Comparison of Internal Sorting Algorithms

Comparison of Internal Sorting Algorithms

Algorithm type	best time complexity	average time complexity	worst time complexity	space complexity	Is it stable	Whether the number of sorting times is related to the initial state of the sequence	Whether the number of comparisons is related to the initial state of the sequence
direct insertion sort	$$O\left(n\right)$$	$$O(n^2)$$	$$O\left(n^2\right)$$	$$O(1)$$	yes	irrelevant	related
Bubble Sort	$$O\left(n\right)$$	$$O\left(n^2\right)$$	$$O\left(n^2\right)$$	$$O\left(1\right)$$	yes	related	related
simple selection sort	$$O\left(n^2\right)$$	$$O\left(n^2\right)$$	O(n^2)	$$O\left(1\right)$$	no	irrelevant	irrelevant
Hill sort	null	null	null	$$O\left(1\right)$$	no	irrelevant	related
quick sort	$$O(nlo{g}_{2}n)$$	$$O\left(nlo{g}_{2}n\right)$$	$$O\left(n^2\right)$$	$$O\left(nlo{g}_{2}n\right)$$	no	related	related
heap sort	$$O\left(nlo{g}_{2}n\right)$$	$$O\left(nlo{g}_{2}n\right)$$	$$O\left(nlo{g}_{2}n\right)$$	$$O\left(1\right)$$	no	irrelevant	related
2-way merge sort	$$O\left(nlo{g}_{2}n\right)$$	$$O\left(nlo{g}_{2}n\right)$$	$$O\left(nlo{g}_{2}n\right)$$	$$O\left(n\right)$$	yes	irrelevant	irrelevant
radix sort	$$O(d(n+r))$$	$$O\left(d\right(n+r))$$	$$O\left(d\right(n+r))$$	$$O\left(r\right)$$	yes	irrelevant	irrelevant

---

Since the time complexity of Hill sorting is a mathematical problem that has not yet been solved, this table is not indicated yet.