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**Sorting:**

It is an algorithm that puts elements of a list in a certain order. The most-utilized orders are lexicographical order and numerical order. Efficient sorting is significant for optimizing the use of other algorithms (such as search and merge algorithms) which needs input data to be in sorted lists; it is also frequently useful for canonicalizing data and for producing human-readable output.

**Some popular Sorting algorithms:**

**Bubble sort:**

It is a simple sorting algorithm. The algorithm begins at the starting of the data set. It compares the primary two elements, and if the first one is greater than the second, it will swap them. It continues doing this for each of the pair of adjacent elements to the end of the data set. Then it starts again with the first two elements, repeating till no swaps have occurred on the last pass. This algorithm's average and worst case both of the performance is O (n^{2}), so it is hardly ever utilized to sort large, data sets, unordered. Bubble sort can be utilized to sort a small number of items (where its asymptotic inefficiency is not a high penalty). Bubble sort can also be utilized efficiently on a list of any length that is closely sorted.

**Insertion sort:**

It is a simple sorting algorithm that is relatively efficient for small lists and mostly sorted lists, and frequently is utilized as part of more sophisticated algorithms. This works through taking elements from the list one by one and inserting them in their right position to a new sorted list. In arrays, the new list and the remaining elements can share the array's space, but insertion is costly, requiring shifting all following elements over by one. Average and worst-case time both is O (n^{2}).

**Merge sort:**

It takes advantage of the easiness of merging already sorted lists into a new sorted list. It begins by comparing every two elements (i.e., 1 with 2, then 3 with 4...) and swapping them if the first must come after the second. then it merges each of the resulting lists of two in lists of four, then merges those lists onto four, and so on; till at last two lists are merged into the final sorted list. Of the algorithms described here, it is the first that scales well to very large lists, since its worst-case running time is O (n log n).

**Quick sort:**

It is based on divide and conquer algorithm which relies on a partition operation: to partition an array an element called a pivot is chosen. All of the elements smaller than the pivot are moved before it and all of greater elements are moved after it. It can be done efficiently in linear time and in-place. The greater and lesser subsists are then recursively sorted. Quick sort executes in O (n log n) on average and O (n^{2}) in the worst-case. Though, along correct precautions, worst-case behavior is very unlikely. It is a non-stable sort. It is not an in-place sort like stack space is needed.

**Shell Sort:**

Shell sort, established through Donald L. Shell, is a non-stable in-place sort. Shell sort develop on the efficiency of insertion sort through rapidly shifting values to their destination. Average sort time is O (n^{1.25}), whereas worst-case time is O (n^{1.5}).

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