Example of Big O of 2^n

Question

So I can picture what an algorithm is that has a complexity of n^c, just the number of nested for loops.

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Answer 1

Think about e.g. iterating over all possible subsets of a set. This kind of algorithms is used for instance for a generalized knapsack problem.

If you find it hard to understand how iterating over subsets translates to O(2^n), imagine a set of n switches, each of them corresponding to one element of a set. Now, each of the switches can be turned on or off. Think of "on" as being in the subset. Note, how many combinations are possible: 2^n.

If you want to see an example in code, it's usually easier to think about recursion here, but I can't think od any other nice and understable example right now.