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Advanced Data Structures

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About This Topic

Advanced data structures, such as tries, disjoint sets and segment trees, are specialised designs that answer particular queries faster than basic structures. Priority queues and their heap variants, including binomial and Fibonacci heaps and their merge costs, come up often. Union-find items test find and union operations and the optimisations of path compression and union by rank, which keep trees shallow. Tries store strings with O(L) insertion for a word of length L. Range-query structures include segment trees, Fenwick trees and sparse tables, while interval trees, K-D trees for multidimensional search, skip lists and treaps, which combine BST ordering with heap priorities, round things out.

Below are 30 practice questions from a pool of 210 Advanced Data Structures MCQs, one of 12 topics in Data Structures & Algorithms. Each shows the correct answer with an explanation; when you are ready, take a timed quiz to test recall under exam conditions.

Practice Questions

Each question below shows the correct answer with a full explanation. Use these to build conceptual understanding before attempting a timed quiz.

Advanced Data StructuresEasy

Q1. What data structure typically implements a priority queue?

  1. A.Stack structure
  2. B.Heap structure✓ Correct
  3. C.Array structure
  4. D.Linked list structure

Explanation

A binary heap is the most common implementation of a priority queue, providing O(log n) insertion and extraction.

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Advanced Data StructuresEasy

Q2. What is a priority queue?

  1. A.A type of stack that also supports priority ordering
  2. B.A queue that processes all elements in strict FIFO order
  3. C.A sorted array of elements ordered by their value
  4. D.A structure where higher priority elements are served first✓ Correct

Explanation

A priority queue is an abstract data type where elements have priorities, and elements with higher priority are dequeued before lower priority ones.

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Advanced Data StructuresEasy

Q3. What is a disjoint set (Union-Find)?

  1. A.A hash set with unique elements
  2. B.A structure tracking non-overlapping subsets✓ Correct
  3. C.A set with no elements at all
  4. D.A sorted set with ordered elements

Explanation

A disjoint set (Union-Find) data structure tracks a collection of elements partitioned into non-overlapping subsets, supporting union and find operations efficiently.

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Advanced Data StructuresEasy

Q4. What is the time complexity of searching for a word of length L in a trie?

  1. A.O(log n)
  2. B.O(L)✓ Correct
  3. C.O(n)
  4. D.O(n × L)

Explanation

Searching in a trie takes O(L) time where L is the length of the word, independent of the number of stored words.

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Advanced Data StructuresEasy

Q5. What operation does 'find' perform in Union-Find?

  1. A.Determines which set an element belongs to✓ Correct
  2. B.Searches for an element in the set
  3. C.Finds the minimum element in all sets
  4. D.Finds all elements in a particular set

Explanation

The find operation determines which set an element belongs to by returning the root representative of that set.

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Advanced Data StructuresEasy

Q6. What is a min-heap?

  1. A.A heap where minimum element is at root✓ Correct
  2. B.A heap where maximum element is at root
  3. C.A sorted array of elements by value
  4. D.A balanced BST with min at leftmost

Explanation

In a min-heap, the minimum element is always at the root, and every parent node has a value less than or equal to its children.

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Advanced Data StructuresEasy

Q7. What is a trie (prefix tree)?

  1. A.A tree for storing and retrieving strings by prefix✓ Correct
  2. B.A graph data structure for string matching
  3. C.A binary search tree for numeric keys
  4. D.A type of hash table for string storage

Explanation

A trie is a tree where each node represents a character, and paths from root to nodes represent prefixes of stored strings. It enables fast prefix-based operations.

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Advanced Data StructuresEasy

Q8. What is the main advantage of a trie over a hash table for string operations?

  1. A.Has a simpler implementation overall
  2. B.Uses less memory usage in practice
  3. C.Supports prefix-based queries efficiently✓ Correct
  4. D.Provides faster exact string lookups

Explanation

Tries excel at prefix-based operations like autocomplete and prefix search, which hash tables cannot do efficiently.

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Advanced Data StructuresEasy

Q9. What does 'union' operation do in Union-Find?

  1. A.Splits a set into two parts
  2. B.Finds common elements between sets
  3. C.Merges two disjoint sets into one✓ Correct
  4. D.Sorts the sets in ascending order

Explanation

The union operation merges two disjoint sets into a single set by connecting their root representatives.

