Sorting Algorithms

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Before delving into the large variety of sorting algorithms, it's important to understand that there are simple ways to perform sorts in most programming languages. For example, in Java, the Collections class contains a sort method that can be implemented as simply as:

Collections.sort(list);

where list is an object such as an ArrayList. Some aspects of the Java sort() method to note are:

  • You can also use the Java Comparator class methods to implement your own list item comparison functions for specialized sorting order needs.
  • The Java Collections class (plural) is different than the Collection class (singular).
  • Which sorting algorithm (see below) is used in the Collections.sort() implementation depends on the implementation approach chosen by the Java language developers. You can find implementation notes for Java Collections.sort() here. It currently uses a modified merge sort that performs in the range of Big O O(n log(n)).

If you don't want to use a built-in sort function and you're going to implement your own sort function, there's a large list of sorting algorithms to choose from.  Factors to consider in choosing a sort algorithm include:

  • Speed of the algorithm for the best, average and worst sort times. Most algorithms have sort times characterized by Big O functions of O(n), O(n log(n)) or O(n^2).
  • The relative importance of the best, average and worst sort times for the sort application.
  • Memory required to perform the sort.
  • Type of data to be sorted (e.g., numbers, strings, documents).
  • The size of the data set to be sorted.
  • The need for sort stability (preserving the original order of duplicate items).
  • Distribution and uniformity of values to be sorted.
  • Complexity of the sort algorithm.

For a comparison of sorting algorithms based on these and other values see: https://en.wikipedia.org/wiki/Sorting_algorithm#Comparison_of_algorithms.

Here's a quick reference for the major algorithms:

  • Exchange Sorts: based on swapping items
    • Bubble sort: for each pair of indices, swap the items if out of order, loop for items and list.
    • Cocktail sort: variation of bubble sort, passes alternately from top to bottom and bottom to top.
    • Comb sort: variation of bubble sort, selective swap of values
    • Gnome sort: also called the stupd sort, moves values back to just above a value less than it
    • Odd-even sort: developed originally for use with parallel processors, examines odd-even pairs and orders them, alternates pairs until list is ordered
    • Quicksort: divide list into two, with all items on the first list coming before all items on the second list.; then sort the two lists. Repeat. Often the method of choice. One of the fastest sort algorithms
  • Hybrid Sorts: mixture of sort techniques
    • Flashsort: Used on data sets with a known distribution, estimates used for where an element should be placed
    • Introsort: begin with quicksort and switch to heapsort when the recursion depth exceeds a certain level
    • Timsort: adaptative algorithm derived from merge sort and insertion sort. 
  • Insertion sorts: builds the final sorted array one item at a time
    • Insertion sort: determine where the current item belongs in the list of sorted ones, and insert it there
    • Library sort: like library shelves, space is created for new entries within groups such as first letters, space is removed at end of sort
    • Patience sorting: based on the solitaire card game, uses piles of "cards"
    • Shell sort: an attempt to improve insertion sort
    • Tree sort (binary tree sort): build binary tree, then traverse it to create sorted list
    • Cycle sort: in-place with theoretically optimal number of writes
  • Merge sorts: takes advantage of the ease of merging already sorted lists into a new sorted list
    • Merge sort: sort the first and second half of the list separately, then merge the sorted lists
    • Strand sort: repeatedly pulls sorted sublists out of the list to be sorted and merges them with the result array
  • Non-comparison sorts
    • Bead sort: can only be used on positive integers, performed using mechanics like beads on an abacus
    • Bucket sort: works by partitioning an array into a number of buckets, each bucket is then sorted individually using the best technique, the buckets are then merged
    • Burstsort: used for sorting strings, employs growable arrays
    • Counting sort: sorts a collection of objects according to keys that are small integers
    • Pigeonhole sort: suitable for sorting lists of elements where the number of elements and number of possible key values are approximately the same, uses auxiliary arrays for grouping values
    • Postman sort: variant of Bucket sort which takes advantage of hierarchical structure
    • Radix sort: sorts strings letter by letter
  • Selection sorts: in place comparison sorts
    • Heapsort: convert the list into a heap, keep removing the largest element from the heap and adding it to the end of the list
    • Selection sort: pick the smallest of the remaining elements, add it to the end of the sorted list
    • Smoothsort
  • Other
  • Unknown class