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Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time by comparisons. 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:
The GNU Standard C++ library, for example, uses a 3-part hybrid sorting algorithm: introsort is performed first (introsort itself being a hybrid of quicksort and heap sort), to a maximum depth given by 2×log 2 n, where n is the number of elements, followed by an insertion sort on the result.
Insertion sort is widely used for small data sets, while for large data sets an asymptotically efficient sort is used, primarily heapsort, merge sort, or quicksort. Efficient implementations generally use a hybrid algorithm , combining an asymptotically efficient algorithm for the overall sort with insertion sort for small lists at the bottom ...
The next pass, 3-sorting, performs insertion sort on the three subarrays (a 1, a 4, a 7, a 10), (a 2, a 5, a 8, a 11), (a 3, a 6, a 9, a 12). The last pass, 1-sorting, is an ordinary insertion sort of the entire array (a 1,..., a 12). As the example illustrates, the subarrays that Shellsort operates on are initially short; later they are longer ...
As another example, many sorting algorithms rearrange arrays into sorted order in-place, including: bubble sort, comb sort, selection sort, insertion sort, heapsort, and Shell sort. These algorithms require only a few pointers, so their space complexity is O(log n). [1] Quicksort operates in-place on the data to be sorted.
For example, if m is chosen proportional to √ n, then the running time of the final insertion sorts is therefore m ⋅ O(√ n 2) = O(n 3/2). In the worst-case scenarios where almost all the elements are in a few buckets, the complexity of the algorithm is limited by the performance of the final bucket-sorting method, so degrades to O ( n 2 ) .
A classic example of an adaptive sorting algorithm is insertion sort. [1] In this sorting algorithm, the input is scanned from left to right, repeatedly finding the position of the current item, and inserting it into an array of previously sorted items. Pseudo-code for the insertion sort algorithm follows (array X is zero-based):
A bidirectional variant of selection sort (called double selection sort or sometimes cocktail sort due to its similarity to cocktail shaker sort) finds both the minimum and maximum values in the list in every pass. This requires three comparisons per two items (a pair of elements is compared, then the greater is compared to the maximum and the ...