The floor and ceiling functions, denoted [x] and [x] respectively, are functions R ? Z defined by

Now define a function T: N ?N by the recurrence

Find a non-recursive formula for T (n), and prove that your formula is correct

Transcribed Image Text:

[x] = max{n € Z ≤ x}, [x] = min{n € Z | n ≥x}. T(1) = 1, T(n) = T([n/2])+T([n/2]) for n ≥ 2. [x] = max{n € Z ≤ x}, [x] = min{n € Z | n ≥x}. T(1) = 1, T(n) = T([n/2])+T([n/2]) for n ≥ 2.

Answer rating: 100% (QA)

Recall that if n is even then And if n is odd then Hence if n is even then T n 2T n2 and if n ... View the full answer