How can I randomly place several non-colliding rects?

Question

I\'m working on some 2D games with Pygame. I need to place several objects at the same time randomly without them intersecting. I have tried a few obvious

Answer 1

an alternative pseudocode, to those already mentioned:

while not enough objects:
  place object randomly
  if overlaps with anything else:
    reduce size until it fits or has zero size
  if zero size: 
    remove

Or something like that.

But this has the advantage of possibly creating some smaller objects than you intended, and creating objects which almost intersect (i.e. touch).

If it's a map for the player to traverse, they may still not be able to traverse it because their path could be blocked.