Show that a running time T(N) = aN + b is an O(N) running time. (Hint: The only issue is the + b. Assume N is always at least 1.) Show that for any two bases a and b for logarithms, if a and b are...

Show that a running time T(N) = aN + b is an O(N) running time. (Hint:

The only issue is the + b. Assume N is always at least 1.)

Show that for any two bases a and b for logarithms, if a and b are both

greater than 1, then there is a constant c such that loga N ≤ c(logb N). Thus,

there is no need to specify a base in O(log N) that is, O(loga N) and O(logb

N) mean the same thing.