#### 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.
Free Chapter
1. Lists, Stacks, and Queues
2. Trees, Heaps, and Graphs
3. Hash Tables and Bloom Filters
4. Divide and Conquer
5. Greedy Algorithms
6. Graph Algorithms I
7. Graph Algorithms II
8. Dynamic Programming I
9. Dynamic Programming II

## The Bellman-Ford Algorithm (Part II) – Negative Weight Cycles

Consider the graph shown in the following figure:

###### Figure 7.2: Graph with a negative weight cycle

The edges highlighted in red indicate a negative weight cycle or a cycle in the graph where the combined edge weights produce a negative sum. In such a situation, this cycle would be considered repeatedly, and the final results would be skewed.

For the sake of comparison, consider a graph with only positive edge weights. A cycle in such a graph would never be considered in the solution because the shortest distance to the first node in the cycle would have been found already. To demonstrate this, imagine that the edge weight between nodes B and D in the preceding figure is positive. Starting from node A, the first iteration through the edges would determine that the shortest distance to node B is equal to 3. After two more iterations, we would also know the shortest distance from A to C (A —> B &...