Treegami is a small library for mapping and folding trees of arbitrary shape. As programmers we often work with trees, either in the open or in hiding, eg. when the're camouflaging as a json document. Treegami makes transforming these structures and extracting data from them easy. The name Treegami is a portmanteau of the words tree and origami.
PHP 7.1+
$ composer require pwm/treegami
As a start, let's just create a tree manually:
$tree = new Tree(
'first', [ // node has 3 children
new Tree('second', [ // node has 2 children
new Tree('third'), // children are optional and defaults to []
new Tree(), // node value is optional and defaults to null
]),
new Tree('fourth', []), // explicitly saying no children
new Tree('fifth', [
new Tree(null, []) // explicitly saying no node value or children
]),
]
);Which results in the following tree:
____first____
/ | \
second fourth fifth
/ \ |
third null null
Let's map this tree using a function that maps a string to its length and null to 0:
$mappedTree = $tree->map(function (?string $node): int {
return is_string($node)
? strlen($node)
: 0;
});Which results in the following tree:
____5____
/ | \
6 6 5
/ \ |
5 0 0
Now let's fold this tree to the sum of its node values:
$foldedTree = $mappedTree->fold(function (int $node, array $acc): int {
return $node + array_sum($acc);
});
assert($foldedTree === 27); // trueFinally an example of unfolding a tree from a seed value:
$tree = Tree::unfold(function (int $x): array {
return $x < 2 ** 3
? [$x, range(2 * $x, 2 * $x + 1)]
: [$x, []];
}, 1);Which results in the following full binary tree:
______1______
/ \
__2__ __3__
/ \ / \
4 5 6 7
/ \ / \ / \ / \
8 9 10 11 12 13 14 15
Some (most?) of the readers will be familiar with the higher-order functions map and fold on lists. In PHP they are called array_map and array_reduce, respectively.
As a quick refresher: the function map maps a list into another list by applying a function to its elements, while the function fold "folds up" a list starting from a seed value by applying a function to its elements accumulating them into a final value. For example if we have a function addOne, which adds one to a number, then map(addOne, [1,2,3,4,5]) results in [2,3,4,5,6]. If we then have a function add, which adds 2 numbers together, then fold(add, 0, [2,3,4,5,6]), 0 being the seed value, results in 0+2+3+4+5+6 = 20.
However map and fold is not specific to lists. In fact many different structures can be mapped and folded, including trees. Mapping a function over a tree results in another tree of the same shape where each node is the result of the function applied to it. Folding a tree using a function means traversing the tree, applying the function to its nodes and accumulating them into a final value.
For example if we have the following tree:
______1______
/ \
__2__ __3__
/ \ / \
4 5 6 7
/ \ \
8 9 10
then mapping addOne over it results in:
______2______
/ \
__3__ __4__
/ \ / \
5 6 7 8
/ \ \
9 10 11
In turn, folding this tree with add, using the root value 2 as the seed value, results in: 2+3+4+5+6+7+8+9+10+11 = 65.
In Treegami the seed value for fold by default is the value of the root node and an empty tree means a tree with no children and null as the node value.
Depending on which order we combine the current value with the accumulated value in our fold function we get different traversal orders. Specifically, if we prepend the current value to the accumulated value we get preorder traversal, while if we append the current value to the accumulated value we get postorder traversal.
In general fold does not need to "collapse" the structure into some scalar value, like an integer. We can just as easily "fold" the structure into another structure. This is exactly how map works in Treegami, meaning that map is expressed via fold.
unfold on the other hand is the "opposite" (or dual, to use the correct terminology) of fold. It takes a function and a seed value and "unfolds" that seed value into a structure, in our case into a tree. What's important to understand is that the function that unfolds the seed returns a pair of values: a node in our tree and a list of seed values, that will be used for subsequent iterations of unfold, until it returns an empty list, essentially terminating the iteration.
For the curious and brave out there: fold is a Catamorphism while its dual unfold is an Anamorphism. You can read more about these terms in the paper Functional programming with bananas, lenses, envelopes and barbed wire.
$ vendor/bin/phpunit
$ composer phpcs
$ composer phpstan
$ composer infection