Can you give an example of a real-world problem solved by algorithms?

Yes, Google's search engine uses algorithms to provide the most relevant search results to users.

Google's search engine is a prime example of a real-world problem solved by algorithms. When you type a query into Google's search bar, it's not human beings on the other end sifting through billions of web pages to present you with the best results. Instead, it's a complex algorithm known as PageRank.

PageRank works by counting the number and quality of links to a page to determine a rough estimate of how important the website is. The underlying assumption is that more important websites are likely to receive more links from other websites. It's not the only algorithm used by Google to order search engine results, but it is the first algorithm that was used by the company, and it is the most well-known.

The algorithm operates on a structure called a web graph, which represents the entire web and links between pages. Each web page is a node in the graph, and each hyperlink on a page creates an edge connecting two nodes. The PageRank of a page is then calculated using a recursive formula, which considers the PageRank of each page that links to it, the total number of links on each of those pages, and the total number of links to the page being ranked.

This algorithm has been instrumental in Google's success as a search engine. It's able to quickly and efficiently sift through the vast amount of information on the web and deliver relevant results to users' queries. It's a perfect example of how algorithms can solve complex real-world problems, and it's a topic that's often studied in computer science courses.

However, it's important to note that Google's search algorithms have evolved significantly since the company's early days. Today, they use a combination of algorithms and techniques, including machine learning and artificial intelligence, to deliver even more accurate and personalised search results. But the fundamental problem – how to find the most relevant information in a vast sea of data – remains the same, and algorithms are still the key to solving it.