Week 41 of 43
CP Track
WEEK 41 LEARNING MODULE
Tries (Prefix Trees) & Prefix Search
Covers Trie (Prefix Tree) data structures, node child pointers, end-of-word flags, $O(L)$ insertion/search/prefix matching, autocomplete suggestions, and wildcard searches.
6 Practice Problems3 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Master Trie (Prefix Tree) node structure: `children` mapping/array of size 26 and `is_end` boolean.
- ✓Implement Trie core operations: `insert(word)` ($O(L)$), `search(word)` ($O(L)$), `startsWith(prefix)` ($O(L)$), and `delete(word)`.
- ✓Analyze Trie Space Complexity: $O(M \times N \times \Sigma)$ with substantial common prefix sharing.
- ✓Combine Tries with DFS for autocomplete search suggestions, longest common prefix, and wildcard search (`.`).
Core Concepts
Trie (Prefix Tree) Node Structure
O(L) per word of length LTree where edges represent characters and nodes mark valid word terminations.
Fast Prefix & Word Lookups
O(L) timeRetrieving whether any stored word starts with a given prefix in O(prefix_len) time.
Shared Prefix Space Optimization
O(M * N * alphabet_size) worst caseWords sharing prefixes share initial root branches, saving memory compared to separate string storage.
Algorithms Covered
Trie Insertion ($O(L)$)Trie Word Search ($O(L)$)Trie Prefix Search ($O(L)$)Trie Autocomplete SuggestionsTrie Wildcard Search with DFS
Data Structures Applied
Trie (Prefix Tree)
“If you can't do great things, do small things in a great way”
— Napoleon Hill
Lecture Materials (1)
Official Slide Deck1.6 MB
In Transit
Trie Lecture.pdf
Topic: Trie Lecture
Format: PDF