f ∈ O(g) says, essentially For at least one choice of a constant k > 0, you can find a constant a such that the inequality 0 <= f(x) <= k g(x) holds for all x > a. Note that O(g) is the set of all functions for which this condition holds. f ∈ o(g) … Read more
Short explanation: If an algorithm is of Θ(g(n)), it means that the running time of the algorithm as n (input size) gets larger is proportional to g(n). If an algorithm is of O(g(n)), it means that the running time of the algorithm as n gets larger is at most proportional to g(n). Normally, even when … Read more
UPDATE: I liked this question so much, I just blogged it. See Strings, immutability and persistence The short answer is: O(n) is O(1) if n does not grow large. Most people extract tiny substrings from tiny strings, so how the complexity grows asymptotically is completely irrelevant. The long answer is: An immutable data structure built … Read more
How to find time complexity of an algorithm You add up how many machine instructions it will execute as a function of the size of its input, and then simplify the expression to the largest (when N is very large) term and can include any simplifying constant factor. For example, lets see how we simplify … Read more
Python includes a profiler called cProfile. It not only gives the total running time, but also times each function separately, and tells you how many times each function was called, making it easy to determine where you should make optimizations. You can call it from within your code, or from the interpreter, like this: import … Read more
I cannot understand how to identify a function with a log time. The most common attributes of logarithmic running-time function are that: the choice of the next element on which to perform some action is one of several possibilities, and only one will need to be chosen. or the elements on which the action is … Read more