Randomly Generate Letters According to their Frequency of Use?

Question

How can I randomly generate letters according to their frequency of use in common speech?

Any pseudo-code appreciated, but an implementation in Java would be fantastic. Otherwise just a poke in the right direction would be helpful.

Note: I don't need to generate the frequencies of usage - I'm sure I can look that up easily enough.

Answer 1

I am assuming that you store the frequencies as floating point numbers between 0 and 1 that total to make 1.

First you should prepare a table of cumulative frequencies, i.e. the sum of the frequency of that letter and all letters before it.

To simplify, if you start with this frequency distribution:

A  0.1
B  0.3
C  0.4
D  0.2

Your cumulative frequency table would be:

A  0.1
B  0.4 (= 0.1 + 0.3)
C  0.8 (= 0.1 + 0.3 + 0.4)
D  1.0 (= 0.1 + 0.3 + 0.4 + 0.2)

Now generate a random number between 0 and 1 and see where in this list that number lies. Choose the letter that has the smallest cumulative frequency larger than your random number. Some examples:

Say you randomly pick 0.612. This lies between 0.4 and 0.8, i.e. between B and C, so you'd choose C.

If your random number was 0.039, that comes before 0.1, i.e. before A, so choose A.

I hope that makes sense, otherwise feel free to ask for clarifications!