Sorting Algorithms
Comparison of fundamental sorting algorithms with time and space complexity.
Sorting algorithms with best, average and worst time, space, stability and notes: bubble, selection, insertion, merge, quick, heap, counting and radix sort, extended with Timsort, introsort, bucket sort and shell sort.
Use it when
- You need to choose a sort or explain the trade-offs among them.
- You need to know whether a sort is stable or in place.
Watch out for
- Counting, radix and bucket sort assume a bounded key range or distribution.
- Standard libraries use hybrid algorithms; textbook sorts are mainly for understanding.
The data
12 rows
| Name | Best | Average | Worst | Space | Stable | Notes |
|---|---|---|---|---|---|---|
| Bubble Sort | O(n) | O(n^2) | O(n^2) | O(1) | true | Simple but inefficient for large inputs. |
| Selection Sort | O(n^2) | O(n^2) | O(n^2) | O(1) | false | Minimizes swaps; good when write cost is high. |
| Insertion Sort | O(n) | O(n^2) | O(n^2) | O(1) | true | Efficient for small or nearly sorted datasets. |
| Merge Sort | O(n log n) | O(n log n) | O(n log n) | O(n) | true | Consistent performance; good for linked lists. |
| Quick Sort | O(n log n) | O(n log n) | O(n^2) | O(log n) | false | In-place; widely used in practice. |
| Heap Sort | O(n log n) | O(n log n) | O(n log n) | O(1) | false | Guaranteed O(n log n); in-place. |
| Counting Sort | O(n + k) | O(n + k) | O(n + k) | O(k) | true | Only for integers in bounded range. |
| Radix Sort | O(nk) | O(nk) | O(nk) | O(n + k) | true | Sorts by digit position; k = number of digits. |
| Timsort | O(n) | O(n log n) | O(n log n) | O(n) | true | Hybrid of merge and insertion sort that exploits existing runs; used in Python and Java for objects. |
| Introsort | O(n log n) | O(n log n) | O(n log n) | O(log n) | false | Starts as quicksort and falls back to heapsort when recursion gets too deep; common in C++ std::sort. |
| Bucket Sort | O(n + k) | O(n + k) | O(n^2) | O(n + k) | true | Distributes items into buckets and sorts each; good for uniformly distributed input. |
| Shell Sort | O(n log n) | Depends on gap sequence | O(n^2) for simple gaps | O(1) | false | Generalizes insertion sort with diminishing gaps; simple and in place. |
Fields
The shape of this dataset, read from the data itself: every column, its type and a real value. Agents can use this to plan a query without fetching the whole document.
| Section | Field | Type | Example |
|---|---|---|---|
| data | name | string | Bubble Sort |
| data | best | string | O(n) |
| data | average | string | O(n^2) |
| data | worst | string | O(n^2) |
| data | space | string | O(1) |
| data | stable | boolean | true |
| data | notes | string | Simple but inefficient for large inputs. |
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