Assign random integer to items in array and summa should ever be a fixed number

Question

this is my problem

I've a variable number of items in an array

array (x, y, z, ..., n)

And i've a fixed total assigned to a variable

$min_int = 0;
$max_int = 8;
$total = 8;

I need to assign to every item in the array a random int from $min_int to $max_int and the total of the items in the array has to be always =8.

For example:

array (red, green, blue);
$min_int = 0;
$max_int = 8;
$total = 8;

the result could be

Array
(
    [0] => 3
    [1] => 5
    [2] => 0
)

OR

Array
    (
        [0] => 3
        [1] => 3
        [2] => 2
    )

I would develop in javascript.

Any suggestions please?

Here's the link of the table i've to populate with random int. Checking the client's checkboxes and the columns of days you want to populate, the loop has to generate the random int for the selected clients in the selected day and the total has to be =8 (col-# SUMMA), so for every days you select.

Answer 1

My most intuitive guess would be

var max_int = 8;
var first = Math.floor(Math.random() * max_int) + 1;
var second = Math.floor(Math.random() * (max_int - first)) + 1;
var third = max_int - first - second;

But there is probably some mathematical bias here. I'm not a mathematician, so this is an invitation to anyone who knows statistics to take a closer look at this. This does work, though, since you always end up with max_int if you sum first, second and third.

Answer 2

This solution should do what you are looking for:

var $min_int = 0;
var $max_int = 8;
var $total = 8;

var array = new Array(3);
var sum = 0;
var currentMax = $max_int;

for (i = 0; i < array.length; i++) {
    if ((i !== (array.length - 1)) && (currentMax > 0)) {
        var randomNum = parseInt(Math.random() * currentMax);
        array[i] = randomNum;
        currentMax -= randomNum;
    }
    else {
        array[i] = currentMax;
    }
}

console.log(array);

This approach: 1. loops through the length of the array, 2. for each array element, it creates a random integer, based on the maximum value and stores it 3. it then reduces the maximum value by the value of the number that was just generated and repeats for the next array element

Note #1: It will also skip the processing, if the "new maximum" has reached 0 (i.e., the generated random number will always be 0, so no need to calculate) or the logic has reached the last element in the array (i.e., the value for that element, should be the remaining "maximum" value).

Note #2: var $min_int and var $total are never actually used in this solution.

Here are some test values:

For var array = new Array(3);

[3, 3, 2]
[0, 2, 6]
[8, 0, 0]
[1, 4, 3]
[0, 4, 4]

For var array = new Array(5);

[4, 0, 1, 0, 3]
[7, 1, 0, 0, 0]
[1, 2, 0, 4, 1]
[3, 4, 1, 0, 0]
[4, 3, 0, 0, 1]

For var array = new Array(8);

[7, 0, 1, 0, 0, 0, 0, 0]
[3, 2, 3, 0, 0, 0, 0, 0]
[5, 3, 0, 0, 0, 0, 0, 0]
[2, 4, 1, 0, 1, 0, 0, 0]
[7, 0, 1, 0, 0, 0, 0, 0]