Write an algorithm to solve the problem

An algorithm is a set of instructions which, if faithfully followed, will produce a solution to a given problem or perform some specified task. When an instruction is followed, we say it is executed. We can speak of an algorithm for finding a word in a dictionary, for changing a punctured tyre or for playing a video game.

For any problem, there will normally be more than one algorithm to solve it. Each algorithm will have its own advantages and disadvantages. When we are searching for a word in the dictionary, one method would be to start at the beginning and look at each word in turn. A second method would be to start at the end and search backwards. Here, an advantage of the first method is that it would find a word faster if it were at the beginning, while the second method would be faster if the word were towards the end.

Another method for searching for the word would be one which used the fact that the words in a dictionary are in alphabetical order—this is the method we all use when looking up a word in a dictionary. In any situation, a programmer would usually have a choice of algorithms, and it is one of her more important jobs to decide which algorithm is the best, and why this is so.

In our example, we must write the instructions in our algorithm in such a way that they can be easily converted into a form which the computer can follow. Computer instructions fall into three main categories:

(1) Input instructions, used for supplying data from the ‘outside world’ to a program; this is usually done via the keyboard or a file.

(2) Processing instructions, used for manipulating data inside the computer. These instructions allow us to add, subtract, multiply and divide; they also allow us to compare two values, and act according to the result of the comparison. Also, we can move data from one location in the computer’s memory to another location.

(3) Output instructions, used for getting information out of the computer to the outside world.