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.

See also sort.

Note: Sorting can be done in place by moving the next item past the end of the sorted items into place by repeatedly swapping it with the preceding item until it is in place - a linear search and move combined.

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.