Algorithms in a Nutshell

Principle: Introduce Just Enough Mathematics

Many treatments of algorithms focus nearly exclusively on proving the correctness of the algorithm and explaining only at a high level its details. Our focus is always on showing how the algorithm is to be implemented in practice. To this end, we only introduce the mathematics needed to understand the data structures and the control flow of the solutions.

For example, one needs to understand the properties of sets and binary trees for many algorithms. At the same time, however, there is no need to include a proof by induction on the height of a binary tree to explain how a red-black binary tree is balanced; read Chapter 13 in (Cormen et al., 2001) if you want those details. We explain the results as needed, and refer the reader to other sources to understand how to prove these results mathematically.

In this book you will learn the key terms and analytic techniques to differentiate algorithm behavior based on the data structures used and the desired functionality.