#### 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

We can use the Bellman-Ford algorithm to handle graphs with negative weights. It replaces Dijkstra's method of greedy selection with an alternative approach of iterating across every edge in the graph V – 1 times (where V is equal to the total number of vertices) and finding progressively optimal distance values from the source node across each iteration. Naturally, this gives it a higher asymptotic complexity than Dijkstra's algorithm, but it also allows it to produce correct results for graphs that Dijkstra's algorithm would misinterpret. The following exercise shows how to implement the Bellman-Ford algorithm.

### Exercise 32: Implementing the Bellman-Ford Algorithm (Part I)

In this exercise, we will work with the basic Bellman-Ford algorithm to find the shortest distance in a graph with negative weights. Let's get started:

1. First, set up your code by including the necessary libraries (as well as the namespace std for convenience):

#include...