subtuples for a tuple

Question

I wish to yield the following:

(('A',), ('B',), ('C',), ('D',))
(('A',), ('B',), ('C','D'))
(('A',), ('B','C'), ('D',))
(('A',), ('B','C','D'))
(('A','B'), ('C',), ('D',))
(('A','B'), ('C','D'))
(('A','B','C'), ('D',))
(('A','B','C','D'),)

when calling sub_combinations(('A', 'B', 'C', 'D'))

Here's my attempt but it doesn't work:

def sub_combinations(segment):
   for i in range(1, len(segment)):
      for j in sub_combinations(segment[i:]):
         yield segment[:i]+j 
      yield segment 

but I think I'm on the right track.

Additionally, I'd like to have a second argument called limit which limits the size of the sub tuples, for example sub_combinations(('A', 'B', 'C', 'D'), 2) would give:

(('A',), ('B',), ('C',), ('D',))
(('A',), ('B',), ('C','D'))
(('A',), ('B','C'), ('D',))
(('A','B'), ('C',), ('D',))
(('A','B'), ('C','D'))

I'm using python 3.

Answer 1

Handle base case - when segment is empty:

def sub_combinations(segment, size=0):
    if segment == ():
        yield ()
        return
    stop = min(size or len(segment), len(segment))
    for i in range(1, stop + 1):
        for j in sub_combinations(segment[i:], size):
            yield (segment[:i],) + j

Example usage:

>>> for x in sub_combinations(('A', 'B', 'C', 'D')):
...     print(x)
...
(('A',), ('B',), ('C',), ('D',))
(('A',), ('B',), ('C', 'D'))
(('A',), ('B', 'C'), ('D',))
(('A',), ('B', 'C', 'D'))
(('A', 'B'), ('C',), ('D',))
(('A', 'B'), ('C', 'D'))
(('A', 'B', 'C'), ('D',))
(('A', 'B', 'C', 'D'),)

---

>>> for x in sub_combinations(('A', 'B', 'C', 'D'), 2):
...     print(x)
...
(('A',), ('B',), ('C',), ('D',))
(('A',), ('B',), ('C', 'D'))
(('A',), ('B', 'C'), ('D',))
(('A', 'B'), ('C',), ('D',))
(('A', 'B'), ('C', 'D'))

Answer 2

In case you also can live with lists instead of tuples (or aren't afraid of converting them later), you can use this:

def subtuples(t):
  for i in range(1<< (len(t)-1)):
    result = [ [ t[0] ] ]
    for j in range(len(t)-1):
      if (1<<j) & i:
        result[-1].append(t[j+1])
      else:
        result.append([ t[j+1] ])
    yield result

for x in subtuples(('a', 'b', 'c', 'd')):
  print(x)