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Selection Sort

  • О(n^2) comparisons, О(n) swaps
  • naive implementation for sorting

Insertion Sort

  • О(n^2) comparisons and swaps
  • O(1) auxiliary space
  • can run online
  • stable

Merge Sort

  • O(n log(n)) by divide and conquer
  • O(n) auxiliary space
  • stable; deterministic

Quick Sort

  • O(n log(n)) by divide and conquer; worst case O(n) though
  • O(1) auxiliary space; one of exchange sorts (cf. bubble sort)
  • unstable; randomized


  • hybrid sorting algorithm
  • derived from quicksort, heapsort, and insertion sort
  • unstable


  • hybrid sorting algorithm
  • derived from merge sort and insertion sort
  • stable

Distribution Sort

  • O(n+m) non-comparative sorting algorithms: radix sort, bucket sort, digital sort, pigeonhole sort
  • it avoids comparison by creating and distributing elements into buckets according to their radix
  • the lower bound for comparative sorting algorithm is O(n log(n)); in certain cases, non-comparative sorting can do better, e.g., O(n)

Topological Sort

  • for directed acyclic graph (DAG)
  • output a linear ordering of its vertices

Tree Sort

  • builds a binary search tree from the elements to be sorted, and then traverses the tree (in-order) so that the elements come out in sorted order.
  • Its typical use is sorting elements online: after each insertion, the set of elements seen so far is available in sorted order.