Why is quicksort faster than mergesort

Example: Pivot about The pivot fits in the slot between them. Note that the pivot element ends up in the correct place in the total order! Example: pivot about 10 17 12 6 19 23 8 5 10 5 12 6 19 23 8 17 5 12 6 19 23 8 17 5 8 6 19 23 12 17 5 8 6 19 23 12 17 5 8 6 19 23 12 17 5 8 6 23 19 12 17 5 8 6 23 19 12 17 5 8 6 10 19 12 17 23 As we scan from left to right, we move the left bound to the right when the element is less than the pivot, otherwise we swap it with the rightmost unexplored element and move the right bound one step closer to the left.

Since the partitioning step consists of at most n swaps, takes time linear in the number of keys. But what does it buy us? The pivot element ends up in the position it retains in the final sorted order. After a partitioning, no element flops to the other side of the pivot in the final sorted order. Thus we can sort the elements to the left of the pivot and the right of the pivot independently! This gives us a recursive sorting algorithm, since we can use the partitioning approach to sort each subproblem.

See Chapter 14 for the explanation of the file handling and Chapter 15 for exception handling, which is used in this example. Passes SIO. Error for bad file format. Best Case for Quicksort Since each element ultimately ends up in the correct position, the algorithm correctly sorts.

But how long does it take? The best case for divide-and-conquer algorithms comes when we split the input as evenly as possible. The partition step on each subproblem is linear in its size. Thus the total effort in partitioning the problems of size is O n. The recursion tree for the best case looks like this: The total partitioning on each level is O n , and it take levels of perfect partitions to get to single element subproblems. When we are down to single elements, the problems are sorted.

Thus the total time in the best case is. Worst Case for Quicksort Suppose instead our pivot element splits the array as unequally as possible. Thus the worst case time for Quicksort is worse than Heapsort or Mergesort. To justify its name, Quicksort had better be good in the average case. Showing this requires some fairly intricate analysis. The divide and conquer principle applies to real life.

If you will break a job into pieces, it is best to make the pieces of equal size! Intuition: The Average Case for Quicksort The book contains a rigorous proof that quicksort is in the average case. I will instead give an intuitive, less formal explanation of why this is so. Suppose we pick the pivot element at random in an array of n keys. Half the time, the pivot element will be from the center half of the sorted array. If we assume that the pivot element is always in this range, what is the maximum number of partitions we need to get from n elements down to 1 element?

At most levels of decent partitions suffices to sort an array of n elements. But how often when we pick an arbitrary element as pivot will it generate a decent partition? If we need levels of decent partitions to finish the job, and half of random partitions are decent, then on average the recursion tree to quicksort the array has levels.

Since O n work is done partitioning on each level, the average time is. More careful analysis shows that the expected number of comparisons is. Unlike arrays, in liked list we can insert items in the middle with O 1 space and O 1 time, therefore the merge operation in merge sort can be implemented without any extra space. However, allocating and de-allocating extra space for arrays have an adverse effect on the run time of merge sort. Merge sort also favors linked list as data is accessed sequentially, without much random memory access.

Quick sort on the other hand requires a lot of random memory access and with an array we can directly access the memory without any traversing as required by linked lists. Also quick sort when used for arrays have a good locality of reference as arrays are stored contiguously in memory. Even though both sorting algorithms average complexity is O NlogN , usually people for ordinary tasks uses an array for storage, and for that reason quick sort should be the algorithm of choice.

Consider time and space complexity both. Now, they both win in one scenerio each. But, using a random pivot you can almost always reduce Time complexity of Quick sort to O nlogn. In addition performance can be much higher with quick sort, for cases where the entire dataset does not fit into the working set. One of the reason is more philosophical. With n elements to sort, there are n! So instead of worrying about establishing any order within a range or a partition,just establish order at a broader level in partitions and reduce the possibilities within a partition.

Any order established earlier within a range will be disturbed later if the partitions themselves are not mutually exclusive. Any bottom up order approach like merge sort or heap sort is like a workers or employee's approach where one starts comparing at a microscopic level early. But this order is bound to be lost as soon as an element in between them is found later on. Quick Sort is like Managerial approach where one is not initially concerned about any order , only about meeting a broad criterion with No regard for order.

Then the partitions are narrowed until you get a sorted set. The real challenge in Quicksort is in finding a partition or criterion in the dark when you know nothing about the elements to sort. That is why we either need to spend some effort to find a median value or pick 1 at random or some arbitrary "Managerial" approach. To find a perfect median can take significant amount of effort and leads to a stupid bottom up approach again. Any way data is random. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Collectives on Stack Overflow. Learn more. Why is quicksort better than mergesort? Ask Question. Asked 13 years, 1 month ago. Active 1 year, 7 months ago.

Viewed k times. Improve this question. This is not a very good interview question. Real-world data isn't shuffled: it often contains a lot of order which a smart sort can make use of, and while neither algorithm does this automatically, it's easier to hack a merge sort to do it than a quicksort.

GNU libc's qsort , Python's list. Jason Orendorff: Why is it "easier to hack a mergesort to do it than a quicksort"? Any specific example that you can quote? If the array initially contains some already-sorted regions, you can save a lot of time just by detecting that they're there before you begin. And you can do that in O n time.

