Counting, Frequency, and Precomputation¶
This category covers techniques for efficiently counting elements, managing frequencies, and preprocessing data to enable faster queries. These methods are fundamental to many algorithmic solutions and are often used as building blocks for more complex algorithms.
Techniques in This Category¶
| Technique | Description | Link |
|---|---|---|
| Frequency Counting Arrays | Using arrays to count occurrences of elements, enabling O(1) lookups for frequency queries. | Frequency Arrays |
| Static Array Queries | Answering range sums, RMQ, and related queries on data that does not change between queries. | Static Array Queries |
| Prefix Arrays | Cumulative sums (1D and 2D) for O(1) range sum queries after preprocessing. | Prefix Arrays |
| Difference Arrays | O(1) range add updates via difference / Imos; reconstruct values with a final prefix scan. | Difference Arrays |
| Sieve of Eratosthenes | An efficient algorithm for finding all prime numbers up to a given limit through systematic elimination. | Sieve of Eratosthenes |
When to Use¶
These techniques are essential when: - You need to answer multiple queries about ranges or frequencies - Working with statistical data or counting problems - Optimizing repeated computations - Building foundations for more complex algorithms
Key Benefits¶
- Time Complexity: Often reduces query time from O(n) to O(1)
- Space Efficiency: Uses simple data structures like arrays
- Simplicity: Easy to implement and understand
- Versatility: Applicable to a wide range of problems