Max.Planck said:You can not use the Master Theorem in this case, just use the recursion tree method. In this case it is easy to see that it will be exponential, since each level has twice the number of nodes of the previous level.
zeion said:Actually nevermind, so if I find a closed form expression it will be 2^n, right?
Yes, Master Theorem can be used even if the partitions are not fractions. The theorem applies to any function that can be written in the form T(n) = aT(n/b) + f(n), where a ≥ 1, b > 1, and f(n) is a positive function.
The main conditions for using Master Theorem are that the function must be in the form T(n) = aT(n/b) + f(n), where a ≥ 1, b > 1, and f(n) is a positive function. Additionally, the function must have a logarithmic term in the recurrence relation.
No, Master Theorem is specifically used for analyzing divide and conquer algorithms that have a logarithmic term in their recurrence relation. It cannot be used for other types of algorithms such as linear or exponential algorithms.
The main advantage of using Master Theorem is that it provides a quick and easy way to determine the time complexity of a divide and conquer algorithm. It also provides a framework for understanding the time complexity of such algorithms and can help in making algorithm design decisions.
Yes, there are some limitations to using Master Theorem. It can only be used for divide and conquer algorithms with a specific form and cannot be applied to other types of algorithms. Additionally, it may not always provide the most accurate time complexity analysis and may need to be supplemented with other analysis techniques.