For specific examples, see the source code of the three projects I mentioned! The best example might be Python's Timsort, described in detail here: svn.

JasonOrendorff: Not sure I buy your argument that mergesort can be more easily modified to take advantage of already-sorted sections. The partitioning step of quicksort can be trivially modified to afterwards check whether both resulting partitions are sorted, and halt recursion if they are. This potentially doubles the number of comparisons, but doesn't alter the O n time complexity of that step. And the partition will screw it up before subsequent calls would check for it.

Meanwhile, merge sorts check for sorted sequences in the division steps before any are moved, and smart ones will look for runs like this specifically during the division step see: Tim Sort — Mooing Duck. Show 5 more comments. Active Oldest Votes. Improve this answer. Konrad Rudolph Konrad Rudolph k gold badges silver badges bronze badges. The Wikipedia article states it switches to heapsort, not mergesort Sev: … as does the orignal paper. Thanks for pointing out the mistake.

All it explains is how quick sorts problems be patched. It still doesnt tell why quick sort is used more than other?. Is the answer "quick sort is used more than other because after one depth you can switch to heapsort"? Quicksort is better in terms of memory as well. Show 10 more comments. Very nice, didn't think about the assumptions made for accessing the data structure. Good insight : — chutsu. Can you explain what you mean by "seek to disk" does it mean searching for some single value when the data is stored on disk?

JamesWierzba I take it from context that he means "seeking to a location on disk". When you access data in the order it was stored, the disk hardware doesn't have to seek, it just plows along at high speed, reading items sequentially.

Can some explain this a bit more? This is how I am seeing it: Quicksort: If we are going with random pivot, the call stack has fragments of the array partitioned in a random way. This requires random access. However, for each call in the stack, both left and right pointers move sequentially. I am assuming these would be kept in the cache. The swaps are operations again on information that's in cache and eventually written to Disk. That is, at the very top level of the loop, once you go from 0 towards n and the next time you go from n towards 0.

This brings the advantage of retreating sorting the data blocks that are already available in the memory cache and attacking twice for only one disk access. I think most DBMS's use this optimization technique.

Show 4 more comments. QuickSort is more popular because it: Is in-place MergeSort requires extra memory linear to number of elements to be sorted. Has a small hidden constant. Dark Shikari Dark Shikari 7, 3 3 gold badges 25 25 silver badges 37 37 bronze badges.

It also depends on the computer architecture. Quicksort benefits from the cache, while MergeSort doesn't. You can implement a mergesort in place. Merge sort may be implemented in a way that only requires O 1 extra storage, but most of those implementations suffer greatly in terms of performance.

Show 20 more comments. Ash Ash Does not answer question about which is better. The name of the algorithm is irrelevant in determining which is better. Add a comment. Javier Javier Antti Rasinen Antti Rasinen 9, 2 2 gold badges 21 21 silver badges 18 18 bronze badges. Roman Glass Roman Glass 1 1 gold badge 13 13 silver badges 20 20 bronze badges.

Mergesort can be implemented in-place, such that it does not need extra space. For example with a double linked list: stackoverflow. Niyaz Niyaz How much does non-ideal pivot selection affect execution time? How fast does this get worse? With this randomization in the mix, we have 2 cases: Small data set. Large data set. Worst case is possible in theory but not in practice. How likely are we to see terrible performance? The chances are vanishingly small. Let's consider a sort of 5, values: Our hypothetical implementation will choose a pivot using a median of 3 randomly chosen indexes.

Bad pivots are always worst case and essentially contribute nothing to the solution. Lance Wisely Lance Wisely 65 1 1 silver badge 7 7 bronze badges. I can't locate them. Do any variations of Quick Sort notify the comparison function about partitions, in such a way that would allow it to exploit situations where a substantial portion of the key will be the same for all items in a partition?

Mat Mannion Mat Mannion 3, 2 2 gold badges 29 29 silver badges 29 29 bronze badges. Worst case of quicksort is O n , mergesort O n log n - so ther'es a big difference there. Also, the answer already addressed your point: "in most real-world data it is possible to make design choices which minimize the probability of requiring quadratic time" — Jim Balter.

Why Quicksort is good? The worst case occurs when data is sorted. This can be mitigated by random shuffle before sorting is started. QuickSort doesn't takes extra memory that is taken by merge sort. If the dataset is large and there are identical items, complexity of Quicksort reduces by using 3 way partition. More the no of identical items better the sort.

If all items are identical, it sorts in linear time. Not really. Mergesort is stable but Quicksort is not. So if you need stability in output, you would use Mergesort. Stability is required in many practical applications. Locality of reference : Quicksort in particular exhibits good cache locality and this makes it faster than merge sort in many cases like in virtual memory environment.

Merge sort is better for large data structures: Mergesort is a stable sort, unlike quicksort and heapsort, and can be easily adapted to operate on linked lists and very large lists stored on slow-to-access media such as disk storage or network attached storage.

Refer this for details Attention reader! The sorting algorithm which it uses is called Introsort. Skip to content. Change Language. Related Articles. Table of Contents. Save Article.