Absorptionsort

Absorptionsort, or absorption sort, is a simple, conceptual sorting algorithm described in some informal texts as a method that builds the sorted sequence by repeatedly absorbing elements from an unsorted pool into a growing output. The metaphor reflects the idea of taking in one item at a time to extend the sorted region.

In a typical description, the algorithm starts with all items in an unsorted region and an empty or growing sorted region. At each step, it scans the unsorted portion to locate the next element to place—usually the smallest (for ascending order)—and moves or copies that element into the boundary between the sorted and unsorted parts. If a secondary buffer is used, the absorbed element is appended to the output, and the process repeats until nothing remains in the unsorted pool. Variants may differ in whether the operation is performed in place or with extra space.

Time complexity for a straightforward in-place variant is commonly O(n^2) in the average and worst cases, since each pass requires scanning the remaining unsorted elements to find the next candidate. Auxiliary space is typically O(1) beyond the input array, though some descriptions use a separate buffer, affecting space characteristics. Stability is not guaranteed in the basic form, as elements can be moved past equal keys during absorption unless special handling is employed.

Absorptionsort is primarily of interest as a teaching or theoretical example rather than a practical sorting technique. It appears in discussions about sorting concepts to illustrate the idea of progressively building a sorted region by absorbing elements from the unsorted set.

See also: sorting algorithms, selection sort, insertion sort, bubble sort.