To be honest, if you feel like showing the guys teaching your course that their problem statement probably isn’t what they intended, I would just do it this way: for(int i = 0; i < c; i++) { /*your code here*/} This is in O(c), and since O(c) is a strict subset of O(ck) for … Read more
Assuming that T(n) doesn’t suddenly become negative at some value of n, we can give a lower bound for the left hand side if we neglect the first term: We define a new function S(n) such that: We can immediately see that it has terms (ignoring off-by-one etc.). Thus if we keep expanding: At this … Read more
Since there is no loop, it is O(1).
For comparison sorting we consider the number of comparisons, sorting complicated objects this usually dominates. Your outer loop always runs count times, your inner loop always runs on average ~count / 2 times. Every iteration of the inner loop always does one comparison. Hence you get best, worst and average case is count * count … Read more