Fast algorithm for repeated calculation of percentile?

Question

In an algorithm I have to calculate the 75th percentile of a data set whenever I add a value. Right now I am doing this:

1. Get value x
2. Inse

Answer 1

If you can do with an approximate answer, you can use a histogram instead of keeping entire values in memory.

For each new value, add it to the appropriate bin. Calculate percentile 75th by traversing bins and summing counts until 75% of the population size is reached. Percentile value is between bin's (which you stopped at) low bound to high bound.

This will provide O(B) complexity where B is the count of bins, which is range_size/bin_size. (use bin_size appropriate to your user case).

I have implemented this logic in a JVM library: https://github.com/IBM/HBPE which you can use as a reference.