This is a simple quicksort algorithm, adapted from Wikipedia. Optimized variants of quicksort are common features of many languages and libraries. Mergesort also takes advantage of pre-existing order, so it would be favored for using sort to merge several sorted arrays. On the other hand, quicksort is often faster for small arrays, and on arrays of a few distinct values, repeated many times.
Back to basics A long time ago in a galaxy far, far away…. And guess what, databases have to deal with both situations! The concept The time complexity is used to see how long an algorithm will take for a given amount of data. To describe this complexity, computer scientists use the mathematical big O notation.
This notation is used with a function that describes how many operations an algorithm needs for a given amount of input data. In this figure, you can see the evolution of different types of complexities.
I used a logarithmic scale to plot it. In other words, the number of data is quickly increasing from 1 to 1 billion. We can see that: The O log n stays low even with billions of data.
The worst complexity is the O n2 where the number of operations quickly explodes. The two other complexities are quickly increasing. Examples With a low amount of data, the difference between O 1 and O n2 is negligible.
Indeed, current processors can handle hundreds of millions of operations per second. This is why performance and optimization are not an issue in many IT projects.
To give you an idea: A bad sorting algorithm has an O n2 complexity Note: There are multiple types of time complexity: I only talked about time complexity but complexity also works for: You can read this article on Wikipedia for the real asymptotic definition.
Merge Sort What do you do when you need to sort a collection? You might not understand right now why sorting data is useful but you should after the part on query optimization. Moreover, understanding the merge sort will help us later to understand a common database join operation called the merge join.
Merge Like many useful algorithms, the merge sort is based on a trick: This operation is called a merge. You can see on this figure that to construct the final sorted array of 8 elements, you only need to iterate one time in the 2 4-element arrays.
Since both 4-element arrays are already sorted: Then you take the rest of the elements of the other array to put them in the 8-element array. If it can help you, I see this algorithm as a two-phase algorithm: The division phase where the array is divided into smaller arrays The sorting phase where the small arrays are put together using the merge to form a bigger array.
Division phase During the division phase, the array is divided into unitary arrays using 3 steps. How do I know that?
The idea is that each step divides the size of the initial array by 2. The number of steps is the number of times you can divide the initial array by two.
This is the exact definition of logarithm in base 2. Sorting phase In the sorting phase, you start with the unitary arrays. The power of the merge sort Why this algorithm is so powerful? The idea is to load in memory only the parts that are currently processed.
This is important when you need to sort a multi-gigabyte table with only a memory buffer of megabytes. This algorithm can turn lead into gold true fact!
If you want to know more, you can read this research paper that discusses the pros and cons of the common sorting algorithms in a database. Array, Tree and Hash table Now that we understand the idea behind time complexity and sorting, I have to tell you about 3 data structures.
Array The two-dimensional array is the simplest data structure. A table can be seen as an array. This 2-dimensional array is a table with rows and columns:Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time.
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. Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge srmvision.comr, insertion sort provides several advantages. Task. Sort an array (or list) elements using the quicksort algorithm. The elements must have a strict weak order and the index of the array can be of any discrete type. For languages where this is not possible, sort an array of integers.
It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge srmvision.comr, insertion sort provides several advantages.
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Motivation. We already know there are tools to measure how fast a program runs. There are programs called profilers which measure running time in milliseconds and can help us optimize our code by spotting bottlenecks.
While this is a useful tool, it isn't really relevant to algorithm complexity. This Technote describes the on-disk format for an HFS Plus volume. It does not describe any programming interfaces for HFS Plus volumes.
This technote is directed at developers who need to work with HFS Plus at a very low level, below the abstraction . With a low amount of data, the difference between O(1) and O(n2) is negligible. For example, let’s say you have an algorithm that needs to process elements.
Priority queues are introduced as a motivation for heaps. The lecture then covers heap operations and concludes with a discussion of heapsort.