The sorting algorithm has evolved over a long period of time, resulting in many different methods. For beginners, it is very important to organize them so that they can easily understand and remember. Each algorithm has its specific use occasions, and it is difficult to be universal. Therefore, it is necessary to summarize all common sorting algorithms.
The sorts with large sorting can be divided into two types: inner sorting and outer sorting. In the sorting process, all records are stored in memory, which is called internal sorting. If external storage is used in the sorting process, it is called external sorting. The following sorts are all sorts within.
The internal sorting can be divided into the following categories:
(1) Insertion sorting: direct insertion sorting, dichotomy insertion sorting, Hill sorting.
(2), selection sorting: direct selection sorting, heap sorting.
(3) Exchange sorting: bubble sorting and quick sorting.
(4), merge sort
(5), cardinality sorting
Tabular version:
| Sorting method | Time complexity (average) | Time complexity (worst) | Time complexity (best) | Space complexity | stability | Complexity |
|---|---|---|---|---|---|---|
| Direct insertion sort | O ( n 2 ) O (n2) | O ( n 2 ) O (n2) | O ( n ) O (n) | O ( 1 ) O (1) | stable | simple |
| Hill Sort | O(nlog2n)O(nlog2n) | O ( n 2 ) O (n2) | O ( n ) O (n) | O ( 1 ) O (1) | Unstable | More complicated |
| Direct selection sort | O ( n 2 ) O (n2) | O ( n 2 ) O (n2) | O ( n 2 ) O (n2) | O ( 1 ) O (1) | Unstable | simple |
| Heap sort | O(nlog2n)O(nlog2n) | O(nlog2n)O(nlog2n) | O(nlog2n)O(nlog2n) | O ( 1 ) O (1) | Unstable | More complicated |
| Bubble Sort | O ( n 2 ) O (n2) | O ( n 2 ) O (n2) | O ( n ) O (n) | O ( 1 ) O (1) | stable | simple |
| Quick sort | O(nlog2n)O(nlog2n) | O ( n 2 ) O (n2) | O(nlog2n)O(nlog2n) | O(nlog2n)O(nlog2n) | Unstable | More complicated |
| Merge sort | O(nlog2n)O(nlog2n) | O(nlog2n)O(nlog2n) | O(nlog2n)O(nlog2n) | O ( n ) O (n) | stable | More complicated |
| Cardinality sorting | O(d(n+r))O(d(n+r)) | O(d(n+r))O(d(n+r)) | O(d(n+r))O(d(n+r)) | O(n+r)O(n+r) | stable | More complicated |
Picture version:
