| Sorting Algorithm | Average Time Complexity | Worst Case Time Complexity | Space Complexity | Stability | Description |
|---|---|---|---|---|---|
| Bubble Sort | O(n^2) | O(n^2) | O(1) | Stable | Simple and easy to implement. Used on small data sets or as a simple teaching tool. |
| Selection Sort | O(n^2) | O(n^2) | O(1) | Unstable | Simple and easy to implement. Used on small data sets or as a simple teaching tool. |
| Insertion Sort | O(n^2) | O(n^2) | O(1) | Stable | Simple and efficient for small data sets or partially sorted data. |
| Merge Sort | O(n log n) | O(n log n) | O(n) | Stable | Efficient for sorting large amounts of data. Used in external sorting and in parallel computing. |
| Quick Sort | O(n log n) | O(n^2) | O(log n) | Unstable | Efficient for sorting large amounts of data. Used in practice for its average case performance, but can have poor worst-case performance. |
| Heap Sort | O(n log n) | O(n log n) | O(1) | Unstable | Efficient for sorting large amounts of data. Used in practice when the size of the data set is unknown or unbounded. |
| Radix Sort | O(dn) | O(dn) | O(n + k) | Stable | Efficient for sorting data with a fixed number of digits or keys. Used in practice for sorting strings, integers, or IP addresses. |
| Counting Sort | O(n + k) | O(n + k) | O(n + k) | Stable | Efficient for sorting integers with a small range. Used in practice for sorting grades, exam scores, and frequencies. |
| Bucket Sort | O(n + k) | O(n^2) | O(n + k) | Stable | Efficient for sorting data with a uniform distribution. Used in practice for sorting letters, names, and ranges. |
| Shell Sort | O(n log n) | Depends on gap sequence | O(1) | Unstable | Efficient for sorting data with a large number of elements. Used in practice for sorting word lists and arrays. |
| Comb Sort | Depends on gap sequence | O(n^2) | O(1) | Unstable | Efficient for sorting data with a large number of elements. Used in practice for sorting word lists and arrays. |
| Cocktail Sort | O(n^2) | O(n^2) | O(1) | Stable | Variation of bubble sort. Used in practice for sorting word lists and arrays. |
| Gnome Sort | O(n^2) | O(n^2) | O(1) | Stable | Efficient for sorting small data sets. Used in practice for sorting word lists and arrays. |
| Pancake Sort | O(n^2) | O(n^2) | O(n) | Unstable | Efficient for sorting data with limited number of flips. Used in practice for sorting word lists and arrays. |
| Bogo Sort | O(n*n!) | O(∞) | O(1) | Unstable | Inefficient and impractical for large data sets. Used as a benchmark for comparing other sorting algorithms. |
| Stooge Sort | O(n^2.71) | O(n^?) | O(n) | Unstable | Recursively sorts a quarter of the array pass by swapping with another quarter. Used in practice for sorting large and small arrays. |
| Batcher Sort | O(n log^2 n) | O(n log^2 n) | O(n) | Unstable | Based on mergesort. Used to sort large and small arrays. |
| Odd-even Sort | O(n^2) | O(n^2) | O(1) | Stable | Similar to bubble sort. Used for sorting small arrays. |
| Bitonic Sort | O(n log^2 n) | O(n log^2 n) | O(n log n) | Unstable | Based on mergesort. Used for data with a power of two size. |
| Cycle Sort | O(n^2) | O(n^2) | O(1) | Stable | Efficient for sorting data with repeated elements. Used in practice for sorting words lists and arrays. |
| Pigeonhole Sort | O(n + k) | O(n + k) | O(n + k) | Stable | Efficient for sorting data with integer keys within a small range. Used in practice for sorting ages, birthdates, phone numbers, and colors. |
| Library Sort | O(n log n) | O(n log n) | O(n log n) | Stable | Based on radix sort. Used for sorting data with variable-length keys. |
| Binary Tree Sort | O(n log n) | O(n^2) | O(n) | Stable | Builds a binary search tree. Used in practice for sorting large and small data sets. |
| Bead Sort | O(n) | O(n^2) | O(n) | Unstable | Efficient for sorting non-negative integers with a small range. Used in practice for sorting trinkets, jewelry, and toys. |
| Smooth Sort | O(n log n) | O(n log n) | O(1) | Unstable | Combines heap sort with Fibonacci heaps. Used in practice for sorting data sets with a skewed distribution. |
| Timsort | O(n log n) | O(n log n) | O(n) | Stable | Combines insertion sort and merge sort. Used in practice for sorting arrays, lists, and stable sorts. |
| Cube Sort | O(n log n) | O(n log n) | O(n log n) | Unstable | Efficient for sorting numeric data. Used in practice for sorting scientific data. |
| Sleep Sort | O(n) | O(n) | O(1) | Unstable | Sorts integers in time proportional to the largest number. Used in practice for fun purposes. |
| Introsort | O(n log n) | O(n log n) | O(log n) | Unstable | Based on quick sort with additional steps. Used in practice for sorting data that contains duplicates. |
| Flashsort | O(n + k) | O(n^2) | O(k) | Unstable | Efficient for sorting data with a uniform distribution. Used in practice for sorting data from physical measurements. |
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