feat(algoritms, datastructures): trie data structure, longest word with prefixes

Author: BrianLusina

algorithms/trie/__init__.py

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+# Longest Word With All Prefixes
+
+You are given an array of strings, words. Your task is to find the longest string in words such that every prefix of
+this string is also present in words.
+
+A prefix of a string is any leading substring. For example, the prefixes of "apple" are "a", "ap", "app", and "appl".
+
+1. If multiple valid strings have the same maximum length, return the lexicographically smallest one. 
+2. If no such string exists, return an empty string "".
+
+
+## Constraints:
+
+- 1 ≤ `words.length` ≤ 10^3
+- 1 ≤ `words[i].length` ≤ 10^3
+- 1 ≤ `sum(words[i].length)` ≤ 10^3
+- `words[i]` consists only of lowercase English letters.
+
+## Examples
+
+![Example 1](./images/examples/longest_word_with_prefixes_example_1.png)
+![Example 2](./images/examples/longest_word_with_prefixes_example_2.png)
+![Example 3](./images/examples/longest_word_with_prefixes_example_3.png)
+![Example 4](./images/examples/longest_word_with_prefixes_example_4.png)
+![Example 5](./images/examples/longest_word_with_prefixes_example_5.png)

algorithms/trie/longest_word_with_prefixes/README.md

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+from typing import List
+from datastructures.trees.trie import TrieNode
+
+
+def longest_word(words: List[str]) -> str:
+    """
+    Find the longest string in words such that every prefix of this string is also present in words.
+
+    Time complexity
+    Building the trie and validating all words takes O(∑∣wordi∣).
+
+    Space complexity
+    The trie stores, at most, one node per character, so the space is O(∑∣wordi∣)
+
+    Args:
+        words (List[str]): list of words
+    Returns:
+        str: longest word
+    """
+    if not words:
+        return ""
+
+    trie = TrieNode()
+
+    for idx, word in enumerate(words):
+        trie.insert(word, idx)
+
+    result = ""
+    for word in words:
+        word_length = len(word)
+        result_length = len(result)
+
+        is_longer = word_length > result_length
+        is_same_length_but_smaller = word_length == result_length and word < result
+
+        if (is_longer or is_same_length_but_smaller) and trie.search(word):
+            result = word
+
+    return result

algorithms/trie/longest_word_with_prefixes/__init__.py

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+import unittest
+from typing import List
+from parameterized import parameterized
+from algorithms.trie.longest_word_with_prefixes import longest_word
+
+LONGEST_WORD_WITH_PREFIXES_TEST_CASES = [
+    (["a", "ab", "abc", "abd", "abde"], "abde"),
+    (["x", "xy", "xyz", "xz"], "xyz"),
+    (["m", "ma", "man", "many", "mat"], "many"),
+    (["dog", "do", "d", "cat"], "dog"),
+    (["car", "ca", "c", "cat"], "car"),
+    (["a", "ap", "app", "apple", "apply"], "app"),
+]
+
+
+class LongestWordWithPrefixesTestCase(unittest.TestCase):
+    @parameterized.expand(LONGEST_WORD_WITH_PREFIXES_TEST_CASES)
+    def test_longest_word_with_prefixes(self, words: List[str], expected: str):
+        actual = longest_word(words)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()

algorithms/trie/longest_word_with_prefixes/images/examples/longest_word_with_prefixes_example_1.png

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+# Bloom Filter
+
+An implementation of a bloom filter data structure.