Data Structures¶
Data structures are fundamental building blocks for efficient algorithm design. This category covers advanced data structures that enable fast queries, updates, and specialized operations essential for solving complex computational problems.
Techniques in This Category¶
| Technique | Description | Link |
|---|---|---|
| Segment Tree / BIT | Efficient range query data structures that allow fast updates and range operations, essential for many competitive programming problems. | Segment Tree / BIT |
| Heap / Priority Queue | Dynamic data structures for maintaining extremal elements (minimum or maximum) with efficient insertion and deletion operations. | Heap / Priority Queue |
| Disjoint Set (DSU) | A data structure for efficiently managing disjoint sets, commonly used for connectivity problems and minimum spanning tree algorithms. | Disjoint Set (DSU) |
When to Use Advanced Data Structures¶
These data structures are essential when: - You need to perform frequent range queries or updates - Maintaining extremal elements with dynamic operations - Working with connectivity or union-find problems - Optimizing time complexity for repeated operations
Common Applications¶
Segment Trees & Binary Indexed Trees¶
- Range Sum Queries: Computing sums over ranges efficiently
- Range Minimum/Maximum: Finding extremal values in ranges
- Range Updates: Applying updates to ranges of elements
- Inversion Counting: Counting inversions in arrays
Heaps & Priority Queues¶
- Dijkstra's Algorithm: Finding shortest paths in graphs
- Median Maintenance: Keeping track of running median
- Task Scheduling: Prioritizing tasks based on urgency or importance
- Merge Operations: Efficiently merging sorted sequences
Disjoint Set Union¶
- Connectivity Problems: Determining if elements are connected
- Minimum Spanning Tree: Kruskal's algorithm implementation
- Cycle Detection: Detecting cycles in undirected graphs
- Component Analysis: Analyzing connected components