# When Does the Stability of Sorting Algorithms Matter?

## Contents

In this post, I will write about the stability of sorting algorithms and why it is important.

When we read articles about sorting algorithms, a term that often appears is the “stability” of an algorithm. The definition of stability is pretty simple: Given an unsorted list and a sorting algorithm. If two equal elements in the original list remain their relative order in the sorted list, then the sorting algorithm is stable, otherwise it is an unstable algorithm.

Now that we know the definition and there tons of article telling you which sorting algorithm is stable and which is not, we may wonder what is the point of identifying if an algorithm is stable or not. In fact, if you only have a list of single items to sort, the stability of the sorting algorithm is not important. However, if you have a list where each element is some kind of record which has several keys, you way want to sort the record based on several keys. That is where stability comes into play.

For example, we have a list of some students who belong to different labs,^{1}

```
Dave A
Alice B
Ken A
Eric B
Carol A
```

We want to sort the records first using the student names as the key, the result is:

```
Alice B
Carol A
Dave A
Eric B
Ken A
```

Then we want to sort the above result further based on their labs, we may get the result of

```
Dave A
Ken A
Carol A
Alice B
Eric B
```

or

```
Carol A
Dave A
Ken A
Alice B
Eric B
```

If the use a stable algorithm, it will ensure that the order of previous sorting will be preserved if two keys are the same. So the names corresponding to the same labs are in sorted order. The result will be

```
Carol A
Dave A
Ken A
Alice B
Eric B
```

In summary, the stability of sorting algorithms is important only when you want to chain multiple sort according to different keys in the record. If your record only has one key, the stability issue is irrelevant.

# References

- https://stackoverflow.com/questions/1517793/what-is-stability-in-sorting-algorithms-and-why-is-it-important
- https://stackoverflow.com/questions/808617/what-is-the-benefit-for-a-sort-algorithm-to-be-stable/808668#808668
- http://www.drdobbs.com/cpp/why-stable-sorting-is-important/231001864