SEARCH & SORT PROBLEM-SOLVING TRICKS
Search Algorithm Tricks
| # | Technique | Description |
|---|---|---|
| 1 | Binary Search Optimization | Use mid = low + (high - low)/2 to prevent overflow. For duplicates, continue searching left/right after match. |
| 2 | Interpolation Search | Guesses position based on value distribution. Faster than binary search for uniformly distributed data. |
| 3 | Exponential Search | Double the range until target is found, then binary search. Ideal for unbounded lists. |
| 4 | Two-Pointer Technique | Use pointers at start and end to find pairs in sorted arrays (e.g., sum to target). |
| 5 | Hashing for Lookups | Use hash tables for O(1) average-case search when memory allows. |
Sorting Algorithms Comparison
| Algorithm | Best Case | Average Case | Worst Case | Space | Stable? | Use Cases |
|---|---|---|---|---|---|---|
| Bubble Sort | O(n) | O(n²) | O(n²) | O(1) | Yes | Education, tiny datasets |
| Selection Sort | O(n²) | O(n²) | O(n²) | O(1) | No | Small datasets, minimize swaps |
| Insertion Sort | O(n) | O(n²) | O(n²) | O(1) | Yes | Small/nearly sorted data |
| Merge Sort | O(n log n) | O(n log n) | O(n log n) | O(n) | Yes | Large datasets, stable sort needed |
| Quick Sort | O(n log n) | O(n log n) | O(n²) | O(log n) | No | General-purpose sorting |
| Heap Sort | O(n log n) | O(n log n) | O(n log n) | O(1) | No | Worst-case O(n log n) required |
| Counting Sort | O(n + k) | O(n + k) | O(n + k) | O(n + k) | Yes | Small integer ranges |
| Radix Sort | O(nk) | O(nk) | O(nk) | O(n + k) | Yes | Fixed-length keys |
| Bucket Sort | O(n + k) | O(n + k) | O(n²) | O(n + k) | Yes | Uniformly distributed data |
How to Choose a Sorting Algorithm
By Dataset Size
- Small (10-20 elements): Insertion Sort
- Medium: Quick Sort (general purpose)
- Large: Merge Sort or Heap Sort
By Requirements
- Stability needed: Merge Sort
- Worst-case guarantee: Heap Sort
- Limited memory: In-place Quick Sort
By Data Type
- Small integer ranges: Counting Sort
- Fixed-length keys: Radix Sort
- Uniform distribution: Bucket Sort
Special Cases
- Nearly sorted data: Insertion Sort
- External sorting: Merge Sort
- Hybrid approach: Intro Sort (Quick + Heap + Insertion)
General Problem-Solving Strategies
Search Optimization
- Pre-sort data for multiple binary search queries
- Use hash tables when O(1) lookups are possible
- Consider interpolation search for uniform distributions
Sort Optimization
- Combine algorithms (hybrid sorts) for best performance
- Use partial sorting (Quickselect) when only some elements are needed
- Choose in-place sorts when memory is constrained
Pro Tip: Always analyze your problem constraints (time, space, data characteristics) before selecting an algorithm.