insertion sort


Definition: Sort by repeatedly taking the next item and inserting it into the final data structure in its proper order with respect to items already inserted. Run time is O(n2) because of moves.

Also known as linear insertion sort.

Generalization (I am a kind of ...)

Specialization (... is a kind of me.)
binary insertion sort.

Aggregate parent (I am a part of or used in ...)
q sort.

See also gnome sort.

Note: Sorting can be done in place by moving the next item into place by repeatedly swapping it with the preceding item until it is in place - a linear search and move combined. This implementation is given in C. J. Shaw and T. N. Trimble, Algorithm 175 Shuttle Sort, CACM, 6(6):312-313, June 1963.

If comparing items is very expensive, use binary search to reduce the number of comparisons needed to find where the item should be inserted, then open a space by moving all later items down one. However a binary search is likely to make this not a stable sort.

Author: PEB


(Java). An implementation (Java) due to Sedgewick and Wayne (search for Insertion sort). Algorithms and Data Structures' explanation and code (Java and C++). Other implementations may be available through the Stony Brook Algorithm Repository, Sorting. (Fortran).

More information

demonstration of several sort algorithms, with particular emphasis on insertion sort; more demonstrations; a animation (Java) of insertion sort.

Insertion sort illustrated through a Romanian folk dance. Created at Sapientia University.

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 8 November 2016.
HTML page formatted Tue Jan 16 10:34:44 2018.

Cite this as:
Paul E. Black, "insertion sort", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 8 November 2016. (accessed TODAY) Available from: