Lets say we have a problem we implemented using X algorithm with O(n) or O(log n) or etc.... When is the value of n big enough that we must consider an alternative implementation? Let’s see if i can explain myself a little better.
For n=10,000
O(n^2) = 100,000,000
O(n) = 10,000
O(Log n) = 4
. . .
Obviously the best algorithm will be the one with the lowest "Big-o".
So lets say we sort an array of length 5 using bubble sort, the result is 25, that’s not that bad. But when is the result of the O notation so large that realistically we must use another implementation.
When it’s a bottleneck in your application.
But in general, aim for algorithms with lowest complexity, while also allowing ease of implementation.