Watch the invariant
Green values satisfy the algorithm’s current guarantee: a sorted suffix, sorted prefix, fixed pivot, completed merge, or finished output position.
Explore one algorithm at a time
Select a method, enter up to 12 non-negative integers, and use the controls to study every meaningful operation.
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Live pseudocode
current step
compare / inspect
move / swap
candidate / auxiliary
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Auxiliary state
This area will show temporary arrays, gaps, heap boundaries, counts, digits, or buckets when the selected method needs them.
Enter between 2 and 12 integers from 0 to 99, separated by spaces or commas.
Choose the right sorting method
The table states the standard textbook bounds. Actual performance also depends on input order, implementation details, cache behavior, pivot choice, and gap sequence.
| Algorithm | Family | Best | Average | Worst | Extra space | Stable? | In place? |
|---|---|---|---|---|---|---|---|
| Bubble Sort | comparison | O(n) | O(n²) | O(n²) | O(1) | Yes | Yes |
| Selection Sort | comparison | O(n²) | O(n²) | O(n²) | O(1) | No | Yes |
| Insertion Sort | comparison | O(n) | O(n²) | O(n²) | O(1) | Yes | Yes |
| Merge Sort | comparison | O(n log n) | O(n log n) | O(n log n) | O(n) | Yes | No |
| Quick Sort | comparison | O(n log n) | O(n log n) | O(n²) | O(log n) average stack | No | Yes |
| Heap Sort | comparison | O(n log n) | O(n log n) | O(n log n) | O(1) | No | Yes |
| Shell Sort | comparison | Depends on gaps | Depends on gaps | O(n²) | O(1) | No | Yes |
| Counting Sort | distribution | O(n + k) | O(n + k) | O(n + k) | O(n + k) | Yes | No |
| Radix Sort | distribution | O(d(n + b)) | O(d(n + b)) | O(d(n + b)) | O(n + b) | Yes | No |
| Bucket Sort | distribution | O(n + k) | O(n + k) | O(n²) | O(n + k) | Can be | No |
Read the auxiliary state
Merge uses temporary storage; Shell exposes its gap; Heap shows the active heap; Counting, Radix, and Bucket Sort reveal their distribution structures.
Compare the counters
Run the same array through different methods. The counters make comparisons, swaps, and writes concrete without pretending that every operation has identical machine cost.