T (n) = T (n −1) + O(n) in lecture. Another technique is applicable if the work term is not a polynomial: 1) take the polynomial upper bound of it, and see what Master theorem gives you, 2) take the polynomial lower bound of it, and see what Master theorem gives you, and 3) if these agree, then you have an answer. (a) T (n) = 12T (n/5)+13n^1.4 (b) T (n) = 6T (n/5)+n^1.3 (c) T (n) = 4T (n/2)+log^3 n (d) T (n) = T (n −3)+log n
Solving recurrences Solve the following recurrence relations and give a Θbound for each of
them. Keep in mind that we’ve seen several examples of how to solve recurrences. You can try to apply
the Master’s theorem or use a recursion tree. You can also try to “unfold” the recurrences, as we saw with T (n) = T (n −1) + O(n) in lecture. Another technique is applicable if the work term is not a polynomial: 1) take the polynomial upper bound of it, and see what Master theorem gives you, 2) take the polynomial lower bound of it, and see what Master theorem gives you, and 3) if these agree, then you have an answer.
(a) T (n) = 12T (n/5)+13n^1.4
(b) T (n) = 6T (n/5)+n^1.3
(c) T (n) = 4T (n/2)+log^3 n
(d) T (n) = T (n −3)+log n
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