===== Recurrences =====

Methods for solving recurrences: 
{{:aa:lab:recurrences.pdf|}}

==== Lab exercises ====
   * $math[T(n) = 4T(n/4) + 1] (the substitution method is interesting)
   * $math[T(n) = 8T(n/2) + \Theta(n^2)] (the substitution method is interesting)
   * $math[T(n) = 2T(n-1) + 1]
   * $math[T(n) = T(n-1) + 1]
   * $math[T(n) = 2T(n/2) + \log(n)] (the iteration method is interesting)

==== Practice exercises ====
Use each possible method, to solve:
   * $math[T(n) = T(n/9) + T(8n/9) + n]
   * $math[T(n) = T(2n/3) + 1]
   * $math[T(n) = T(\sqrt{n}) + 1] (hint: substitute $math[n] by $math[2^k])
   * $math[T(n) = 2T(\sqrt{n}) + n] (hint: substitute $math[n] by $math[2^k])
   * $math[T(n) = \sqrt{n}T(\sqrt{n}) + n] (harder exercise. hint: substitute $math[n] by $math[2^k])