#### Overview of this book

Learning about data structures and algorithms gives you a better insight on how to solve common programming problems. Most of the problems faced everyday by programmers have been solved, tried, and tested. By knowing how these solutions work, you can ensure that you choose the right tool when you face these problems. This book teaches you tools that you can use to build efficient applications. It starts with an introduction to algorithms and big O notation, later explains bubble, merge, quicksort, and other popular programming patterns. You’ll also learn about data structures such as binary trees, hash tables, and graphs. The book progresses to advanced concepts, such as algorithm design paradigms and graph theory. By the end of the book, you will know how to correctly implement common algorithms and data structures within your applications.
Title Page
Packt Upsell
Contributors
Preface
Free Chapter
Algorithms and Complexities
Sorting Algorithms and Fundamental Data Structures
Hash Tables and Binary Search Trees
String Matching Algorithms
Graphs, Prime Numbers, and Complexity Classes
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Index

## Naive Search Algorithm

The string matching problem has two inputs, as follows:

• An arrayT[1, 2, ...n]of lengthn
• An arrayP[1, 2, ...m]of lengthm (<= n)

The elements of `T` and `P` are characters from the same finite alphabet (usually called ∑).

For instance, we may be searching in binary strings, in which case our alphabet is {0, 1}, or we may be searching in strings of lowercase letters, in which case our alphabet is {a, b… z}.

The following diagram represents this terminology:

Figure 5.1: Representation of text arrayT, pattern arrayP, and finite alphabet ∑

The character arrays `P` and `T` are usually called "strings of characters". We're interested in finding occurrences of pattern `P` in text `T`.

We say that pattern `P` occurs in text `T` if we can align the pattern `P` with text `T` so that all characters in `P` match the ones in `T`. When aligning, we need to shift pattern `P` zero or more times to the right.

Therefore, in the string matching problem, we're interested in valid shifts with which pattern `P` occurs in...