Sorting means putting items in a chosen order. In ascending order, smaller values come first. In descending order, larger values come first. The key is the value we compare to decide which item should come first.

An algorithm must produce that order and keep all the original items. Losing an item is not a correct sorting method, even if the remaining items look ordered. Repeated values must keep their correct number of occurrences.

Several algorithms solve this same task. In the next lesson, we will follow Selection Sort and Insertion Sort one move at a time. First, learn how to describe the task and its constraints; you do not need to memorise a long list of algorithm names.

A map of names, not a ranking

Group	Examples	What to notice now
Direct comparison methods	Selection Sort, Insertion Sort	Simple steps; the usual versions have quadratic worst-case time
Other comparison methods	Merge Sort, Quick Sort, Heap Sort	Their guarantees depend on the algorithm and the case being analysed
Other names you will meet	Bubble Sort, Comb Sort, Shell Sort	A similar name does not imply the same running time
Distribution methods	Counting Sort, Radix Sort, Bucket Sort	These use properties of the values, their digits, or their distribution

There is no rule that every algorithm in one row is always better than every algorithm in another row. For example, ordinary Quick Sort can take quadratic time in the worst case; $O(n\log n)$ is not a guarantee for every execution of every version.