What is a stable sorting algorithm?

A stable sorting algorithm is defined by its ability to preserve the relative order of records with equal keys. This means that if two elements are considered equal according to the sorting criteria, their order in the sorted output will reflect the order they appeared in the original input. This characteristic is particularly useful in scenarios where multiple fields are involved in sorting, such as sorting a list of people by last name and then by first name. After sorting by last name, if two people share the same last name, their original order by first name should remain unchanged in the final sorted list.

The other provided choices do not accurately describe what a stable sorting algorithm is. For instance, a stable sorting algorithm is not limited to arranging elements in ascending order, as it can sort in descending order while still maintaining stability—so the first option is not correct. The speed of a sorting algorithm can vary widely, and stable sorting algorithms can be faster or slower than others, depending on the context and the methods used—thus, the claim about being the fastest does not define stability. Finally, while some stable sorting algorithms may use constant space, many do not; they may require additional memory for their operations, making the assertion about constant space incorrect as well.