Introducing computer algorithms

In the previous section, we discussed computational thinking and three of its primary pillars. The fourth and final pillar of computational thinking is algorithms. In this section, we will start with the definition of the linear search algorithm and see how it works. Then, we will discuss briefly the divide-and-conquer algorithms for searching. First, let's define what an algorithm is.

Defining an algorithm

An algorithm is a proper sequence of steps or rules that can be implemented in a computer to solve problems or perform calculations. It is like a recipe used to solve problems using computational thinking and is one of the most important parts of the computational process because this is where things start to get implemented in the real world. The algorithm is the very first step to writing a computer program!

Consider the example of making tea, which involves a sequence of steps that we need to follow in a certain order to make it successful. First of all, you will require the ingredients and resources, such as water, an electric kettle, a teabag, and a cup. Now we fill the kettle with water, switch it on, and let it boil. As soon as the kettle's boiled, we pour the water into the cup and then put the teabag into the cup. We let the teabag brew there for a few minutes and then we remove it. That's it – our tea is ready!

Now consider the steps for adding two numbers as performed by a computer. We know that for this, we would require the two numbers, and we will get an answer to our problem by the addition of the two numbers.

An algorithm for this would involve defining three variables that can store those two numbers and the answer. We would perform the addition and store the answer in the third variable. Finally, we could print the value of the third variable, which has the answer. You might wonder, can the tea-making job be done by a computer? And the answer is yes, it can! But the process is way more complex: for that, you have to teach a robot how to make tea! For a computer algorithm, we simply use the sequence of steps as instructions that are given to the computer to solve a particular problem.

Let's now learn about the way in which a linear search algorithm works. This is the most basic and simple of all the searching algorithms.

The linear search algorithm

Let's consider a searching problem where we have to search for a specific element in an array and return the index of the element when it is found. Some sample Python 3 code to do the searching is given as follows:

a = ['t','u','t','o','r','i','a','l']
x = 'o'
def linearsearch(a, x):
   for i in range(len(a)):
      if a[i] == x:
         return i
   return -1
print("element found at index "+str(linearsearch(a,x)))

The preceding code is used for a linear search operation. In linear searching, a user will provide a specific element to search in an array and the program will compare the value of the element with each of the values present in the array sequentially.

If you run the preceding code, you will get the output as element found at index 3. This is because indexing in Python starts at 0 and the a element is located at the sixth index. The input is the a element. You can clearly see in the code that each value present in the array is being compared with the input value provided. This means that the time of execution in this case linearly depends upon the length of the array.

There is another type of very famous algorithm called the divide-and-conquer algorithm, which represents the idea of computational thinking very well. It takes a bigger problem and then divides it into smaller sub-problems, solves each of those sub-problems individually, and then returns the solution, which is usually the solution to the whole problem. The most common example of a divide-and-conquer algorithm is the binary search algorithm, where the array is decomposed into parts and then searching is performed on the individual parts until the element is found.

Let's now learn about the complexity of algorithms and how we can make our algorithm implementations better in the next section.