Iterated Logarithm log*(n)

Iterated Logarithm or Log*(n) is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1.

 

Applications: It is used in the analysis of algorithms (Refer Wiki for details)

Output : 

Log*(100) = 2

Time Complexity: O(logn)

Auxiliary Space: O(logn) due to recursive stack space
Iterative Implementation : 

Time Complexity: O(logn)

Auxiliary Space: O(1)