Lecture Notes for stringlengths 1 100 | Unnamed: 1 stringclasses 7
values | Unnamed: 2 float64 | Unnamed: 3 float64 |
|---|---|---|---|
algorithms based upon them. | null | null | null |
Often we want to talk about data structures without having to worry about all the im- | null | null | null |
plementational details associated with particular programming languages, or how the data is | null | null | null |
stored in computer memory. We can do this by formulating abstract mathematical models | null | null | null |
of particular classes of data structures or data types which have common features. These are | null | null | null |
called abstract data types, and are defined only by the operations that may be performed on | null | null | null |
them. Typically, we specify how they are built out of more primitive data types (e.g., integers | null | null | null |
or strings), how to extract that data from them, and some basic checks to control the flow of | null | null | null |
processinginalgorithms. Theideathattheimplementationaldetailsarehiddenfromtheuser | null | null | null |
and protected from outside access is known as encapsulation. We shall see many examples of | null | null | null |
abstract data types throughout these notes. | null | null | null |
At an even higher level of abstraction are design patterns which describe the design of | null | null | null |
algorithms, rather the design of data structures. These embody and generalize important | null | null | null |
design concepts that appear repeatedly in many problem contexts. They provide a general | null | null | null |
structure for algorithms, leaving the details to be added as required for particular problems. | null | null | null |
These can speed up the development of algorithms by providing familiar proven algorithm | null | null | null |
structures that can be applied straightforwardly to new problems. We shall see a number of | null | null | null |
familiar design patterns throughout these notes. | null | null | null |
1.4 Textbooks and web-resources | null | null | null |
To fully understand data structures and algorithms you will almost certainly need to comple- | null | null | null |
ment the introductory material in these notes with textbooks or other sources of information. | null | null | null |
The lectures associated with these notes are designed to help you understand them and fill in | null | null | null |
some of the gaps they contain, but that is unlikely to be enough because often you will need | null | null | null |
to see more than one explanation of something before it can be fully understood. | null | null | null |
There is no single best textbook that will suit everyone. The subject of these notes is a | null | null | null |
classical topic, so there is no need to use a textbook published recently. Books published 10 | null | null | null |
or 20 years ago are still good, and new good books continue to be published every year. The | null | null | null |
reasonisthatthesenotescoverimportantfundamentalmaterialthatistaughtinalluniversity | null | null | null |
degrees in computer science. These days there is also a lot of very useful information to be | null | null | null |
found on the internet, including complete freely-downloadable books. It is a good idea to go | null | null | null |
to your library and browse the shelves of books on data structures and algorithms. If you like | null | null | null |
any of them, download, borrow or buy a copy for yourself, but make sure that most of the | null | null | null |
7topics in the above contents list are covered. Wikipedia is generally a good source of fairly | null | null | null |
reliable information on all the relevant topics, but you hopefully shouldn’t need reminding | null | null | null |
that not everything you read on the internet is necessarily true. It is also worth pointing | null | null | null |
out that there are often many different equally-good ways to solve the same task, different | null | null | null |
equally-sensible names used for the same thing, and different equally-valid conventions used | null | null | null |
by different people, so don’t expect all the sources of information you find to be an exact | null | null | null |
match with each other or with what you find in these notes. | null | null | null |
1.5 Overview | null | null | null |
These notes will cover the principal fundamental data structures and algorithms used in | null | null | null |
computerscience,andbringtogetherabroadrangeoftopicscoveredelsewhereintoacoherent | null | null | null |
framework. Data structures will be formulated to represent various types of information in | null | null | null |
such a way that it can be conveniently and efficiently manipulated by the algorithms we | null | null | null |
develop. Throughout, the recurring practical issues of algorithm specification, verification | null | null | null |
and performance analysis will be discussed. | null | null | null |
