What does algorithm stability mean?

The stability of the algorithm refers to the fact that in a set of records to be sorted, if there are any two equal records R and S, and R is before S in the records to be sorted, if R is still before sorting S means that their front and back positions do not change before and after sorting, then the sorting algorithm is said to be stable.

Algorithm stability: In a set of records to be sorted, if there are any two equal records R and S, and in the records to be sorted, R is in Before S, if R is still before S after sorting, that is, their front and back positions do not change before and after sorting, then the sorting algorithm is said to be stable.

Stability of common sorting algorithms

Heap sort, quick sort, Hill sort, and direct selection sort are unstable sorting algorithms, while radix sort , bubble sort, direct insertion sort, half insertion sort, and merge sort are stable sorting algorithms.

First of all, everyone should know the stability of the sorting algorithm. In layman's terms, it can ensure that the order of the front and back positions of the two equal numbers before sorting is the same as the order of the front and back positions of the two after sorting. In simple formalization, if Ai = Aj, Ai is originally in front of the position, and Ai will still be in front of the position of Aj after sorting.

Secondly, let’s talk about the benefits of stability. If the sorting algorithm is stable, then sorting from one key and then sorting from another key, the result of the first key sorting can be used for the second key sorting. Radix sorting is like this, sorting by low bits first, then sorting by high bits. The order of elements with the same low bits will not change when the high bits are the same.

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