So as the title says, given a binary string of length n (1<=n<=10^5) , find the number of unique decimals that can be obtained from subsequences of the binary string:

Example : 101

0=0

1=1

01 (same as 1) so rejected

10= 2

101= 5

11= 3

So, number of unique decimals are 5. I can only think of recursive solution.

How to approach this question ?

Btw it was asked today in Google hiring contest.