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Pseudo-lists containing arrangements of item selection types that commonly arise in combinatorics, such as combinations, permutations and subsets.

Project description


Welcome to trotter, a set of Python classes for representing sequences of structures of item selections commonly encountered in combinatorics.

Classes have been defined according to whether order is important, items may be repeated, and length is specified:

Class Order Important Repetition Allowed Specified Length
Amalgams Yes Yes Yes
Permutations Yes No Yes
Compounds Yes No No
Compositions No Yes Yes
Combinations No No Yes
Subsets No No No

Instances of these classes are indexable pseudo-lists containing all possible selections of items. Since the number of possible arrangements can grow very quickly with the number of items available (and the number of items taken at a time, where applicable), instances do not actually store all arrangements but are rather containers of mappings between integers and arrangements. This makes it possible to create instances that "contain" very large numbers of arrangements.


pip install trotter

Example: combinations of words

from trotter import Combinations

items = ["the", "parrot", "is", "not", "pining"]
combos = Combinations(3, items)

Combinations(3, ['the', 'parrot', 'is', 'not', 'pining'])
A pseudo-list containing 10 3-combinations of ['the', 'parrot', 'is', 'not', 'pining'].
for combo in combos:
    print(" ".join(combo))
the parrot is
the parrot not
the parrot pining
the is not
the is pining
the not pining
parrot is not
parrot is pining
parrot not pining
is not pining
print(combos.index("the parrot pining".split()))
['the', 'parrot', 'pining']

Example: subsets of characters in a string

The items can be presented as a list of objects or a string, which is interpreted as a list of characters. Here's an example where we use a string.

for i, subset in enumerate(Subsets("spam")):
     print(f"[{i}] '{subset}'")
[0] ''
[1] 's'
[2] 'p'
[3] 'sp'
[4] 'a'
[5] 'sa'
[6] 'pa'
[7] 'spa'
[8] 'm'
[9] 'sm'
[10] 'pm'
[11] 'spm'
[12] 'am'
[13] 'sam'
[14] 'pam'
[15] 'spam'

Example: many permutations!

from trotter import Permutations
letters = "abcdefghijklmnopqrstuvwxyz"
permutations = Permutations(10, letters)
A pseudo-list containing 19275223968000 10-permutations of 'abcdefghijklmnopqrstuvwxyz'.

That's almost twenty trillion! Luckily, we're only dealing with a pseudo-list, and those permutations are not actually stored!

Notice that the word algorithms is a ten-letter permutation of the letters of the alphabet. At what position in the pseudo-list is this word?


Luckily, we were able to find it without a brute-force search! Let's check that result...


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