Reverse engineer one-hot encoded categorical variable

reverse.py

import collections
import itertools


df = pd.DataFrame({
    'a': [1, 0, 0, 0],
    'b': [0, 1, 0, 0],
    'c': [0, 0, 1, 0],
    'd': [0, 0, 0, 1],
    'e': [1, 1, 0, 0],
    'f': [0, 0, 1, 1]
}) == 1

columns = df.columns.tolist()
candidates = collections.defaultdict(set)

for a, b in itertools.permutations(columns, 2):
    if (df[a] & df[b]).any():
        continue
    candidates[a].update([b])
        
combos = []
seen = set()
for col in sorted(candidates):
    seen.update([col])
    combo = set([col])
    for candidate in candidates:
        if candidate in seen:
            continue
        ok = True
        for member in combo:
            if candidate not in candidates[member] or member not in candidates[candidate]:
                ok = False
                break
        if ok:
            combo.update([candidate])
        
    combos.append(combo)