Are there any cases where you would prefer a higher big-O time complexity algorithm over the lower one?

Question

Are there are any cases where you would prefer O(log n) time complexity to O(1) time complexity? Or O(n) to O(log n)?

Answer 1

At any point when n is bounded and the constant multiplier of O(1) algorithm is higher than the bound on log(n). For example, storing values in a hashset is O(1), but may require an expensive computation of a hash function. If the data items can be trivially compared (with respect to some order) and the bound on n is such that log n is significantly less than the hash computation on any one item, then storing in a balanced binary tree may be faster than storing in a hashset.