Beyond the foundational nature of these results and the modern motivations for faster algorithms, this suite of algorithmic advances is particularly exciting due to the wide range of tools they employ and the non-trivial interplay between them. These fast algorithms apply continuous optimization methods to solve combinatorial problems, dynamic data structures to solve static problems, sketching techniques to solve problems without memory limitations, and more. In some cases these faster algorithms have then in turn led to improvements for these tools, e.g. optimization techniques have been used in sketching routines and to yield improved dynamic graph algorithms. There have even been recent instances where a large suite of continuous, combinatorial, dynamic data structures, and sketching techniques are all combined for a faster algorithm for a single problem.
A data structure is a specialized format for organizing, processing, retrieving and storing data. There are several basic and advanced types of data structures, all designed to arrange data to suit a specific purpose. Data structures make it easy for users to access and work with the data they need in appropriate ways. Most importantly, data structures frame the organization of information so that machines and humans can better understand it.
Data Structuresl
In computer science and computer programming, a data structure may be selected or designed to store data for the purpose of using it with various algorithms. In some cases, the algorithm's basic operations are tightly coupled to the data structure's design. Each data structure contains information about the data values, relationships between the data and -- in some cases -- functions that can be applied to the data.
For instance, in an object-oriented programming language, the data structure and its associated methods are bound together as part of a class definition. In non-object-oriented languages, there may be functions defined to work with the data structure, but they are not technically part of the data structure.
Typical base data types, such as integers or floating-point values, that are available in most computer programming languages are generally insufficient to capture the logical intent for data processing and use. Yet applications that ingest, manipulate and produce information must understand how data should be organized to simplify processing. Data structures bring together the data elements in a logical way and facilitate the effective use, persistence and sharing of data. They provide a formal model that describes the way the data elements are organized.
Data structures are the building blocks for more sophisticated applications. They are designed by composing data elements into a logical unit representing an abstract data type that has relevance to the algorithm or application. An example of an abstract data type is a "customer name" that is composed of the character strings for "first name," "middle name" and "last name."
It is not only important to use data structures, but it is also important to choose the proper data structure for each task. Choosing an ill-suited data structure could result in slow runtimes or unresponsive code. Five factors to consider when picking a data structure include the following:
In general, data structures are used to implement the physical forms of abstract data types. Data structures are a crucial part of designing efficient software. They also play a critical role in algorithm design and how those algorithms are used within computer programs.
Early programming languages -- such as Fortran, C and C++ -- enabled programmers to define their own data structures. Today, many programming languages include an extensive collection of built-in data structures to organize code and information. For example, Python lists and dictionaries, and JavaScript arrays and objects are common coding structures used for storing and retrieving information.
Software engineers use algorithms that are tightly coupled with the data structures -- such as lists, queues and mappings from one set of values to another. This approach can be fused in a variety of applications, including managing collections of records in a relational database and creating an index of those records using a data structure called a binary tree.
If data structures are the building blocks of algorithms and computer programs, the primitive -- or base -- data types are the building blocks of data structures. The typical base data types include the following:
The data structure type used in a particular situation is determined by the type of operations that will be required or the kinds of algorithms that will be applied. The various data structure types include the following:
Series is a one-dimensional labeled array capable of holding any datatype (integers, strings, floating point numbers, Python objects, etc.). The axislabels are collectively referred to as the index. The basic method to create a Series is to call:
A key difference between Series and ndarray is that operations between Seriesautomatically align the data based on label. Thus, you can write computationswithout giving consideration to whether the Series involved have the samelabels.
The result of an operation between unaligned Series will have the union ofthe indexes involved. If a label is not found in one Series or the other, theresult will be marked as missing NaN. Being able to write code without doingany explicit data alignment grants immense freedom and flexibility ininteractive data analysis and research. The integrated data alignment featuresof the pandas data structures set pandas apart from the majority of relatedtools for working with labeled data.
In general, we chose to make the default result of operations betweendifferently indexed objects yield the union of the indexes in order toavoid loss of information. Having an index label, though the data ismissing, is typically important information as part of a computation. Youof course have the option of dropping labels with missing data via thedropna function.
DataFrame is a 2-dimensional labeled data structure with columns ofpotentially different types. You can think of it like a spreadsheet or SQLtable, or a dict of Series objects. It is generally the most commonly usedpandas object. Like Series, DataFrame accepts many different kinds of input:
Along with the data, you can optionally pass index (row labels) andcolumns (column labels) arguments. If you pass an index and / or columns,you are guaranteeing the index and / or columns of the resultingDataFrame. Thus, a dict of Series plus a specific index will discard all datanot matching up to the passed index.
To construct a DataFrame with missing data, we use np.nan torepresent missing values. Alternatively, you may pass a numpy.MaskedArrayas the data argument to the DataFrame constructor, and its masked entries willbe considered missing. See Missing data for more.
NumPy ufuncs are safe to apply to Series backed by non-ndarray arrays,for example arrays.SparseArray (see Sparse calculation). If possible,the ufunc is applied without converting the underlying data to an ndarray.
About BIDSNeuroimaging experiments result in complicated data that can be arranged in many different ways.So far there is no consensus how to organize and share data obtained in neuroimaging experiments.Even two researchers working in the same lab can opt to arrange their data in a different way.Lack of consensus (or a standard) leads to misunderstandings and time wasted on rearranging data or rewriting scripts expecting certain structure.With the Brain Imaging Data Structure (BIDS), we describe a simple and easy to adopt way of organizing neuroimaging and behavioral data.
A few of the key elements of this ecosystem are the BIDS-validator, to automatically check datasets for adherence to the specification, OpenNeuro, as a database for BIDS formatted datasets, and BIDS-Apps, a collection of portable neuroimaging pipelines that understand BIDS datasets.
If the labels property of the main data property is used, it has to contain the same amount of elements as the dataset with the most values. These labels are used to label the index axis (default x axes). The values for the labels have to be provided in an array.The provided labels can be of the type string or number to be rendered correctly. In case you want multiline labels you can provide an array with each line as one entry in the array.
This is also the internal format used for parsed data. In this mode, parsing can be disabled by specifying parsing: false at chart options or dataset. If parsing is disabled, data must be sorted and in the formats the associated chart type and scales use internally.
VisuAlgo was conceptualised in 2011 by Dr Steven Halim as a tool to help his students better understand data structures and algorithms, by allowing them to learn the basics on their own and at their own pace.
Though specifically designed for National University of Singapore (NUS) students taking various data structure and algorithm classes (e.g., CS1010/equivalent, CS2040/equivalent, CS3230, CS3233, and CS4234), as advocators of online learning, we hope that curious minds around the world will find these visualizations useful too.
The most exciting development is the automated question generator and verifier (the online quiz system) that allows students to test their knowledge of basic data structures and algorithms. The questions are randomly generated via some rules and students' answers are instantly and automatically graded upon submission to our grading server. This online quiz system, when it is adopted by more CS instructors worldwide, should technically eliminate manual basic data structure and algorithm questions from typical Computer Science examinations in many Universities. By setting a small (but non-zero) weightage on passing the online quiz, a CS instructor can (significantly) increase his/her students mastery on these basic questions as the students have virtually infinite number of training questions that can be verified instantly before they take the online quiz. The training mode currently contains questions for 12 visualization modules. We will soon add the remaining 12 visualization modules so that every visualization module in VisuAlgo have online quiz component. 2ff7e9595c
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