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Stability in sorting algorithm Assignment Help

A sorting algorithm will be reported to be secure when two objects together with the same keys appear inside the identical order inside taken care of output while they can be found in the particular input unsorted array. Some sorting algorithms are usually secure stable by nature such as Insertion sort, Merge Sort, Bubble Sort, etc. And some sorting algorithms are not, such as Heap Sort, Quick Sort, etc.

However, any kind of provided sorting algorithm that is not really stable could be altered to become stable. There might be sorting algorithm specific methods to allow it to be stable, however in common, any kind of comparison dependent sorting algorithm that is not really stable through nature could be modified to become stable by changing the key comparison operation so that the comparison of two keys considers position like a element with regard to objects along with equal keys.

Let A be an array, and let < be a strict weak ordering on the elements regarding A.

A sorting algorithm is stable if

Stability in sorting algorithm

Where π is the sorting permutation (sorting moves A[i] to position π(i).)