Book Image

PHP 7 Data Structures and Algorithms

By : Mizanur Rahman
5 (1)
Book Image

PHP 7 Data Structures and Algorithms

5 (1)
By: Mizanur Rahman

Overview of this book

PHP has always been the the go-to language for web based application development, but there are materials and resources you can refer to to see how it works. Data structures and algorithms help you to code and execute them effectively, cutting down on processing time significantly. If you want to explore data structures and algorithms in a practical way with real-life projects, then this book is for you. The book begins by introducing you to data structures and algorithms and how to solve a problem from beginning to end using them. Once you are well aware of the basics, it covers the core aspects like arrays, listed lists, stacks and queues. It will take you through several methods of finding efficient algorithms and show you which ones you should implement in each scenario. In addition to this, you will explore the possibilities of functional data structures using PHP and go through advanced algorithms and graphs as well as dynamic programming. By the end, you will be confident enough to tackle both basic and advanced data structures, understand how they work, and know when to use them in your day-to-day work
Table of Contents (14 chapters)

Understanding the big O (big oh) notation

The big O notation is very important for the analysis of algorithms. We need to have a solid understanding of this notation and how to use this in the future. We are going to discuss the big O notation throughout this section.

Our algorithm for finding the books and placing them has n number of items. For the first book search, it will compare n number of books for the worst case situation. If we say time complexity is T, then for the first book the time complexity will be:

T(1) = n

As we are removing the founded book from the list, the size of the list is now n-1. For the second book search, it will compare n-1 number of books for the worst case situation. Then for the second book, the time complexity will be n-1. Combining the both time complexities, for first two books it will be:

T(2) = n + (n - 1)

If we continue like this, after the n-1 steps the last book search will only have 1 book left to compare. So, the total complexity will look like:

T(n) = n + (n - 1) + (n - 2) + . . . . . . .  . . . . + 3 + 2 + 1 

Now if we look at the preceding series, doesn't it look familiar? It is also known as the sum of n numbers equation as shown:

So we can write:

T(n) = n(n + 1)/2 

Or:

T(n) = n2/2 + n/2 

For asymptotic analysis, we ignore low order terms and constant multipliers. Since we have n2, we can easily ignore the n here. Also, the 1/2 constant multiplier can also be ignored. Now we can express the time complexity with the big O notation as the order of n squared:

T(n) = O(n2) 

Throughout the book, we will be using this big O notation to describe complexity of the algorithms or operations. Here are some common big O notations:

Type

Notation

Constant

O (1)

Linear

O (n)

Logarithmic

O (log n)

n log n

O (n log n)

Quadratic

O (n2)

Cubic

O (n3)

Exponential

O (2n)