🧱 Data Structures
Context: Choosing the right data structure is the first step towards performance. In day-to-day operations, this translates to selecting the collection that minimizes the time complexity for the most frequent operation.
📊 Complexity Table (Big-O)
Section titled “📊 Complexity Table (Big-O)”| Structure | Access | Search | Insertion | Removal |
|---|---|---|---|---|
| Arrays | O(1) | O(n) | O(n) | O(n) |
| Hash Tables | N/A | O(1) | O(1) | O(1) |
| BST (Balanced) | O(log n) | O(log n) | O(log n) | O(log n) |
| Graphs | — | O(V + E) | — | — |
📂 Main Categories
Section titled “📂 Main Categories”1. Lists and Arrays
Section titled “1. Lists and Arrays”- Dynamic Arrays: Contiguous memory, fast access by index.
- Linked Lists: Useful when insertion/removal at the beginning is frequent (O(1)), but terrible for random access.
2. Trees
Section titled “2. Trees”Essential for representing hierarchies and for quick searches.
- Binary Search Trees (BST): They keep the data organized.
- Tries: Essential for autocomplete systems and prefix search.
3. Graphs
Section titled “3. Graphs”Used to model complex relationships (social media, GPS routes, packet dependencies).
4. Hash Tables
Section titled “4. Hash Tables”The basis of almost all caching and fast indexing systems.
- Critical Concepts: Hash Functions, Collisions (Chaining vs. Open Addressing), and Load Factor.
⚖️ Trade-offs and Decisions
Section titled “⚖️ Trade-offs and Decisions”Memory vs. Performance
Section titled “Memory vs. Performance”Structures like Hash Tables and B+ Trees (used in databases) trade memory space for search speed. As a Programmer, you should ask: “Does the extra RAM cost justify the millisecond gain for this volume of data?”
Reference Location
Section titled “Reference Location”Arrays are usually faster than Linked Lists on modern CPUs, not because of theoretical complexity, but because contiguous memory makes better use of the processor’s L1/L2 Cache.
💡 Note: Beware of the “obsession with Big-O”. In small data volumes (n < 100), a simple array with O(n) can be faster than a complex O(log n) structure due to the overhead of pointer management and memory allocation.