algorithm - Randomly choosing from a list with weighted probabilities -

I have an array of N elements (representing N characters of a given alphabet), and each cell of the array To be an integer value, that integer value, which means that the number of incidents occurring in a given text of that letter Now I randomly choose a letter from all the letters of the alphabet, which is based on the number of obstacles given to them:

• If the letter contains a positive (noorio ) Value, it can always be chosen by algorithm (certainly with big or small probability).

• If letter A gets more value than B, then it should be more likely to be chosen by algorithms.

  Now, keeping that account in mind, I have come up with a simple algorithm that can work, but I was wondering what was a better job . It seems quite original, and I think that more clever things can be done to accomplish this more efficiently. This is the algorithm I thought:

  • Add all instances in the array. Store it in SUM
  • Choose random values ​​from 0 to SUM. Store it in RAN
  • [While] RAN & gt; 0, start from the beginning, go to each cell in the array (in order), and decrease the value of that cell with RAN
  • The last visit cell is selected

    So, is there any better work than this? Am I missing something?

    I know that modern computers can calculate this so fast I will not even know whether my algorithm is inefficient, so it is not practical, but more of a theoretical question.

    I prefer an explained algorithm instead of code for an answer, but if you feel more comfortable providing your answer in the code, then I have no problem with it.

    Thoughts:

    • All elements Repeat through and set the value of each
    • Generate a random number between the sum of 1 and all the frequencies
    • One for values ​​on this number (one above the first value) Or equal to the number).

      Example:

        element ABCD frequency 1 4 3 2 cumulative 1 5 8 10   
       Generate a random number in the category 1-10 (1 + 4 + 3 + 2 = 10, the last value in the cumulative list), perform a binary search, which will return the value as follows:  < Pre>  number element back 1a2b3b4b5b6c7c8c9d10d