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Insertion Sort

Problem Size:  20 · 30 · 40 · 50     Magnification:  1x · 2x · 3x
Algorithm:  Insertion · Selection · Bubble · Shell · Merge · Heap · Quick · Quick3


for i = 2:n,
    for (k = i; k > 1 and a[k] < a[k-1]; k--) 
        swap a[k,k-1]
    → invariant: a[1..i] is sorted


  • Stable
  • O(1) extra space
  • O(n2) comparisons and swaps
  • Adaptive: O(n) time when nearly sorted
  • Very low overhead


Although it is one of the elementary sorting algorithms with O(n2) worst-case time, insertion sort is the algorithm of choice either when the data is nearly sorted (because it is adaptive) or when the problem size is small (because it has low overhead).

For these reasons, and because it is also stable, insertion sort is often used as the recursive base case (when the problem size is small) for higher overhead divide-and-conquer sorting algorithms, such as merge sort or quick sort.


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  • Black values are sorted.
  • Gray values are unsorted.
  • A red triangle marks the algorithm position.


Algorithms in Java, Parts 1-4, 3rd edition by Robert Sedgewick. Addison Wesley, 2003.

Programming Pearls by Jon Bentley. Addison Wesley, 1986.

Quicksort is Optimal by Robert Sedgewick and Jon Bentley, Knuthfest, Stanford University, January, 2002.

Dual Pivot Quicksort: Code and Discussion.

Bubble-sort with Hungarian ("Csángó") folk dance YouTube video, created at Sapientia University, Tirgu Mures (Marosvásárhely), Romania.

Select-sort with Gypsy folk dance YouTube video, created at Sapientia University, Tirgu Mures (Marosvásárhely), Romania.

Sorting Out Sorting, Ronald M. Baecker with the assistance of David Sherman, 30 minute color sound film, Dynamic Graphics Project, University of Toronto, 1981. Excerpted and reprinted in SIGGRAPH Video Review 7, 1983. Distributed by Morgan Kaufmann, Publishers. Excerpt.