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Trie

A trie supports prefix search.

Trie

A trie is a tree that stores words by their prefix. Each node represents a letter; the path from root to leaf forms a word.

It is efficient for prefix searches like autocomplete or spell check. Insert and search run in O(L) time; L is word length.

Dictionary structure

Trie nodes are represented as a dictionary. Each node holds a mapping from letter to child node. Word end is marked with '$'.

This representation lets the tree grow automatically as new letters are added. An empty trie starts with {}.

Practice init_trie function

Write init_trie(). Return an empty trie root (dictionary). Print it with print(init_trie()).

Starter code

solution.py
def init_trie():
    # Return empty trie root

Sample solution

solution.py
def init_trie():
    # Return empty trie root
    return {}
print(init_trie())

Expected output

{}

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 Letter loop

Question 
for ____ in word:
Answer 
for ch in word:

Explanation: ch is right.

2 What does an empty trie start with?

  • []
  • {} Correct answer
  • 0
  • ()

Explanation: An empty trie starts with {}.

3 Trie: match the terms

Term Meaning
root Start
letter Node
'+' Word end
dictionary Node structure

All lessons in Advanced

1 DP - Memoization

  1. What is memoization?
  2. Fibonacci memoization
  3. Dict-based cache
  4. Summary - Memoization

2 DP - Tabulation

  1. What is tabulation?
  2. Building the table
  3. Fibonacci tabulation
  4. Summary - Tabulation

3 LCS

  1. LCS definition
  2. DP table
  3. Backtracking the table
  4. Summary - LCS

4 Knapsack

  1. Knapsack problem
  2. 0/1 knapsack DP
  3. Decision table
  4. Summary - Knapsack

5 DP project

  1. Project: Overview
  2. Cost table
  3. DP solution
  4. Print the result

6 Matrix chain

  1. Multiplication order
  2. DP table
  3. Split point
  4. Summary - Matrix chain

7 Floyd-Warshall

  1. All pairs
  2. Triple loop
  3. Table update
  4. Summary - Floyd-Warshall

8 Dijkstra

  1. Single source
  2. Priority queue
  3. Relaxation
  4. Summary - Dijkstra

9 Bellman-Ford

  1. Negative weights
  2. Edge relaxation loop
  3. Negative cycle
  4. Summary - Bellman-Ford

10 Kruskal

  1. Minimum spanning tree
  2. Edge sorting
  3. Cycle check
  4. Summary - Kruskal

11 Prim

  1. Prim idea
  2. Priority queue
  3. Visited set
  4. Summary - Prim

12 Topological sort

  1. Dependency order
  2. DFS-based sort
  3. Kahn algorithm
  4. Summary - Topological sort

13 Union-find, trie, segment tree

  1. Union-find
  2. Trie
  3. Segment tree
  4. Summary - Advanced structures

14 Advanced final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4