We shall begin by looking at some widely used basic data structures (namely arrays, | null | null | null |
linked lists, stacks and queues), and the advantages and disadvantages of the associated | null | null | null |
abstract data types. Then we consider the ubiquitous problem of searching, and how that | null | null | null |
leads on to the general ideas of computational efficiency and complexity. That will leave | null | null | null |
us with the necessary tools to study three particularly important data structures: trees (in | null | null | null |
particular, binarysearchtreesandheaptrees), hashtables, andgraphs. Weshalllearnhowto | null | null | null |
develop and analyse increasingly efficient algorithms for manipulating and performing useful | null | null | null |
operations on those structures, and look in detail at developing efficient processes for data | null | null | null |
storing, sorting, searching and analysis. The idea is that once the basic ideas and examples | null | null | null |
covered in these notes are understood, dealing with more complex problems in the future | null | null | null |
should be straightforward. | null | null | null |
8Chapter 2 | null | null | null |
Arrays, Iteration, Invariants | null | null | null |
Data is ultimately stored in computers as patterns of bits, though these days most program- | null | null | null |
ming languages deal with higher level objects, such as characters, integers, and floating point | null | null | null |
numbers. Generally, we need to build algorithms that manipulate collections of such objects, | null | null | null |
so we need procedures for storing and sequentially processing them. | null | null | null |
2.1 Arrays | null | null | null |
In computer science, the obvious way to store an ordered collection of items is as an array. | null | null | null |
Array items are typically stored in a sequence of computer memory locations, but to discuss | null | null | null |
them, we need a convenient way to write them down on paper. We can just write the items | null | null | null |
in order, separated by commas and enclosed by square brackets. Thus, | null | null | null |
[1,4,17,3,90,79,4,6,81] | null | null | null |
is an example of an array of integers. If we call this array a, we can write it as: | null | null | null |
a = [1,4,17,3,90,79,4,6,81] | null | null | null |
This array a has 9 items, and hence we say that its size is 9. In everyday life, we usually start | null | null | null |
counting from 1. When we work with arrays in computer science, however, we more often | null | null | null |
(though not always) start from 0. Thus, for our array a, its positions are 0,1,2,...,7,8. The | null | null | null |
element in the 8th position is 81, and we use the notation a[8] to denote this element. More | null | null | null |
generally, for any integer i denoting a position, we write a[i] to denote the element in the ith | null | null | null |
position. This position i is called an index (and the plural is indices). Then, in the above | null | null | null |
example, a[0] = 1, a[1] = 4, a[2] = 17, and so on. | null | null | null |
It is worth noting at this point that the symbol = is quite overloaded. In mathematics, | null | null | null |
it stands for equality. In most modern programming languages, = denotes assignment, while | null | null | null |
equality is expressed by ==. We will typically use = in its mathematical meaning, unless it | null | null | null |
is written as part of code or pseudocode. | null | null | null |
We say that the individual items a[i] in the array a are accessed using their index i, and | null | null | null |
one can move sequentially through the array by incrementing or decrementing that index, | null | null | null |
or jump straight to a particular item given its index value. Algorithms that process data | null | null | null |
stored as arrays will typically need to visit systematically all the items in the array, and apply | null | null | null |
appropriate operations on them. | null | null | null |
92.2 Loops and Iteration | null | null | null |
The standard approach in most programming languages for repeating a process a certain | null | null | null |
numberoftimes,suchasmovingsequentiallythroughanarraytoperformthesameoperations | null | null | null |
on each item, involves a loop. In pseudocode, this would typically take the general form | null | null | null |
For i = 1,...,N, | null | null | null |
do something | null | null | null |
and in programming languages like C and Java this would be written as the for-loop | null | null | null |
for( i = 0 ; i < N ; i++ ) { | null | null | null |
// do something | null | null | null |
} | null | null | null |
in which a counter i keep tracks of doing “the something” N times. For example, we could | null | null | null |
compute the sum of all 20 items in an array a using | null | null | null |
for( i = 0, sum = 0 ; i < 20 ; i++ ) { | null | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.