Data Structures u0026 Algorithms: Tries and Prefix Trees Quiz

Challenge your understanding of Tries (Prefix Trees), their applications in autocomplete, dictionary matching, and word search problems through ten complex and thought-provoking questions.

1. Trie Node Structure Essentials

   Which component is typically essential in each node of a trie to efficiently support prefix-based searches, given the string dataset {'car', 'care', 'cart'}?

   1. A count of total children in the subtree
   2. A doubly linked list of child nodes
   3. A mapping from character to child node
   4. A boolean flag indicating leafness only at the root
   5. A direct index of suffixes

2. Autocomplete Feature Implementation

   During the implementation of an autocomplete feature using a standard trie, what is the time complexity of finding all words with the given prefix 'pre' if the trie contains n words and k is the number of matching completions?

   1. O(nk)
   2. O(k log n)
   3. O(3 + k)
   4. O(n)
   5. O(k)

3. Space Requirement in Sparse Tries

   Given an English dictionary with 50,000 words, what is a primary reason the space required by a basic trie can grow much larger than the total number of characters stored in all words combined?

   1. Minimal path compression
   2. Wasted pointers in sparsely filled nodes
   3. Compression of duplicate substrings
   4. Efficient character compaction
   5. Nearly zero redundancy in nodes

4. Dictionary Matching with Trie Variants

   For matching a set of exact strings in a large body of text, which trie variant augments nodes with failure pointers to optimize multi-pattern search?

   1. Suffix trie
   2. De La Briandais trie
   3. Bloom trie
   4. Aho-Corasick automaton
   5. Radix trie

5. Word Search in 2D Grids Using Tries

   When using a trie to solve word search in a 2D character grid, what optimization can most significantly reduce redundant traversal?

   1. Disabling prefix pruning
   2. Removing matched words from the trie during DFS traversal
   3. Allowing repeated cells in a path
   4. Ignoring visited cell tracking
   5. Building a trie for every starting position

6. Complex Operations in Tries

   Which of the following operations requires non-trivial modifications to a standard trie structure to support efficiently: delete all words starting with a given prefix?

   1. Leaf node detection
   2. Recursive path compression
   3. Bulk subtree deletion for prefix nodes
   4. Lazy node initialization
   5. Incrementing word counts

7. Radix Tree Distinction

   Which characteristic distinguishes a radix tree (compressed trie) from a standard trie when storing the words 'pan', 'pane', and 'paneer'?

   1. Maintaining leaf nodes only
   2. Ordering edges alphabetically
   3. Storing edges as bidirectional pointers
   4. Requiring balanced height
   5. Combining consecutive non-branching edges into a single edge

8. Memory Optimization Technique

   To optimize space in a trie holding a vast, sparse set of lowercase words, which approach is commonly used for child pointers in each node?

   1. Allocating a fixed-size array of 256 entries
   2. Using a hash map for child nodes
   3. Eagerly allocating all levels
   4. Linking to parent nodes only
   5. Reversible bidirectional traversal

9. Failure Case in Prefix Search

   If a user queries a prefix 'xyz' that does not exist in the trie, which behavior best describes the outcome of the search process?

   1. Traverses to a random node
   2. Returns after failing to find a matching child at the first unmatched character
   3. Skips to a fallback root node
   4. Finds the lexicographically closest word
   5. Returns the nearest valid suffix

10. Complexity Trade-offs of Trie Usage

    In which scenario does a trie provide worst-case performance inferior to a hash table for full-word lookup among a set of short, fixed-length strings?

    1. When all words are identical length and uniformly distributed
    2. When words are stored in sorted order
    3. When there are no duplicate prefixes
    4. When the trie supports only insert operations
    5. When most trie paths share few prefixes