Program Pascal Counting Sort Serial Sorting Algorithms

The frequency array is then iterated over to use distinct elements and their occurrences and put them into the output array in a sorted way.

Then the array A is iterated over to store the number of occurrences of each distinct element in frequency array, by mapping the distinct elements with index number of frequency array.

Along with this, the same concept can be used with negative input data as well.

The overall time complexity of counting sort is (NK) in all cases.

We use cookies to ensure best browsing experience on our website.

While using this website, you acknowledge to have read and accepted our cookie and privacy policy.

In the card example, cards are represented as a record (rank, suit), and the key is the rank.

Please help improve this section by adding citations to reliable sources.

Unsourced material may be challenged and removed.

The most frequently used orders are numerical order and lexicographical order.

Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists.

Sorting is also often useful for canonicalizing data and for producing human-readable output.

More formally, the output of any sorting algorithm must satisfy two conditions.

Among the authors of early sorting algorithms around 1951 was Betty Holberton (born Snyder), who worked on ENIAC and UNIVAC.

Bubble sort was analyzed as early as 1956.

Comparison sorting algorithms have a fundamental requirement of ( n log n ) comparisons (some input sequences will require a multiple of n log n comparisons, where n is the number of elements in the array to be sorted).

Algorithms not based on comparisons, such as counting sort, can have better performance.

Asymptotically optimal algorithms have been known since the mid-20th centuryuseful new algorithms are still being invented, with the now widely used Timsort dating to 2002, and the library sort being first published in 2006.

Program Pascal Counting Sort Serial Sorting Algorithms

For typical serial sorting algorithms good behavior is O( n log n ), with parallel sort in O(log 2 n ), and bad behavior is O( n 2 ).

See Big O notation.) Ideal behavior for a serial sort is O( n ), but this is not possible in the average case.

Comparison-based sorting algorithms need at least ( n log n ) comparisons for most inputs.

Strictly, an in-place sort needs only O(1) memory beyond the items being sorted; sometimes O(log( n )) additional memory is considered in-place.

A comparison sort examines the data only by comparing two elements with a comparison operator.

The remainder of this discussion almost exclusively concentrates upon serial algorithms and assumes serial operation.

Algorithms that take this into account are known to be adaptive.

When the cards are sorted by rank with a stable sort, the two 5s must remain in the same order in the sorted output that they were originally in.

When they are sorted with a non-stable sort, the 5s may end up in the opposite order in the sorted output.

When sorting some kinds of data, only part of the data is examined when determining the sort order.

For example, in the card sorting example to the right, the cards are being sorted by their rank, and their suit is being ignored.

This allows the possibility of multiple different correctly sorted versions of the original list.

Stable sorting algorithms choose one of these, according to the following rule: if two items compare as equal, like the two 5 cards, then their relative order will be preserved, so that if one came before the other in the input, it will also come before the other in the output.

If a stable sorting algorithm is used in both cases, the sort-by-class-section operation will not change the name order; with an unstable sort, it could be that sorting by section shuffles the name order.

Using a stable sort, users can choose to sort by section and then by name, by first sorting using name and then sort again using section, resulting in the name order being preserved.

Some spreadsheet programs obey this behavior: sorting by name, then by section yields an alphabetical list of students by section.) Another reason: unstable sort may yield different output for the same input from run to run.

Such behavior is unsuitable for some applications, for example for client-server applications where the server uses pagination for output and performs a new search-and-sort for every new page requested by the client.