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Divide and Conquer Algorithms
Does anyone read the book "Algorithms" by Papadimitriou et al.? I found it to be an excellent book, just sometime need a little bit of explanation in some parts of it. For example, in chapter 2 about divide and conquer algorithms it presents a master theorem about the time complexity for this kind of algoritms. It saids something like this:
Re: Divide and Conquer Algorithms
When you have a divide and conquer algorithm, they do something on each step after they divide. O(n^d) is the cost of what they do on this step. So let's say my imaginary algorithm divides a list in half, then sorts each part of that list with bubble sort. The cost of the bubble sort is n^2, so d = 2.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."