#### Overview of this book

Building your own applications is exciting but challenging, especially when tackling complex problems tied to advanced data structures and algorithms. This endeavor demands profound knowledge of the programming language as well as data structures and algorithms – precisely what this book offers to C# developers. Starting with an introduction to algorithms, this book gradually immerses you in the world of arrays, lists, stacks, queues, dictionaries, and sets. Real-world examples, enriched with code snippets and illustrations, provide a practical understanding of these concepts. You’ll also learn how to sort arrays using various algorithms, setting a solid foundation for your programming expertise. As you progress through the book, you’ll venture into more complex data structures – trees and graphs – and discover algorithms for tasks such as determining the shortest path in a graph before advancing to see various algorithms in action, such as solving Sudoku. By the end of the book, you’ll have learned how to use the C# language to build algorithmic components that are not only easy to understand and debug but also seamlessly applicable in various applications, spanning web and mobile platforms.
Chapter 1: Data Types
Free Chapter
Chapter 2: Introduction to Algorithms
Chapter 3: Arrays and Sorting
Chapter 4: Variants of Lists
Chapter 5: Stacks and Queues
Chapter 6: Dictionaries and Sets
Chapter 7: Variants of Trees
Chapter 8: Exploring Graphs
Chapter 9: See in Action
Chapter 10: Conclusion
Index
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# A Sudoku puzzle

Have you ever solved Sudoku? It is a very popular game that requires you to fill empty cells of a 9x9 board with numbers from 1 to 9. However, each row, each column, and each 3x3 box must contain only unique numbers. An exemplary starting board and a solved one are shown as follows:

Figure 9.7 – An example of non-solved and solved Sudoku puzzles

Now, you will learn how to solve Sudoku not with the usage of a pencil and a piece of paper but with an algorithm! You can perform this task using the back-tracking approach, trying to assign numbers to empty cells if, of course, they meet the conditions regarding unique numbers in each row, column, and box. If an entered number does not result in solving the whole puzzle, you assign another number and perform the check again. Let’s take a look at the most important part of the code:

bool Solve()
{
(int row, int col) = GetEmpty();
...