🧠 Advanced Data Structures

Level 8 — Performance Analysis

Measure and compare the efficiency of algorithms with clear reasons.

• Time and space complexity
• Best, average and worst cases
• O, Ω and Θ notation
• Growth-rate comparison

Level 9 — Disjoint Sets

Maintain non-overlapping groups efficiently using the Union-Find structure.

• Make-Set, Find and Union
• Tree representation
• Path compression
• Union by rank and size

Level 10 — Sparse Matrices

Store and process matrices containing mostly zero values without wasting memory.

• Triplet representation
• CSR and CSC formats
• Transpose and addition
• Storage comparison

Level 11 — String Pattern Matching

Find patterns in text using preprocessing, hashing and character-skipping strategies.

• Naive matching
• KMP and LPS array
• Rabin–Karp hashing
• Boyer–Moore method

Level 12 — Advanced Sorting

Compare comparison-based and non-comparison-based sorting algorithms.

• Merge, Quick and Shell Sort
• Counting, Radix and Bucket Sort
• Stability and in-place behavior
• Algorithm selection

Level 13 — Advanced Searching

Choose searching strategies by considering ordering, distribution and access cost.

• Interpolation Search
• Jump and Fibonacci Search
• Exponential Search
• Skip List searching

Level 14 — Balanced BST

Preserve efficient search and update operations by controlling tree height.

• AVL Trees and rotations
• Red–Black Trees
• Splay Trees
• Tree comparison

Level 15 — Digital Search Trees

Store keys by their characters or bits for fast prefix and pattern operations.

• Standard and Binary Tries
• Patricia Tries
• Suffix Tries
• Prefix-search applications

Level 16 — Multiway Search Trees

Organize many keys per node for efficient storage and database indexing.

• B-Tree operations
• 2–3 Trees
• B* Trees
• B+ Trees and indexing

Level 17 — Heaps

Implement priority operations and compare merge-friendly heap structures.

• Binary Heap and Heap Sort
• Binomial Heap
• Fibonacci Heap
• Complexity comparison

Level 18 — Hashing

Design hash tables and resolve collisions while maintaining efficient access.

• Hash functions
• Separate chaining
• Open addressing
• Load factor and resizing

Level 19 — Files & File Organization

Understand persistent storage models, access methods and indexing strategies.

• File concepts and attributes
• Sequential organization
• Indexed and direct access
• Indexing techniques

Level 20 — Advanced Graph Algorithms

Solve connectivity, routing, dependency and network-optimization problems.

• Prim and Kruskal MST
• Dijkstra and Bellman–Ford
• Floyd–Warshall
• Topological ordering and SCCs

Level 21 — Placement Problems

Level 22 — ADS Case Studies