## Introduction

In the previous chapter, we studied some commonly used data structures. Data structures are organizations of data in different forms, and a data structure enables and controls the cost of access to the data stored inside it. However, what makes software useful is not just the ability to store and retrieve data in various formats, but the ability to make transformations on data in order to solve computational problems. For a given problem, the precise definition and order of transformations on data is determined by a sequence of instructions called an **algorithm**.

An algorithm takes in a set of inputs that define an instance of a problem, applies a series of transformations, and outputs a set of results. If these results are the correct solutions to the computational problem at hand, our algorithm is said to be *correct*. The *goodness* of an algorithm is determined by its efficiency, or how few instructions the algorithm needs to perform to produce correct results: