Big O – O(log(n)) code example

Like the Big O notation “O(1)” can describe following code:

O(1):

    for (int i = 0; i < 10; i++) {
        // do stuff 
        a[i] = INT;
    }

O(n):

    for (int i = 0; i < n; i++) {
        // do stuff 
        a[i] = INT;
    }

O(n^2):
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            // do stuff
            a[i][j] = INT;
        }
    }

• What code can O(log(n)) describe?

Another question:

• What solutions are there for “Big O problems” (what to do, when getting a lot of data as an input)?

Answer

Classic example:

while (x > 0) {  
   x /= 2;  
}  

This will be:

Iteration |   x
----------+-------
    0     |   x
    1     |  x/2
    2     |  x/4
   ...    |  ...
   ...    |  ...
    k     |  x/2^k 

2^k = x → Applying log to both sides → k = log(x)