Iterating over multiple indices with i > j ( > k) in a pythonic way

Question

i need to iterate over a tuple of indices. all indices must be in the range [0, N) with the condition i > j. The toy example I present here deal

Answer 1

You could solve this generally as follows:

def indices(N, length=1):
    """Generate [length]-tuples of indices.

    Each tuple t = (i, j, ..., [x]) satisfies the conditions 
    len(t) == length, 0 <= i < N  and i > j > ... > [x].

    Arguments:
      N (int): The limit of the first index in each tuple.
      length (int, optional): The length of each tuple (defaults to 1).

    Yields:
      tuple: The next tuple of indices.

    """
    if length == 1:
       for x in range(N):
           yield (x,)
    else:
       for x in range(1, N):
            for t in indices(x, length - 1):
                yield (x,) + t

In use:

>>> list(indices(5, 2))
[(1, 0), (2, 0), (2, 1), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (4, 3)]
>>> list(indices(5, 3))
[(2, 1, 0), (3, 1, 0), (3, 2, 0), (3, 2, 1), (4, 1, 0), (4, 2, 0), (4, 2, 1), (4, 3, 0), (4, 3, 1), (4, 3, 2)]