Which of the three functions above (runtime_increment, runtime_print and runtime_pow) has time performance ‘closer’ (or more similar) to that of the runtime_rec in the code below? Note that you do not need to compute the time complexity for runtime_rec. We did not cover that yet. Use other methods (e. g. look at the actual time it takes to execute for different values of N and see to which function from above).

Suppose there is a relation r(a, b, c) with a b+-tree index with search keys (a, b).1. what is the worst-case cost of finding records satisfying 10 < a < 50 using this index, in terms of the number of records n1, retrieved and the height h of the tree? 2. what is the worst-case cost of finding records satisfying 10 < a < 50 and 5 < b < 10 using this index, in terms of the number of records n2 that satisfy this selection, as well as n1 and h defined above? 3. under what conditions on n1 and n2, would the index be an efficient way of finding records satisfying the condition from part (2)?