Comparison of the time complexity of various sorting algorithms
| Sorting Algorithm |
Worst time complexity |
Average time complexity |
Optimal time complexity |
Space complexity |
stability |
| Bubble Sort |
O (n ^ 2) |
O (n ^ 2) |
O (n) |
O (1) |
stable |
| Insertion sort |
O (n ^ 2) |
O (n ^ 2) |
O (n) |
O (1) |
stable |
| Hill sort |
O (n ^ 2) |
O (n ^ 1.5) |
O (nlogn) |
O (1) |
Unstable |
| Select sort |
O (n ^ 2) |
O (n ^ 2) |
O (n ^ 2) |
O (1) |
Unstable |
| Quick sort |
O (n ^ 2) |
O (nlogn) |
O (nlogn) |
O (logn) |
Unstable |
| Merge sort |
O (nlogn) |
O (nlogn) |
O (nlogn) |
O (n) |
stable |
| Heap sort |
O (nlogn) |
O (nlogn) |
O (nlogn) |
O (1) |
Unstable |
| Count sort |
O(n+k) |
O(n+k) |
O(n+k) |
O(k) |
stable |
| Bucket sort |
O (n ^ 2) |
O(n+k) |
O(n+k) |
O (n) |
Depends on the sorting in the bucket |
| Base sort |
O(d(n+k)) |
O(d(n+k)) |
O(d(n+k)) |
O(n+k) |
stable |
