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 have a known set of values, following will be very fast:

Create a large array of integers (even bytes will work) with number of elements equal to maximum value of your data. For example, if the maximum value of t is 100,000 create an array

int[] index = new int[100000]; // 400kb

Now iterate over the entire set of values, as

for each (int t : set_of_values) {
  index[t]++;
}

// You can do a try catch on ArrayOutOfBounds just in case :)

Now calculate percentile as

int sum = 0, i = 0;
while (sum < 0.9*set_of_values.length) {
  sum += index[i++];
}

return i;

You can also consider using a TreeMap instead of array, if the values don't confirm to these restrictions.