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Advanced Data StructuresHard

Q10. What is a van Emde Boas tree?

  1. A.A tree with O(log log U) operations for integer keys✓ Correct
  2. B.A tree with variable branching factor per level
  3. C.A cache-oblivious tree for external memory
  4. D.A self-balancing BST with color properties

Explanation

A van Emde Boas tree supports operations in O(log log U) time for integer keys in the universe [0, U), by recursively partitioning the universe.

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Advanced Data StructuresHard

Q11. What is a rope data structure?

  1. A.A linked list variant for characters
  2. B.A hash map for string key-value pairs
  3. C.A graph connecting strings with edges
  4. D.A balanced binary tree for efficient string operations✓ Correct

Explanation

A rope is a balanced binary tree where leaves contain short strings. It supports efficient concatenation, insertion, and deletion of substrings.

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Advanced Data StructuresHard

Q12. What is a wavelet tree?

  1. A.A tree for signal processing operations
  2. B.A frequency-based heap for priority ordering
  3. C.A Fourier transform data structure for arrays
  4. D.A tree for rank, select, and range queries on sequences✓ Correct

Explanation

A wavelet tree recursively partitions the alphabet to support rank, select, quantile, and range frequency queries on a sequence in O(log σ) time, where σ is the alphabet size.

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Advanced Data StructuresMedium

Q13. What is a circular buffer?

  1. A.A buffer shaped like a circle visually
  2. B.A buffer for circular linked list nodes
  3. C.A double-ended buffer with two pointers
  4. D.A fixed-size buffer that wraps around when full✓ Correct

Explanation

A circular buffer uses a fixed-size array with wrap-around to efficiently implement a FIFO queue, overwriting the oldest data when full.

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Advanced Data StructuresMedium

Q14. What is union by rank in Union-Find?

  1. A.Attaching shorter tree under taller tree during union✓ Correct
  2. B.Sorting all elements by their assigned rank
  3. C.Ranking all elements before performing union
  4. D.Using ranked hash functions for set operations

Explanation

Union by rank attaches the tree with lower rank (approximate height) under the root of the tree with higher rank, keeping the overall structure balanced.

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Advanced Data StructuresMedium

Q15. What is the nearly constant amortized time complexity of Union-Find with path compression and union by rank?

  1. A.O(1) constant time
  2. B.O(log log n) iterated log
  3. C.O(log n) logarithmic
  4. D.O(α(n)) inverse Ackermann✓ Correct

Explanation

With both path compression and union by rank, each operation takes O(α(n)) amortized time, where α is the inverse Ackermann function, which is effectively constant.

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Advanced Data StructuresMedium

Q16. What is a Fibonacci heap?

  1. A.A heap with better amortized decrease-key and insert✓ Correct
  2. B.A Fibonacci sequence number generator structure
  3. C.A binary heap variant with extra child pointers
  4. D.A heap that stores Fibonacci numbers only

Explanation

A Fibonacci heap supports insert and decrease-key in O(1) amortized time and extract-min in O(log n) amortized time, used to optimize Dijkstra's algorithm.

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Advanced Data StructuresMedium

Q17. What is a k-d tree?

  1. A.A space-partitioning tree for k-dimensional data✓ Correct
  2. B.A tree with k children per node always
  3. C.A tree of exactly depth k levels
  4. D.A k-ary heap data structure

Explanation

A k-d tree is a binary tree that partitions k-dimensional space, useful for nearest neighbor searches and range queries in multidimensional data.

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Advanced Data StructuresMedium

Q18. What is an interval tree?

  1. A.A tree for querying overlapping intervals efficiently✓ Correct
  2. B.A tree storing time intervals as keys
  3. C.A segment tree with interval-based updates
  4. D.A tree with regular spacing between nodes

Explanation

An interval tree stores intervals and supports efficient queries for all intervals that overlap with a given point or interval, in O(log n + k) time where k is the number of results.

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Advanced Data StructuresMedium

Q19. What is path compression in Union-Find?

  1. A.Making every node in find path point to root✓ Correct
  2. B.Compressing the storage used by the structure
  3. C.Shortening paths between nodes in a graph
  4. D.Compressing the data stored in each node

Explanation

Path compression optimizes find by making every node encountered during a find operation point directly to the root, flattening the tree structure.

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Advanced Data StructuresEasy

Q20. What is a multiset?

