Question

1. Suppose you are given 3 algorithms A1, A2 and A3 solving the same problem. You know that in the worst case the running times are Ti(n) = 101#nº + n, Ta(n) = 10”, TS(n) = 101 nº logo n10 (a) Which algorithm is the fastest for very large inputs? Which algorithm is the slowest for very large inputs? (Justify your answer.) (b) For which problem sizes is Al the best algorithm to use (out of the three)? Answer the same question for A2 and then for A3. (Justify your answer.) You can consider inputs only of size > 2.

Answer 1

(a) A₃ is fastest for very large inputs as the complexity is logarithmic and polynomial only in second degree. So if we consider n=300,

T₁(300)=2.7e+21

T₂(300)=3e+302

T₃(300)=2.229e+16

Thus, as T₃(300) is least, therefore, A₃ is fastest and as T₂(300) is largest, therefore, time taken is most and A₂ is slowest for large inputs.

(b) A₁ is best for input size n>10 and n<100.

A₂ is best for input size n<=10.

A₃ is best for input size n>=100 and.