Insertion sort is a simple sorting algorithm, a comparison sort in which the sorted array (or list) is built one entry at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages: simple implementation, efficient for (quite) small data sets, adaptive, i.e. efficient for data sets that are already substantially sorted: the time complexity is O(n + d), where d is the number of inversions, more efficient in practice than most other simple quadratic (i.e. O(n2)) algorithms such as selection sort or bubble sort: the average running time is n2/4[citation needed], and the running time is linear in the best case, stable, i.e. does not change the relative order of elements with equal keys, in-place, i.e. only requires a constant amount O(1) of additional memory space, online, i.e. can sort a list as it receives it. Most humans when sorting—ordering a deck of cards, for example—use a method that is similar to insertion sort.

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