Algorithms complexity

Big O notation

Big O notation is used in Computer Science to describe the performance or complexity of an algorithm. Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g. in memory or on disk) by an algorithm.

O(1) describes an algorithm that will always execute in the same time (or space) regardless of the size of the input data set.

O(N) describes an algorithm whose performance will grow linearly and in direct proportion to the size of the input data set.

O(N²) represents an algorithm whose performance is directly proportional to the square of the size of the input data set. This is common with algorithms that involve nested iterations over the data set. Deeper nested iterations will result in O(N³), O(N⁴) etc.

O(2^N) denotes an algorithm whose growth doubles with each addition to the input data set. The growth curve of an O(2^N) function is exponential — starting off very shallow, then rising meteorically. An example of an O(2^N) function is the recursive calculation of Fibonacci numbers.

O(log N). Binary search is a good example of it. Binary search is a technique used to search sorted data sets. It works by selecting the middle element of the data set, essentially the median, and compares it against a target value. If the values match, it will return success. If the target value is higher than the value of the probe element, it will take the upper half of the data set and perform the same operation against it. Likewise, if the target value is lower than the value of the probe element, it will perform the operation against the lower half. It will continue to halve the data set with each iteration until the value has been found or until it can no longer split the data set. Doubling the size of the input data set has little effect on its growth as after a single iteration of the algorithm the data set will be halved and therefore on a par with an input data set half the size. This makes algorithms like binary search extremely efficient when dealing with large data sets.

See more details here: https://rob-bell.net/2009/06/a-beginners-guide-to-big-o-notation/