The master theorem
In the analysis of algorithms, the master theorem plays a crucial role in solving recurrences for divide-and-conquer algorithms. Introduced in 1980, it has become a mainstream approach for estimating the complexity of a wide range of recurrence functions. The master theorem provides a straightforward framework for determining the asymptotic behavior of recurrences of the following form:
Here, 
and 
are constants, and f(n), the driving function, is an asymptotically positive function bounded by polynomial functions. This means there exist two polynomial functions 
and 
such that the following is the case:
The importance of the master theorem lies in its ability to simplify the complexity analysis of many common algorithms, such as merge sort, quicksort, and binary search, among others. By categorizing the behavior of the recurrence based on the relationship between 
and 
, the master theorem allows for quick and accurate complexity estimation without...
