# 1.2. Algorithms¶

If problem solving is a central part of computer science, then the solutions that you create through the problem solving process are also important. In computer science, we refer to these solutions as algorithms. An algorithm is a step by step list of instructions that if followed exactly will solve the problem under consideration.

For example, an algorithm to compute the area of a circle given its radius might look like this:

Algorithm Example 1 (English)

2. Compute area by squaring radius and multiplying the result by pi

3. Display the computed area

Notice that this algorithm consists of a set of numbered steps. It is written in English, for ease of understanding. Although simple algorithms are easily understood when written in English, more complicated algorithms need more precise notation. For improved precision, algorithms are often written in pseudocode. Pseudocode is a notation that is more precise than English but generally not as precise as a programming language. The same algorithm expressed in pseudocode might look something like this:

Algorithm Example 2 (Pseudocode)

2. let area = (radius2) × π

3. Display area

Note how the pseudocode example expresses step 2 more precisely, specifying the formula in mathematical terms.

Our goal in computer science is to take a problem and develop an algorithm that can serve as a general solution. Once we have such a solution, we can use our computer to automate its execution using programming. Programming is a skill that allows a computer scientist to take an algorithm and represent it in a notation (a program) that can be followed by a computer. A program is written in a programming language such as Python, the language you will learn in this book.

To help you understand the difference between an algorithm and a program, consider this program to compute the area of a circle:

A program is an algorithm expressed in a programming language. We might also say that a program is an implementation of an algorithm. In this example, both the algorithm and the program have three steps. The first step gets some input from the user and the input into something the computer can do math with; the second step performs a calculation using the information obtained in the first step; and the final step displays the result to the user. Even though we haven’t covered any details of Python, hopefully you can see the correspondence between the steps of the algorithm, which could be followed by a human (but not executed by a computer), and the steps of the program, which can be executed by a computer (try executing this one using the Run button).

Algorithms are important because the process of solving a problem through programming often begins by designing an algorithm. The programmer often expresses the algorithm in pseudocode, then converts the algorithm to a program for the computer to execute. In the next section, you will learn how to execute Python programs on a computer.