Non biased return a list of n random positive numbers (>=0) so that their sum == total_sum

Question

I\'m either looking for an algorithm or a suggestion to improve my code to generate a list of random numbers that their sum equals some arbitrary number. With my code below

Answer 1

Here's how I would do it:

1. Generate n-1 random numbers, all in the range [0,max]
2. Sort those numbers
3. For each pair made up of the i-th and (i+1)-th number in sorted list, create an interval (i,i+1) and compute its length. The last interval will start at the last number and end at max and the first interval will start at 0 and end at the first number in the list.

Now, the lengths of those intervals will always sum up to max, since they simply represent segments inside [0,max].

Code (in Python):

#! /usr/bin/env python
import random

def random_numbers(n,sum_to):
    values=[0]+[random.randint(0,sum_to) for i in xrange(n-1)]+[sum_to]
    values.sort()
    intervals=[values[i+1]-values[i] for i in xrange(len(values)-1)]
    return intervals

if __name__=='__main__':
    print random_numbers(5,100)