Methods for solving recurrences: recurrences.pdf

• $ T(n) = 4T(n/4) + 1$ (the substitution method is interesting)
• $ T(n) = 8T(n/2) + \Theta(n^2)$ (the substitution method is interesting)
• $ T(n) = 2T(n-1) + 1$
• $ T(n) = T(n-1) + 1$
• $ T(n) = 2T(n/2) + \log(n)$ (the iteration method is interesting)

Use each possible method, to solve:

• $ T(n) = T(n/9) + T(8n/9) + n$
• $ T(n) = T(2n/3) + 1$
• $ T(n) = T(\sqrt{n}) + 1$ (hint: substitute $ n$ by $ 2^k$ )
• $ T(n) = 2T(\sqrt{n}) + n$ (hint: substitute $ n$ by $ 2^k$ )
• $ T(n) = \sqrt{n}T(\sqrt{n}) + n$ (harder exercise. hint: substitute $ n$ by $ 2^k$ )