Measuring algorithm-s efficiency and amortized efficiency

Question

1) Describe in detail about the “Average-case efficiency” of algorithm with suitable example.

2) What do you understand by “Amortized efficiency”?

3) Explain in what way we can measure the algorithm’s efficiency?

4) What is known as the basic operation of the algorithm? How to measure the algorithm’s running time?

5) What do you understand by order of growth?

6) Explain Big oh notation in detail with appropriate example.

7) Prove that 100n+5∈O (n²)?

8) Explain Ω notation in detail with appropriate example.

9) Prove that n³∈ Ω (n²)?

10) Explain Θ – notation in detail with appropriate example.

11) Prove that( ½)n(n-1) ∈ Θ(n²)

12) Expalin the use of Asymptotic Notations?