Finding recurrence relations of an algorithm

Posted by Roarke on Stack Overflow See other posts from Stack Overflow or by Roarke
Published on 2010-05-27T08:53:48Z Indexed on 2010/05/27 9:01 UTC
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I'm reading my algorithms text book, and I'm reading about recurrence relations and finding the algorithms big O complexity. I run across this line

"In the case of the merge-sort algorithm, we get the recurrence equation:

    t(n) = b                  if n < 2

         = 2t(n/2) +bn        if n >= 2

for b > 0

my response was "how the heck did we know that?!?!"

So i'm wondering if there is a systematic approach, or just a logical way of getting these recurrence relations from the algorithms

can some one explain where the b and the two 2's come from?

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