posts: trie: add construction

content/posts/2024-06-30-trie/index.md

@@ -34,3 +34,32 @@ spell correction, as it can easily be used to fuzzy match words under a given
 edit distance (think [Levenshtein])
 
 [Levenshtein]: https://en.wikipedia.org/wiki/Levenshtein_distance
+
+## Implementation
+
+This implementation will be in Python for exposition purposes, even though
+it already has a built-in `dict`.
+
+### Representation
+
+Creating a new `Trie` is easy: the root node starts off empty and without any
+mapped values.
+
+```python
+class Trie[T]:
+    _children: dict[str, Trie[T]]
+    _value: T | None
+
+    def __init__(self):
+        # Each letter is mapped to a Trie
+        self._children = defaultdict(Trie)
+        # If we match a full string, we store the mapped value
+        self._value = None
+```
+
+We're using a `defaultdict` for the children for ease of implementation in this
+post. In reality, I would encourage you exit early when you can't match a given
+character, etc...
+
+The string key will be implicit by the position of a node in the tree: the empty
+string at the root, one-character strings as its direct children, etc...