Allocate an array of integers proportionally compensating for rounding errors

Question

I have an array of non-negative values. I want to build an array of values who\'s sum is 20 so that they are proportional to the first array.

This would be an easy probl

Answer 1

A naïve solution that doesn't perform well, but will provide the right result...

Write an iterator that given an array with eight integers (candidate) and the input array, output the index of the element that is farthest away from being proportional to the others (pseudocode):

function next_index(candidate, input)
    // Calculate weights
    for i in 1 .. 8
        w[i] = candidate[i] / input[i]
    end for
    // find the smallest weight
    min = 0
    min_index = 0
    for i in 1 .. 8
        if w[i] < min then
            min = w[i]
            min_index = i
        end if
    end for

    return min_index
 end function

Then just do this

result = [0, 0, 0, 0, 0, 0, 0, 0]
result[next_index(result, input)]++ for 1 .. 20

If there is no optimal solution, it'll skew towards the beginning of the array.

Using the approach above, you can reduce the number of iterations by rounding down (as you did in your example) and then just use the approach above to add what has been left out due to rounding errors:

result = <>
while sum(result) < 20
    result[next_index(result, input)]++