Filtering Trees

October 25, 2015

Today we are going to look at how to filter items in tree data structures using Python 3. We are going to compare a stateful approach and a functional and recursive approach. In the end we will discuss the advantages of a functional implementation.

The Task

Assume we have a tree data structure in the form of nested lists, like the following

tree = ['root', [
    ['left_child', []],
    ['middle_child', [
        ['a leaf!', []]],
    ['right_child', [
        ['right_grandchild', [
            ['another leaf!']]]],
Tree diagram

Tree diagram Open in new tab (full image size 8 KiB)

Find out path to all nodes that have the value “Foobar”. There are no constraints on the tree, such as being sorted, so at least all nodes need to be inspected at least once.

There are a few ways to do it, following one of many programming styles. We will explore a few. What all methods have in common, that there needs to be some mechanism of traversing the tree in order to visit all nodes, and to extract and return the nodes that match “Foobar”.

Before we can get started, we need to create some trees. I like creating helpers, so a tree generator is going to be very helpful. gen_tree will recursively create a random tree with a maximum depth of 3.

def gen_tree(depth=0, max_depth=3):
    return (
        "Foobar" if randbool() else "Qux",
        tuple(gen_tree(depth + 1) for _ in range(randint(0, 3)))
        if depth < max_depth else tuple(),

If you want, you can include from random import seed; seed(1) in your code to ensure that you get the same random tree for every execution. Of course, using a fixed is stretching the definition of randomness. But for debugging it can be tremendously helpful.

>>> pprint(gen_tree())
 (('Foobar', (('Qux', (('Foobar', ()),)),)),
  ('Foobar', ()),
   (('Qux', (('Qux', ()), ('Qux', ()), ('Foobar', ()))),
    ('Qux', (('Foobar', ()), ('Qux', ()), ('Qux', ()))),
    ('Foobar', (('Qux', ()), ('Qux', ()), ('Qux', ())))))))

Now, let’s see how easily we can find ‘Foobar’.

Stack-based Traversal

If we’re going to traverse a tree structure, we need to take note of which nodes we’ve already visited and which we have not seen yet. If we traverse a tree in a predetermined order, for example depth-first in {pre,in,post}-order, we only need to be aware of which we need to visit in the future.

Wikipedia has some really nice illustrations showing the different kinds of tree traversals, so I won’t try to do a better job at it. Take a look right here.

def filter_tree(tree, keyword="Foobar"):
    # Our first goal is the tree's root
    # Additionally, we are going to store the path to the node
    # As the second item in the tuple
    goals = [(tree, [tree[0]])]
    while goals:
        node, path = goals.pop()  # pop the first item in the goal queue
        for child_node in node[1]:
            # the path is the current path plus the turn taken
            goals.append((child_node, path + [child_node[0]]))
        if node[0] == keyword:
            yield tuple(path)

I am going to be honest with you there. This code is messy and hard to debug. We have to manually keep track of which paths in the tree need to be visited and what the path to every node looks like. But it works. Here are all the paths to nodes that have the value ‘Foobar’:

>>> pprint(tuple(filter_tree(tree)))
(('Qux', 'Qux', 'Foobar'),
 ('Qux', 'Qux', 'Qux', 'Foobar'),
 ('Qux', 'Qux', 'Qux', 'Foobar'),
 ('Qux', 'Foobar'),
 ('Qux', 'Foobar'),
 ('Qux', 'Foobar', 'Qux', 'Foobar'))

Luckily, using yield allows us to let the caller take of retrieving the individual results. That means no result temporary list. In general, using yield statements allows for more concise code and better streaming behavior. Instead of allocating memory for a full list, you can leverage yields paired with other iterators to only need memory for the end result. This can be useful if you nest list operations like

map(operator, filter(operator, reduce(operator, ...)))

It is important to not forget to unpack a iterable stream once you want to retrieve the results. Otherwise you will see a result like <generator object <genexpr> at 0x...>.

Recursion-based Traversal

Instead of explicitly tracking our current path and position in the tree, we can use a trick that functional programmers have figured out before it became cool: Recursion.

In functional programming state often is encapsulated in the way functions are called. This has the neat advantage that if you call a function the same way twice, you will get the same result. Not only does this make your code more predictable, it also helps writing saner tests with less dependency injection.

Let’s dive into the code

def filter_tree_recursive(tree, path=tuple(), keyword="Foobar"):
    # Look ma, no assignment statements
    if tree[0] == keyword:
        yield (path + (tree[0], ))
    for child_node in reversed(tree[1]):
        yield from filter_tree_recursive(child_node, path + (tree[0], ))

Note the use of yield from, which is only available in Python 3. It lets us delegate yield to another method. Otherwise we would have to unpack the result of filter_tree_recursive into individual yields. This way, we can shave off one line of code.

What our code does is return the path to the current node if it matches the search keyword plus call itself on all child nodes. Using the yield statement, we can avoid storing results in temporary variables. This makes the function itself store the state of execution. This can have side-effects, but not in our case.

Our code always fully evaluates the function and does not suspend execution since we are constructing a tuple out of all yield results, as can be seen below. That means that once we are done calculating, the Python runtime discards the execution state of the current filter_tree_recursive call.

>>> pprint(tuple(filter_tree_recursive(tree)))
(('Qux', 'Qux', 'Foobar'),
 ('Qux', 'Qux', 'Qux', 'Foobar'),
 ('Qux', 'Qux', 'Qux', 'Foobar'),
 ('Qux', 'Foobar'),
 ('Qux', 'Foobar'),
 ('Qux', 'Foobar', 'Qux', 'Foobar'))

The result is the same, but our code is more predictable and testable.

I would be thrilled to hear from you! Please share your thoughts and ideas with me via email.

Back to Index