4. Given a collection of algorithms whose runtime complexities are 6(1), (NlogN)

Question

4. Given a collection of algorithms whose runtime complexities are 6(1), (NlogN), (N!) (N) eo (log N); order the algorithm's runtime complexities from fastest to slowest: a. (1), (logN), (N), (N*), (N logN), (N!) b, (1), (N log N), (N), (N 2), (log N),(N!) c, (1), (log N), (N), (N log N), (N2), (N) d, (1), (log N), (N logN), (N), (N2), (N!) e, (1), (N), (logN), (N log N), (N°), (NI) . Which of the following is/are the levels of implementation of a data structure a. Abstract level b. Application level c. Implementation level d. All of the above

Explanation / Answer

4. The runtime complexity means the time required to run a piece of code. The one which
takes least time will be the fastest to finish off the task.
So, ordering the given complexities is:
theta(1): Constant. Which means the time required is not dependent on the size of input.
                   This is the best possible complexity.
theta(logN): Logarithmic. Which means the time required grows logarithmic to the size of input.
theta(N):   Linear. Which means the time required grows linear to the size of input.
theta(N logN): N logarithmic. Which means the time required grows N* logN times the size of input.
theta(N^2):   Quadratic. Which means the time required grows quadratically with the size of input.
theta(N!):   Factorial. Which means the time required grows factorially with the size of input.
           This is the worst possible complexity. And next to impossible this kind of problems for huge data.
So, the answer is: C.

5. Abstract Level, Application Level, and Implementation level are the various levels of
implementation of a data structure.
So, the answer is: D.

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