SumNeuron SumNeuron - 1 year ago 149
Python Question

Python 3: Reverse consecutive runs in sorted list?

This is a question is an extension of What's the most Pythonic way to identify consecutive duplicates in a list?.

Suppose you have a list of tuples:

my_list = [(1,4), (2,3), (3,2), (4,4), (5,2)]


and you sort it by each tuple's last value:

my_list = sorted(my_list, key=lambda tuple: tuple[1])
# [(3,2), (5,2), (2,3), (1,4), (4,4)]


then we have two consecutive runs (looking at the last value in each tuple), namely
[(3,2), (5,2)]
and
[(1,4), (4,4)]
.

What is the pythonic way to reverse each run (not the tuples within), e.g.

reverse_runs(my_list)
# [(5,2), (3,2), (2,3), (4,4), (1,4)]


Is this possible to do within a generator?

UPDATE



It has come to my attention that perhaps the example list was not clear. So instead consider:

my_list = [(1,"A"), (2,"B"), (5,"C"), (4,"C"), (3,"C"), (6,"A"),(7,"A"), (8,"D")]


Where the ideal output from
reverse_runs
would be

[(7,"A"), (6,"A"), (1,"A"), (2,"B"), (3,"C"), (4,"C"), (5,"C"), (8,"D")]


To be clear on terminology, I am adopting the use of "run" as used in describing
TimSort
which is what Python's sort function is based upon - giving it (the sort function) its safety.

Thus if you sort on a collection, should the collection be multi-faceted, then only the specified dimension is sorted on and if two elements are the same for the specified dimension, their ordering will not be altered.

Thus the following function:

sorted(my_list,key=lambda t: t[1])


yields:

[(1, 'A'), (6, 'A'), (7, 'A'), (2, 'B'), (5, 'C'), (4, 'C'), (3, 'C'), (8, 'D')]


and the run on
"C"
(i.e.
(5, 'C'), (4, 'C'), (3, 'C')
) is not disturbed.

So in conclusion the desired output from the yet to be defined function
reverse_runs
:

1.) sorts the tuples by their last element

2.) maintaining the order of the first element, reverses runs on the last element

Ideally I would like this in a generator functions, but that does not (to me at the moment) seem possible.

Thus one could adopt the following strategy:

1.) Sort the tuples by the last element via
sorted(my_list, key=lambda tuple: tuple[1])


2.) Identify the indexes for the last element in each tuple when the succeeding tuple (i+1) is different than the last element in (i). i.e. identify runs

3.) Make an empty list

4.) Using the splice operator, obtain, reverse, and the append each sublist to the empty list

Answer Source

The most general case requires 2 sorts. The first sort is a reversed sort on the second criteria. The second sort is a forward sort on the first criteria:

pass1 = sorted(my_list, key=itemgetter(0), reverse=True)
result = sorted(pass1, key=itemgetter(1))

We can sort in multiple passes like this because python's sort algorithm is guaranteed to be stable.

However, in real life it's often possible to simply construct a more clever key function which allows the sorting to happen in one pass. This usually involves "negating" one of the values and relying on the fact that tuples order themselves lexicographically:

result = sorted(my_list, key=lambda t: (t[1], -t[0]))

In response to your update, it looks like the following might be a suitable solution:

from operator import itemgetter
from itertools import chain, groupby
my_list = [(1,"A"), (2,"B"), (5,"C"), (4,"C"), (3,"C"), (6,"A"),(7,"A"), (8,"D")]

pass1 = sorted(my_list, key=itemgetter(1))
result = list(chain.from_iterable(reversed(list(g)) for k, g in groupby(pass1, key=itemgetter(1))))
print(result)

We can take apart the expression:

chain.from_iterable(reversed(list(g)) for k, g in groupby(pass1, key=itemgetter(1)))

to try to figure out what it's doing...

First, let's look at groupby(pass1, key=itemgetter(1)). groupby will yield 2-tuples. The first item (k) in the tuple is the "key" -- e.g. whatever was returned from itemgetter(1). The key isn't really important here after the grouping has taken place, so we don't use it. The second item (g -- for "group") is an iterable that yields consecutive values that have the same "key". This is exactly the items that you requested, however, they're in the order that they were in after sorting. You requested them in reverse order. In order to reverse an arbitrary iterable, we can construct a list from it and then reverse the list. e.g. reversed(list(g)). Finally, we need to paste those chunks back together again which is where chain.from_iterable comes in.

If we want to get more clever, we might do better from an algorithmic standpoint (assuming that the "key" for the bins is hashible). The trick is to bin the objects in a dictionary and then sort the bins. This means that we're potentially sorting a much shorter list than the original:

from collections import defaultdict, deque
from itertools import chain

my_list = [(1,"A"), (2,"B"), (5,"C"), (4,"C"), (3,"C"), (6,"A"),(7,"A"), (8,"D")]

bins = defaultdict(deque)
for t in my_list:
    bins[t[1]].appendleft(t)

print(list(chain.from_iterable(bins[key] for key in sorted(bins))))

Note that whether this does better than the first approach is very dependent on the initial data. Since TimSort is such a beautiful algorithm, if the data starts already grouped into bins, then this algorithm will likely not beat it (though, I'll leave it as an exercise for you to try...). However, if the data is well scattered (causing TimSort to behave more like MergeSort), then binning first will possibly make for a slight win.

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