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)
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.
If u feel any doubt feel free to ask
What is the range of input sizes for the following time complexities to compute an answer...
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