GFact | Which Sorting Algorithm is Best and Why?

A sorting algorithm is an algorithm that makes the input data set arranged in a certain order. The fundamental task is to put the items in the desired order so that the records are re-arranged for making searching easier.

Which is the best sorting algorithm?

Quicksort is one of the most efficient sorting algorithms, and this makes of it one of the most used as well. The first thing to do is to select a pivot number, this number will separate the data, on its left are the numbers smaller than it and the greater numbers on the right.

Why is quicksort the best sorting algorithm?

A good reason why Quicksort is so fast in practice compared to most other O(nlogn) algorithms such as Heapsort, is because it is relatively cache-efficient. Its running time is actually O((n/B)log(n/B)), where B is the block size. Heapsort, on the other hand, doesn’t have any such speedup: it’s not at all accessing memory cache efficiently.

The reason for this cache efficiency is that it linearly scans the input and linearly partitions the input. This means we can make the most of every cache load we do as we read every number we load into the cache before swapping that cache for another. In particular, the algorithm is cache-oblivious, which gives good cache performance for every cache level, which is another win.

Cache efficiency could be further improved to O((n/B)Log_(M/B)(n/B)) , where M is the size of our main memory, if we use k-way Quicksort. Note that Merge sort also has the same cache-efficiency as Quicksort, and its k-way version in fact has better performance (through lower constant factors) if memory is a severe constrain. This gives rise to the next point: we’ll need to compare Quicksort to Merge sort on other factors.

Comparison of the Quick Sort with other Sorting Algorithms:

We can compare the Complexities of the various Sorting Algorithms with the help of below Table:

Sorting Algorithm	Best Case Time Complexity	Average Time Complexity	Worst Time Complexity	Space Complexity
Quick Sort	Ω(N log N)	Θ(N log N)	O(N2)	O(log N)
Bubble Sort	Ω(N)	Θ(N2)	O(N2)	O(1)
Selection Sort	Ω(N2)	Θ(N2)	O(N2)	O(1)
Insertion Sort	Ω(N)	Θ(N2)	O(N2)	O(1)
Merge Sort	Ω(N log N)	Θ(N log N)	O(N log N)	O(N)
Heap Sort	Ω(N log N)	Θ(N log N)	O(N log N)	O(1)
Redix Sort	Ω(N * K)	Θ(N * K)	O(N * K)	O(N + K)
Count Sort	Ω(N + K)	Θ(N + K)	O(N + K)	O(K)
Bubble Sort	Ω(N + K)	Θ(N + K)	O(N2)	O(N)

Which is better Merge Sort or Quick Sort?

This comparison is completely about constant factors (if we consider the typical case). In particular, the choice is between a suboptimal choice of the pivot for Quicksort versus the copy of the entire input for Merge sort (or the complexity of the algorithm needed to avoid this copying). It turns out that the former is more efficient: there’s no theory behind this, it just happens to be faster.

Note that Quicksort will make more recursive calls, but allocating stack space is cheap (almost free in fact, as long as you don’t blow the stack) and you re-use it. Allocating a giant block on the heap (or your hard drive, if n is really large) is quite a bit more expensive, but both are O(logn) overheads that pale in comparison to the O(n) work mentioned above.