When at each level the size of data shrink by a factor of 2 then we get the complexity of o(Log n) but when the same shrink by the square root then we get the o(log log n).

Assume we have n data points where n = 256 then data will shrink in the following pattern i..e QuickSort etc

256/2 = 128

128/2 = 64

64/2 = 32

32/2 = 16

16/2 = 8

8/2 = 4

4/2 = 2

2/1 = 1

Total 8 steps

But if data is shrinking in the square root way then the pattern would be

256^.5 = 16

16^.5 = 4

4^.5 = 2

2^.1 = 1

Total 4 steps

**Example of such algorithm**

Van Emde Boas tree (Check http://en.wikipedia.org/wiki/Van_Emde_Boas_tree for more detail)

```
Space O(N)
Search O(log log N)
Insert O(log log N)
Delete O(log log N)
```