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

Tabulation – the Bottom-Up Approach

The heart of dynamic programming is tabulation, which is the inverse approach to memoization. In fact, though the term dynamic programming is sometimes applied to both memoization and tabulation, its use is generally assumed to refer specifically to the latter.

The standard implementation of tabulation consists of storing the solutions for the base cases and then iteratively filling a table with the solutions for every subproblem, which can then be reused to find the solutions for other subproblems. Tabulated solutions are generally considered to be a bit harder to conceptualize than memoized ones because the state of each subproblem must be represented in a way that can be expressed iteratively.

A tabulated solution to computing the Fibonacci sequence would look like this:

int Fibonacci(int n)

{

vector<int> DP(n + 1, 0);

DP[1] = 1;

...