputs are small/cheap to compare, so if your inputs are large enough that efficient sorting matters, they're large enough for efficient indexing to matter too.

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