Question

What is the range of input sizes for the following time complexities to compute an answer in no more than 1 second?

1 to ____ for each:

Solving for max possible value of n to produce an answer in 1 second

O(lgn)

O(square-root(n))

O(n)

O(n2)

O(n3)

Answer 1

Since it is known that atmost 10^7 lines are compiled in 1 second it is clear that

1 . n= very very large as log(n) is highly optimsed

logn=10^7 which means n=10^(10^7) which is extremely large.

2 . n=10^14 nearly for sqrt(n)

as n^1/2 =10^7 which is extreme case and hence n=(10^7)^2 which is nearly equal to 10^14.

3. n=10^7 nearly for n

as n^1 =10^7 which is extreme case and hence n=(10^7)^1 which is nearly equal to 10^7.

4. n= 10^3 for n^2

as n^2 =10^7 which is extreme case and hence n=(10^7)^1/2 which is nearly equal to 1000.

5. n=10^2 nearly for n^3

as n^3 =10^7 which is extreme case and hence n=(10^7)^1/3 which is nearly equal to 100.

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