Question

I have numerical strings that represent trees (I don’t know if there’s an official name for this):

012323301212

The above example represents 2 trees. The root is signified with 0. Immediate children of the root are ‘1’s, immediate children of ‘1’s are ‘2’s, and so on. I need to group these into sub trees that consist of parents and their immediate children. So the above would be decomposed into…

01 122 23 233 011 12 12

I was thinking one possible way to do this would be to build a tree structure from the string then visit each node and generate a subtree of it and its immediate children (if it had any), but this seems relatively complicated. Is there some clever way I can do this without resorting to creating a tree structure and traversing it?

Answer 1

The output you’re requesting essentially is the tree structure. That said, you can treat your input as a pre-order depth-first traversal and read off the tree structure without holding all of it in memory at once:

depths = [0, 1, 2, 3, 2, 3, 3, 0, 1, 2, 1, 2]   # Our input

next_id = 0                                 # Id of the next node
ids = []                                    # The ids of nodes as we traverse
parents = {}                                # Maps children to parents
children = {}                               # Maps parents to lists of children

for depth in depths
  # First we give this node an id
  id = next_id
  next_id += 1

  if ids.length <= depth
    # If this is our first time to this depth, push a new level onto ids.
    ids.append(id)
  else
    # Otherwise just insert the id into the list at its depth
    ids[depth] = id

    # And truncate off all elements after.  This preserves the invariant
    # that each id is the descendent of ids that appears before it.
    ids[depth].resize(depth + 1)

  assert(ids.length == depth + 1)

  # Emit the link between this node and its parent
  if depth > 0
    parents[ids[depth]] = ids[depth - 1]
    children[ids[depth - 1]] ||= []       # add the empty list first if needed
    children[ids[depth - 1]].append(ids[depth])