When is quicksort used

We need to sort this array in the most efficient manner without using extra place inplace sorting. Step 1 :. Thus the pivot 32 comes at its actual position and all elements to its left are lesser, and all elements to the right are greater than itself. Step 2 : The main array after the first step becomes. Step 3 : Now the list is divided into two parts:. Step 4 : Repeat the steps for the left and right sublists recursively.

The final array thus becomes 9, 18, 23, 32, 50, The following diagram depicts the workflow of the Quick Sort algorithm which was described above. Partition Method. Best case scenario: The best case scenario occurs when the partitions are as evenly balanced as possible, i.

Worst case scenario: This happens when we encounter the most unbalanced partitions possible, then the original call takes n time, the recursive call on n-1 elements will take n-1 time, the recursive call on n-2 elements will take n-2 time, and so on. The worst case time complexity of Quick Sort would be O n 2. The space complexity is calculated based on the space used in the recursion stack. The worst case space used will be O n. The average case space used will be of the order O log n.

The worst case space complexity becomes O n , when the algorithm encounters its worst case where for getting a sorted list, we need to make n recursive calls. What is the average case run time complexity of Quick Sort?

Related Articles. Table of Contents. Save Article. Improve Article. Like Article. Quicksort : Quick sort is an Divide Conquer algorithm and the fastest sorting algorithm. In quick sort, it creates two empty arrays to hold elements less than the pivot element and the element greater than the pivot element and then recursively sort the sub-arrays.

Quicksort is the comparison-sort algorithm with the lowest K. Average asymptotic order of QuickSort is O nlogn and it's usually more efficient than heapsort due to smaller constants tighter loops. In fact, there is a theoretical linear time median selection algorithm that you can use to always find the best pivot, thus resulting a worst case O nlogn. However, the normal QuickSort is usually faster than this theoretical one. To make it more sensible, consider the probability that QuickSort will finish in O n 2.

Interestingly, quicksort performs more comparisons on average than mergesort - 1. If all that mattered were comparisons, mergesort would be strongly preferable to quicksort. The reason that quicksort is fast is that it has many other desirable properties that work extremely well on modern hardware.

For example, quicksort requires no dynamic allocations. It can work in-place on the original array, using only O log n stack space worst-case if implemented correctly to store the stack frames necessary for recursion. Although mergesort can be made to do this, doing so usually comes at a huge performance penalty during the merge step.

Other sorting algorithms like heapsort also have this property. Additionally, quicksort has excellent locality of reference. The partitioning step, if done using Hoare's in-place partitioning algorithm, is essentially two linear scans performed inward from both ends of the array.

This means that quicksort will have a very small number of cache misses, which on modern architectures is critical for performance. Heapsort, on the other hand, doesn't have very good locality it jumps around all over an array , though most mergesort implementations have reasonably locality. Quicksort is also very parallelizable. Once the initial partitioning step has occurred to split the array into smaller and greater regions, those two parts can be sorted independently of one another.

In Robert Sedgewick's books, e. You find there. As you see, this does not readily allow comparisons of algorithms as the exact runtime analysis, but results are independent from machine details. As noted above, average cases are always with respect to some input distribution, so one might consider ones other than random permutations. 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.

Note that Mergesort 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 Mergesort on other factors. 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 Mergesort 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. Lastly, note that Quicksort is slightly sensitive to input that happens to be in the right order, in which case it can skip some swaps.

Mergesort doesn't have any such optimizations, which also makes Quicksort a bit faster compared to Mergesort. In conclusion: no sorting algorithm is always optimal. Choose whichever one suits your needs. If you need an algorithm that is the quickest for most cases, and you don't mind it might end up being a bit slow in rare cases, and you don't need a stable sort, use Quicksort.

Otherwise, use the algorithm that suits your needs better. In one of the programming tutorials at my university, we asked students to compare the performance of quicksort, mergesort, insertion sort vs. Python's built-in list. The experimental results surprised me deeply since the built-in list.

So it's premature to conclude that the usual quicksort implementation is the best in practice. But I'm sure there much better implementation of quicksort, or some hybrid version of it out there. This is a nice blog article by David R.

MacIver explaining Timsort as a form of adaptive mergesort. I think one of the main reasons why QuickSort is so fast compared with other sorting algorithms is because it's cache-friendly. When QS processes a segment of an array, it accesses elements at the beginning and end of the segment, and moves towards the center of the segment.

And when you try to access the second element, it's most likely already in the cache, so it's very fast. Other algorithms like heapsort don't work like this, they jump in the array a lot, which makes them slower.

Others have already said that the asymptotic average runtime of Quicksort is better in the constant than that of other sorting algorithms in certain settings.

What does that mean? Assume any permutation is chosen at random assuming uniform distribution. But, additionally, merging partial solutions obtained by recursing takes only constant time as opposed to linear time in case of Mergesort.

Of course, separating the input in two lists according to the pivot is in linear time, but it often requires few actual swaps. Note that there are many variants of Quicksort see e. Sedgewick's dissertation. They perform differently on different input distributions uniform, almost sorted, almost inversely sorted, many duplicates, Another fact worth noting is that Quicksort is slow on short inputs compared to simper algorithms with less overhead.

In other words, we don't need much more memory to store the members of the array. For some tasks it might be better to use other sorting algorithms. Comparison of quick-sort with other sorting algorithms. Comparison of heap-sort with other sorting algorithms. My experience working with real world data is that quicksort is a poor choice.

Quicksort works well with random data, but real world data is most often not random. Back in I tracked a hanging software bug down to the use of quicksort. A while later I wrote simple implentations of insertion sort, quicksort, heap sort and merge sort and tested these.

My merge sort outperformed all the others while working on large data sets. Since then, merge sort is my sorting algorithm of choice. It is elegant. It is simple to implement. It is a stable sort. It does not degenerate to quadratic behaviour like quicksort does.

I switch to insertion sort to sort small arrays. On many occasions I have found my self thinking that a given implementation works surprisingly well for quicksort only to find out that it actually isn't quicksort.