Determining the complexities given codes

Question

Given a snipplet of code, how will you determine the complexities in general. I find myself getting very confused with Big O questions. For example, a very simple question:

Answer 1

Big-O is just an approximation, it doesn't say how long an algorithm takes to execute, it just says something about how much longer it takes when the size of its input grows.

So if the input is size N and the algorithm evaluates an expression of constant complexity: O(1) N times, the complexity of the algorithm is linear: O(N). If the expression has linear complexity, the algorithm has quadratic complexity: O(N*N).

Some expressions have exponential complexity: O(N^N) or logarithmic complexity: O(log N). For an algorithm with loops and recursion, multiply the complexities of each level of loop and/or recursion. In terms of complexity, looping and recursion are equivalent. An algorithm that has different complexities at different stages in the algorithm, choose the highest complexity and ignore the rest. And finally, all constant complexities are considered equivalent: O(5) is the same as O(1), O(5*N) is the same as O(N).