Show that a running time T(N) = aN + b is an O(N) running time. (Hint: The only issue is the plus 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 plus 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.