# Exercise 4.3.2

Show that the solution of $T(n) = T(\lceil n/2 \rceil) + 1$ is $O(\lg{n})$

We guess $T(n) \le c\lg(n - 2)$:

$$T(n) \le c\lg(\lceil n/2 \rceil - 2) + 1 \le c\lg(n/2 + 1 - 2) + 1 \le c\lg((n - 2)/2) + 1 \le c\lg(n - 2) - c\lg2 + 1 \le c\lg(n - 2)$$