Suppose we need to write an efficient program to store N employee records for ABC Inc where each employee record is identified by unique employee id. Consider the following ways to store the records. 1. An array list sorted by employee id 2. A linked list sorted by employee id 3. A linked list not sorted 4. A balanced binary search tree with employee id as key For data structure 1 -4, what is the average time to find an employee record given employee id as a key? a. O(log N), O(N), O(N), O(log N) O(N), O(log N), O(N), O(1) c. O(log N), O(log N), O(N), O(log N) d. O(log N), O(log N), O(log N), O(1) e. O(log N), O(log N), O(N), O(1)

Prove a) 1000000n2 + 0.0000001n5 is Ω(n3) b ) n! is Ω(2n) if you use an example c and n PLEASE EXPLAIN WHY YOU CHOSE IT

For each of the following expressions, find if they are O(1), O(2"), O(n²), O(log n), O(n2022), O(n log n) or O(n): (i) 2022 + 15 log n (ii) 42 n + 5 n² + 2n log n (iii) n log n + 2" + n2022 + 500n Briefly explain your answer in each case.

Dear Sir/Madam,   May I get an explanation how the computation was obtained?I do understand why the input size is squared for O(n2) 30002 / 10002 I just don't know where the idea to square the denominator comes from?The same for the n * log(n) solution.   Also what topic of Maths deals with calculations of this kind? I would like to learn more to be able to solve similar problems.