Question

I’ve been thinking about how to implement something that, frankly, is beyond my mathematical skills. So here goes, feel free to try and point me in the right direction rather than complete code solutions any help I’d be grateful for.

So, imagine I’ve done an analysis of text and generated a table of the frequencies of different two-character combinations. I’ve stored these in a 26×26 array.
eg.

  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A 1 15 (frequency of AA, then frequency of AB etc.)
B 12 0 (freq of BA, BB etc..)
... etc.

So I want to randomly choose these two-character combinations but I’d like to ‘weight’ my choice based on the frequency. ie. the AB from above should be 15 times ‘more likely’ than AA. And, obviously, the selection should never return something like BB (ie. a frequency of 0 – in this example, obviously BB does occur in words like Bubble!! 🙂 ). For the 0 case I realise I could loop until I get a non-0 frequency but that’s just not elegant because I have a feeling/intuition that there is a way to skew my average.

I was thinking to chose the first char of my pair – ie. the row – (I’m generating a 4-pair-sequence ultimately) I could just use the system random function (Random class.Next) then use the ‘weighted’ random algorithm to pick the second char.

Any ideas?

Answer 1

Given your example sample, I would first create a cumulative series of all of the numbers (1, 15, 12, 0 => 1, 16, 28, 28).

Then I would produce a random number between 0 and 27 (let’s say 19).

Then I would calculate that 19 was >=16 but <28, giving me bucket 3 (BA).