Book Image

C++ Data Structures and Algorithm Design Principles

By : John Carey, Anil Achary, Shreyans Doshi, Payas Rajan
Book Image

C++ Data Structures and Algorithm Design Principles

By: John Carey, Anil Achary, Shreyans Doshi, Payas Rajan

Overview of this book

C++ is a mature multi-paradigm programming language that enables you to write high-level code with a high degree of control over the hardware. Today, significant parts of software infrastructure, including databases, browsers, multimedia frameworks, and GUI toolkits, are written in C++. This book starts by introducing C++ data structures and how to store data using linked lists, arrays, stacks, and queues. In later chapters, the book explains the basic algorithm design paradigms, such as the greedy approach and the divide-and-conquer approach, which are used to solve a large variety of computational problems. Finally, you will learn the advanced technique of dynamic programming to develop optimized implementations of several algorithms discussed in the book. By the end of this book, you will have learned how to implement standard data structures and algorithms in efficient and scalable C++ 14 code.
Table of Contents (11 chapters)

The Vertex Coloring Problem

The vertex coloring problem can be stated as follows:

"Given a graph, G, assign a color to each vertex of the graph so that no two adjacent vertices have the same color."

As an example, the following figure shows a valid coloring of the graph that was shown in figure 5.11:

Figure 5.21: Coloring an uncolored graph
Figure 5.21: Coloring an uncolored graph

Graph coloring has applications in solving a large variety of problems in the real world – making schedules for taxis, solving sudoku puzzles, and creating timetables for exams can all be mapped to finding a valid coloring of the problem, modeled as a graph. However, finding the minimum number of colors required to produce a valid vertex coloring (also called the chromatic number) is known to be an NP-complete problem. Thus, a minor change in the nature of the problem can make a massive difference to its complexity.

As an example of the applications of the graph coloring problem, let's consider the case of sudoku solvers...