Difference Betwixt Comparing (Quicksort) Together With Non-Comparison (Counting Sort) Based Sorting Algorithms?

For many of you, this powerfulness last a surprise that how y'all tin give notice variety or accommodate items without comparing amongst each other, but it's possible. There are some sorting algorithms that perform sorting without comparing the elements rather past times making sure enough supposition most the information they are going to sort. The procedure is known every bit non-comparison sorting in addition to algorithms are known every bit the non-comparison based sorting algorithms. No comparing sorting includes Counting variety which sorts using key value, Radix sort, which examines private bits of keys, in addition to Bucket Sort which examines bits of keys. These are too known every bit Liner sorting algorithms because they variety inwards O(n) time. They brand sure enough supposition most information thence they don't bespeak to become through comparing determination tree.


So, based upon how they work, y'all tin give notice broadly course the sorting algorithms into 2 categories, comparing based e.g. QuickSort or MergeSort, in addition to non-comparison based e.g. Counting variety or Radix Sort. As the advert suggest, the key deviation betwixt a comparing based in addition to a non-comparison based sorting algorithm is the comparing decision.

In the showtime type, a comparator is required to compare numbers or items. Basically, this comparator defines the ordering e.g. numerical order, lexicographical order, too known every bit lexicon social club to accommodate elements. On the other hand, non-comparison based sorting algorithms don't role comparing but rely on integer arithmetics on keys.

Why Non-Comparison based Algorithms?

Some of y'all powerfulness last thinking why create nosotros bespeak non-comparison based algorithms at all, isn't comparing based sorting algorithms is enough? Well, if y'all await at the performance of comparing based sorting algorithm, y'all volition realize that Bubble sort, Selection Sort, in addition to Insertion sort takes only about O(n^2) fourth dimension to variety n items.

While, heap sort, quick sort, in addition to merge variety takes O(NlogN) fourth dimension inwards the best instance in addition to only about O(n^2) inwards the worst case. Can nosotros create amend than O(NlogN) using sorting algorithm? tin give notice nosotros variety items inwards O(n) fourth dimension using these sorting algorithms? Well, the response is No.

It tin give notice last proven that whatever comparison-based sorting algorithm volition receive got at least O(NlogN) operations to variety n elements, thence y'all bespeak a non-comparison based sorting algorithm which allows y'all to variety elements inwards linear time.

The linear sorting algorithms are too i of the pop data construction in addition to algorithm questions inwards recent times, so y'all amend know most it.

Comparison based Sorting vs NonComparison based Sorting

Due to the working deviation betwixt these 2 types of algorithms, generally, the non-comparison based sorting algorithms similar Radix Sort, Counting Sort, in addition to Bucket Sort are faster than QuickSort, Merge Sort in addition to Heap Sort. Let's consider a duo of to a greater extent than differences betwixt these sorting algorithms to empathise better.

The latter type is too known every bit Integer variety because it relies on integer arithmetics for sorting rather than comparison.


Speed
One of the most critical differences betwixt these 2 sorting algorithms is speed. Non-comparison sorting is unremarkably faster than sorting because of non doing the comparison. The limit of speed for comparison-based sorting algorithm is O(NlogN) land for non-comparison based algorithms its O(n) i.e. linear time.


Comparator
Comparison based sorting algorithm e.g. QuickSort, Merge Sort. or Heap Sort requires a Comparator to variety elements e.g. land sorting an array of String, but non-comparison based sorting algorithms doesn't require whatever comparator.


Usage
Non-Comparison based sorting algorithm tin give notice role to variety whatever object provided it provides Comparator to define ordering, but a non-comparison based sorting algorithm tin give notice non last used to variety anything other than integers, that's why the are too known every bit integer sorting. You tin give notice too consider Introduction of Algorithms to larn to a greater extent than most the O(n) sorting algorithms.

Examples
The QuickSort, Merge Sort, Heap Sort, Selection Sort, Bubble Sort in addition to Insertion Sort, land some pop illustration of non-comparison based sorting is Radix Sort, Counting Sort, Bucket Sort etc


Memory Complexity
The best instance for retentivity complexity amongst the comparing based sorting is O(1) because it's possible to variety an array of numbers inwards house i.e. without using whatever additional memory. You tin give notice consider the code for inwards house Quicksort algorithm here. On the other hand, retentivity complexity for non-comparison based sorting algorithm is ever O(n).


CPU complexity
The lower leap of CPU complexity or how much fourth dimension it receive got for the algorithm to variety due north numbers inwards the worst instance is O(NlogN), but inwards the instance of non-comparison based sorting the CPU complexity lower leap is O(n) i.e. the worst instance is fifty-fifty worse amongst non-comparison based sorting algorithms.

Here is a squeamish animation of some of the pop comparison-based sorting algorithms:

That's all most the difference betwixt comparing in addition to non-comparison based sorting algorithms. Most of the mutual sorting algorithms autumn into the category of comparing based sorting algorithms e.g. quicksort, mergesort etc in addition to those are the to a greater extent than probable y'all volition role inwards the existent world, but specialized non-comparison algorithms e.g. counting variety in addition to bucket variety tin give notice last real useful if the fix of input run across the pre-conditions required. You tin give notice farther read, Introduction to Algorithms past times Thomas H. Cormen to larn to a greater extent than most non-comparison based sorting algorithms e.g. bucket sort.

Further Learning
Data Structures in addition to Algorithms: Deep Dive Using Java
see here)

Top twenty String coding interview questions (see here)

133 centre Java interview questions of terminal v years (see here)

Top xxx Array Coding Interview Questions amongst Answers (see here)

Top xxx linked listing coding interview questions (see here)

Top 50 Java Programs from Coding Interviews (see here)

Top v books on Programming/Coding Interviews (list)

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