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Consider the function F: 2^(3*n) + n^2
Can the function A: 2^(3*n) be used as a Big Theta, Omega or O as a characterisation of F? Why?
I’m revising the concepts of Big Omega, Big Theta and Big O and I came across this example but don’t know where to start.
No.
2^(3*n) is the leading term, but unless you’re doing something very wrong it’s not going to take you that long to compute. Wikipedia has a good list of time complexities of various functions. The most complicated operation you’re doing is raising to a power, the complexity of which is discussed in other posts.
Since you’re looking at a function of the form g(f(x)) where g(x) = 2^x and f(x) = 3x, the time to compute is going to be O(h) + O(k), where h is the time complexity of g, k is the time complexity of f. Think about it: it should never be more than this, if it were you could just break the operation in two and save time by doing the parts separately. Because h is going to dominate this sum you’ll typically leave the k term off.