Topological sort

# TODO: reformat the parameter specifications and add examples.

It is sometimes convenient to topological sort.

source

natsort_comparison

 natsort_comparison (str1:str, str2:str)

Parameters - str1 - str - str2 - str

source

default_str_comparison

 default_str_comparison (str1:str, str2:str)

Parameters - str1 - str - str2 - str

source

containing_string_priority

 containing_string_priority (str1:str, str2:str)

*Returns 1, 0, -1 depending on whether one string contains the other.

TODO make the string containment criterion looser, e.g. finite Galois etale cover “contains” finite etale cover.

Parameters - str1 - str - str2 - str*

source

graph_for_topological_sort

 graph_for_topological_sort (items_to_sort:collections.abc.Iterable[str],
                             key_order:Callable[[str,str],int])

*Parameters - items_to_sort - Iterable[str] - key_order: Callable[[str, str], int] - Comparing str1 against str2 results in a positive number if str1 is “greater” than str2 (i.e. str1 is of a later priority)

Returns - dict[str, set[str]] - A dict whose keys are the elements k of items_to_sort and whose values are sets of elements k2 of items_to_sort such that key_order(k, k2) > 0.*

source

dict_with_keys_topologically_sorted

 dict_with_keys_topologically_sorted (dict_to_sort:dict[str],
                                      key_order:Callable[[str,str],int],
                                      reverse:bool=False)

*Returns an OrderedDict whose keys are sorted topologically by the specified key order.

Parameters - dict_to_sort - dict[str] - The dict whose keys need to be ordered. - key_order - The comparison function on the keys of dict_to_sort. Defaults to the key function for the comparison [containing_string_priority](https://hyunjongkimmath.github.io/trouver/helper.topological_sort.html#containing_string_priority). - reverse - bool - Defaults to False

Returns - OrderedDict[str]*

# TODO: test