History[ edit ] From the beginning of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. Classification[ edit ] Sorting algorithms are often classified by: Computational complexity worstaverage and best behavior in terms of the size of the list n.

Tim Peters created Timsort for the Python programming language in Timsort first analyses the list it is trying to sort and then chooses an approach based on the analysis of the list. To learn about Big O notation, read this. Peters designed Timsort to use already-ordered elements that exist in most real-world data sets.

It iterates over the data collecting the elements into runs and simultaneously merging those runs together into one. An insertion sort is a simple sort which is most effective on small lists. It is quite slow at larger lists, but very fast with small lists. The idea of an insertion sort is as follows: If the part is decreasing, it will reverse that part.

Image from my website, skerritt. The algorithm selects it so that most runs in a random array are, or become minrun, in length.

Merging 2 arrays is more efficient when the number of runs is equal to, or slightly less than, a power of two. Timsort chooses minrun to try to ensure this efficiency, by making sure minrun is equal to or less than a power of two. The algorithm chooses minrun from the range 32 to 64 inclusive.

It chooses minrun such that the length of the original array, when divided by minrun, is equal to or slightly less than a power of two.

If the length of the run is less than minrun, you calculate the length of that run away from minrun. Using this new number, you grab that many items ahead of the run and perform an insertion sort to create a new run.

You then grab 30 elements from in front of the end of the run, so this is 30 items from run[33] and then perform an insertion sort to create a new run.

After this part has completed we should now have a bunch of sorted runs in a list. Merging Gif from Giphy Timsort now performs mergesort to merge the runs together. However, Timsort makes sure to maintain stability and merge balance whilst merge sorting.

To maintain stability we should not exchange 2 numbers of equal value. This not only keeps their original positions in the list but enables the algorithm to be faster.

We will shortly discuss the merge balance. As Timsort finds runs, it adds them to a stack. A simple stack would look like this: You cannot take plates from the bottom, so you have to take them from the top.

The same is true about a stack. Timsort tries to balance two competing needs when mergesort runs. On one hand, we would like to delay merging as long as possible in order to exploit patterns that may come up later. But we would like even more to do the merging as soon as possible to exploit the run that the run just found is still high in the memory hierarchy.

To make sure we have this compromise, Timsort keeps track of the three most recent items on the stack and creates two laws that must hold true of those items:Merge Sort is a recursive algorithm and time complexity can be expressed as following recurrence relation. T(n) = 2T(n/2) + The above recurrence can be solved either .

Merge Sort using Java with program code In computer science, merge sort or mergesort is a sorting algorithm for rearranging lists (or any such linear sequential data storage structure) into a .

I have an ArrayList that I want to output completely as a String. Essentially I want to output it in order using the toString of each element separated by tabs. Is there any fast way to do this? You could loop through it (or remove each element) and concatenate it to a String but I think this will be very slow.

Apache POI is a powerful Java library to work with different Microsoft Office file formats such as Excel, Power point, Visio, MS Word etc. The name POI was originally an acronym for Poor Obfuscation Implementation, referring humorously to the fact that the file formats seemed to be deliberately obfuscated, but poorly, since they were successfully reverse-engineered.

Algorithm to merge sorted arrays. In the article we present an algorithm for merging two sorted arrays. One can learn how to operate with several arrays and master read/write indices.

Also, the algorithm has certain applications in practice, for instance in merge sort. Merge algorithm. In contrast, an algorithm is a step by step process that describes how to solve a problem and/or complete a task, which will always give the correct result.

For our previous non-computing example, the algorithm might be 1) Go to the kitchen. 2) Pick up a glass. 3) Turn on the tap. 4) Put the glass under the running water and remove it once it is almost full.

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Timsort — the fastest sorting algorithm you’ve never heard of