How many algorithms are there for sorting purpose and what are they?

Answer 1

There are many sorting algorithms however there are only a small handful that we actually use: insertion sort (stable) is typically used for small sets while large data sets primarily use heapsort (unstable), merge sort (stable) or quicksort (unstable). Efficient implementations typically use a hybrid sort such as Timsort (stable) or introsort (unstable).

The following lists all the documented algorithms currently listed in Wikipedia's "Sorting algorithm" page:

Quicksort, merge sort, in-place merge sort, heapsort, insertion sort, introsort, selection sort, Timsort, cubesort, shell sort, bubble sort, binary tree sort, cycle sort, library sort, patience sorting, smoothsort, strand sort, tournament sort, cocktail sort, comb sort, gnome sort, unshuffle sort, Franceschini's sort, block sort, odd-even sort, pigeonhole sort, bucket sort (uniform keys), bucket sort (integer keys), counting sort, LSD radix sort, MSD radix sort, MSD radix sort in-place, spreadsort, burstsort, flashsort, postman sort bead sort, simple pancake sort, spaghetti sort, sorting network, bitonic sorter, bogo sort, stooge sort, Han's algorithm, Thorup's algorithm.