# insertion sort

(algorithm)

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 ...)
sort.

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

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

## Implementation

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). Flower Brackets using scanners, objects, and recursion (Java). (Python). use binary search to find where to insert (Python).

Insertion sort illustrated followed by a race between insertion sort and bubble sort and then analysis of bubble sort, insertion sort, and quick sort.

A race between Shell sort and insertion sort followed by a race between them where Shell sort has a gap sequence optimized for 10 items.

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