The third may be used with some nested loops. Suppose we have a loopwhich is executed O(f (n)) times, and each execution takes time O(g (n)).Then the execution of the loop takes time O(f (n) · g (n))

The statement you provided is a common concept in computer science, specifically in the analysis of algorithms. It's about the time complexity of nested loops in an algorithm.

Here's a step-by-step explanation:

1. O(f(n)) is the time complexity of the outer loop. This means that the number of times the outer loop is executed is proportional to f(n).

2. O(g(n)) is the time complexity of the inner loop (or the operation inside the outer loop). This means that the number of operations performed in each execution of the outer loop is proportional to g(n).

3. When you have a loop inside another loop (nested loops), you multiply their time complexities to get the total time complexity. This is because for each iteration of the outer loop, the inner loop runs g(n) times.

4. Therefore, the total time complexity of the nested loops is O(f(n) · g(n)). This means that the total number of operations performed by the nested loops is proportional to f(n) times g(n).

Remember, this is a simplification. The actual time an algorithm takes to run depends on many factors, including the specific inputs, the hardware it's running on, etc. But this kind of analysis gives us a way to compare the efficiency of different algorithms in a general way.