Examples of Algorithms which has O(1), O(n log n) and O(log n) complexities

0(logn)-Binary search, peak element in an array(there can be more than one peak) 0(1)-in python calculating the length of a list or a string. The len() function takes 0(1) time. Accessing an element in an array takes 0(1) time. Push operation in a stack takes 0(1) time. 0(nlogn)-Merge sort. sorting in python takes nlogn time. so when you use listname.sort() it takes nlogn time.

Note-Searching in a hash table sometimes takes more than constant time because of collisions.

O(2^N)

O(2^N) denotes an algorithm whose growth doubles with each additon 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:

int Fibonacci (int number)
{
if (number <= 1) return number;
return Fibonacci(number - 2) + Fibonacci(number - 1);
}