  1. A.A sorted set with unique elements
  2. B.A collection allowing duplicate elements✓ Correct
  3. C.A set with multiple data types
  4. D.A set of sets nested together

Explanation

A multiset (bag) is like a set but allows duplicate elements, counting the number of occurrences of each element.

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Advanced Data StructuresMedium

Q21. What is a sparse table?

  1. A.A table with many empty cells throughout
  2. B.A compressed hash table for sparse data
  3. C.A sparse matrix representation structure
  4. D.A structure for O(1) static range minimum queries✓ Correct

Explanation

A sparse table preprocesses data in O(n log n) time and space to answer range minimum (or maximum) queries in O(1) time for static arrays.

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Advanced Data StructuresMedium

Q22. What is the time complexity of inserting into a trie for a word of length L?

  1. A.O(n)
  2. B.O(log n)
  3. C.O(L)✓ Correct
  4. D.O(1)

Explanation

Insertion into a trie takes O(L) time, where L is the length of the word, as each character is processed once.

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Advanced Data StructuresHard

Q23. What is a count-min sketch?

  1. A.A data structure for exact element counting
  2. B.A compressed hash table with min values
  3. C.A min-heap variant tracking element counts
  4. D.A probabilistic structure for approximate frequency counts✓ Correct

Explanation

A count-min sketch uses multiple hash functions and a 2D array to approximate frequency counts in a data stream with possible overestimates but no underestimates.

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Advanced Data StructuresMedium

Q24. What is a suffix array?

  1. A.An array of string prefixes
  2. B.A compressed trie structure
  3. C.A sorted array of all string suffixes✓ Correct
  4. D.An array suffix pointer

Explanation

A suffix array is a sorted array of all suffixes of a string, providing an efficient alternative to suffix trees for many string processing problems.

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Advanced Data StructuresHard

Q25. What is a suffix tree?

  1. A.A tree that stores all string prefixes
  2. B.A compressed trie of all suffixes for O(m) matching✓ Correct
  3. C.An array of suffix pointers with sorting
  4. D.A binary tree of sorted suffix indices

Explanation

A suffix tree is a compressed trie containing all suffixes of a string. It enables pattern matching in O(m) time and many other string operations.

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Advanced Data StructuresHard

Q26. What is a link-cut tree?

  1. A.A tree where links can be physically cut
  2. B.A doubly linked tree with removable nodes
  3. C.A dynamic forest supporting link, cut, and path queries✓ Correct
  4. D.A tree with removable edges but fixed vertices

Explanation

A link-cut tree (by Sleator and Tarjan) maintains a dynamic forest supporting link (add edge), cut (remove edge), and path aggregate queries in O(log n) amortized time.

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Advanced Data StructuresHard

Q27. What is a persistent data structure?

  1. A.A data structure saved to disk permanently
  2. B.A data structure that cannot ever be deleted
  3. C.A data structure that persists across program runs
  4. D.A structure preserving all previous versions on modification✓ Correct

Explanation

A persistent data structure preserves all previous versions of itself when modified, allowing queries on any past version.

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Advanced Data StructuresHard

Q28. What is an order-statistic tree?

  1. A.An augmented BST supporting O(log n) rank and select✓ Correct
  2. B.A tree for statistical analysis of data sets
  3. C.A tree that orders elements statistically
  4. D.A heap that tracks insertion order of elements

Explanation

An order-statistic tree is a BST (often Red-Black) augmented with subtree sizes, supporting select (k-th smallest) and rank queries in O(log n) time.

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Advanced Data StructuresHard

Q29. What is a binomial heap?

  1. A.A heap with binomial probability distribution
  2. B.A heap used in statistical analysis methods
  3. C.A binary heap with extra pointer fields added
  4. D.A collection of binomial trees with O(log n) merge✓ Correct

Explanation

A binomial heap is a collection of binomial trees supporting merge, insert, and extract-min in O(log n) time. Merge is its key advantage over binary heaps.

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Advanced Data StructuresHard

Q30. What is a succinct data structure?

  1. A.A brief textual description of a data structure
  2. B.A structure using near information-theoretic minimum space✓ Correct
  3. C.A small fixed-capacity array with limited size
  4. D.A compressed hash table designed for very dense data

Explanation

A succinct data structure uses space close to the information-theoretic lower bound (within lower-order terms) while still supporting efficient query operations.

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