What are the applications of the Master Theorem in algorithm analysis?

What are the applications of the Master Theorem in algorithm analysis?

The Master Theorem is used to analyze the time complexity of divide-and-conquer algorithms. It provides a method to solve recurrence relations.

Can you give me an example of a recurrence relation that can be solved using the Master Theorem?

Sure! A common example is T(n) = 2T(n/2) + n, which represents the time complexity of merge sort.

How do I apply the Master Theorem to solve that recurrence?

To apply the Master Theorem, identify a, b, and f(n) from the recurrence. Here, a=2, b=2, and f(n)=n. Then, compare f(n) with n^(log_b(a)). In this case, f(n) is Θ(n), which matches n^(log_b(a)), so T(n) = Θ(n log n).

Are there any limitations to using the Master Theorem?

Yes, the Master Theorem has limitations. It only applies to recurrences that fit specific forms and may not work for all types of functions.