components and component_mapping methods can be speed up by a factor of len(distinct_roots) #2
Description
When you group elements into components (in methods components and component_mapping), the time complexity of your current way of doing it is O(N x M) (where N is len(self._elts) and M is len(distinct_roots)).
O(N x M) because looping over distinct roots is O(M) and boolean indexing over elements elts[roots == root] is O(N).
The optimized code below using a defaultdict (hashmap) has time complexity O(N). The higher M is, the bigger is the speed up.
from collections import defaultdict
def components(self):
dict_components = defaultdict(list)
for elem in self._elts:
root = self.find(elem)
dict_components[root].append(elem)
return dict_components