Why merge sort is stable

We are asked to sort "by last name, then by first". We could first sort stable or unstable by the first name, then stable sort by the last name.

After these sorts, the list is primarily sorted by the last name. However, where last names are the same, the first names are sorted. A stable sorting algorithm is the one that sorts the identical elements in their same order as they appear in the input, whilst unstable sorting may not satisfy the case.

Sorting stability means that records with the same key retain their relative order before and after the sort. So stability matters if, and only if, the problem you're solving requires retention of that relative order.

If you don't need stability, you can use a fast, memory-sipping algorithm from a library, like heapsort or quicksort, and forget about it. If you need stability, it's more complicated. Which of the following most closely approximates the maximum input size of a problem that can be solved in 6 minutes?

GATE It is given that a merge sort algorithm in the worst case takes 30 seconds for an input of size Watch this Video Lecture. Next Article- Quick Sort. Get more notes and other study material of Design and Analysis of Algorithms. Tag: Why Merge Sort is Stable. Merge Sort- Merge sort is a famous sorting algorithm.

It uses a divide and conquer paradigm for sorting. It divides the problem into sub problems and solves them individually. It then combines the results of sub problems to get the solution of the original problem.

How Merge Sort Works? It may be the case that the relative order is maintained in an Unstable Sort but that is highly unlikely. Which sorting algorithms are stable? Comparison based stable sorts such as Merge Sort and Insertion Sort, maintain stability by ensuring that- Element comes before if and only if , here i, j are indices and. Since , the relative order is preserved i.

Other non-comparison based sorts such as Counting Sort maintain stability by ensuring that the Sorted Array is filled in a reverse order so that elements with equivalent keys have the same relative position. Some sorts such as Radix Sort depend on another sort, with the only requirement that the other sort should be stable.

Which sorting algorithms are unstable? Quick Sort , Heap Sort etc. This change may be done in a way which does not compromise a lot on the performance and takes some extra space, possibly. Can we make any sorting algorithm stable? Any given sorting algo which is not stable can be modified to be stable. There can be sorting algo specific ways to make it stable, but in general, any comparison based sorting algorithm which is not stable by nature can be modified to be stable by changing the key comparison operation so that the comparison of two keys considers position as a factor for objects with equal keys.

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