Based on Number of Swaps or Inversion This is the number of times the algorithm swaps elements to sort the input. Selection Sort requires the minimum number of swaps.

基于交換次數或反轉次數這是算法交換元素以對輸入進行排序的次數。 Selection Sort要求最少數量的交換。

Based on Number of Comparisons This is the number of times the algorithm compares elements to sort the input. Using Big-O notation, the sorting algorithm examples listed above require at least O(nlogn) comparisons in the best case and O(n^2) comparisons in the worst case for most of the outputs.

基于比較次數這是算法比較元素以對輸入進行排序的次數。 使用Big-O表示法 ，上面列出的排序算法示例在大多數情況下對于大多數輸出??至少需要O(nlogn)比較，而在最壞情況下至少需要O(n^2)比較。

Based on Recursion or Non-Recursion Some sorting algorithms, such as Quick Sort, use recursive techniques to sort the input. Other sorting algorithms, such as Selection Sort or Insertion Sort, use non-recursive techniques. Finally, some sorting algorithm, such as Merge Sort, make use of both recursive as well as non-recursive techniques to sort the input.

基于遞歸或非遞歸一些排序算法(例如Quick Sort )使用遞歸技術對輸入進行排序。 其他排序算法(例如Selection Sort或Insertion Sort )使用非遞歸技術。 最后，一些排序算法(例如Merge Sort )利用遞歸和非遞歸技術對輸入進行排序。

Based on Stability Sorting algorithms are said to be stable if the algorithm maintains the relative order of elements with equal keys. In other words, two equivalent elements remain in the same order in the sorted output as they were in the input.

基于穩定性的排序算法被認為是stable是該算法使用相同的鍵維持元素的相對順序。 換句話說，兩個等效元素在排序輸出中的順序與輸入中的順序相同。

Insertion sort, Merge Sort, and Bubble Sort are stable

Insertion sort ， Merge Sort和Bubble Sort穩定

Heap Sort and Quick Sort are not stable

Heap Sort和Quick Sort不穩定

Based on Extra Space Requirement Sorting algorithms are said to be in place if they require a constant O(1) extra space for sorting.

基于額外空間要求，如果排序算法需要恒定的O(1)額外空間來進行排序，則可以說已經in place 。

Insertion sort and Quick-sort are in place sort as we move the elements about the pivot and do not actually use a separate array which is NOT the case in merge sort where the size of the input must be allocated beforehand to store the output during the sort.

Insertion sort和Quick-sort是in place我們圍繞樞軸移動元素時in place排序，實際上并沒有使用單獨的數組，在合并排序中情況并非如此，在合并排序中，必須事先分配輸入的大小以在輸出期間存儲輸出分類。

Merge Sort is an example of out place sort as it require extra memory space for it’s operations.

Merge Sort是一個例子out place的排序，因為它需要它的運營的額外存儲空間。