Issue creating better random algorithm - daily spread

Question

i need a algoritm that spreads some numbers across a day in percentages, following min / max percentage for that time rule, this is what i have atm:

public function getSpread() {

    $rules = [
        '00-07' => ['min' => 5, 'max' => 10],
        '08-12' => ['min' => 20, 'max' => 30],
        '13-16' => ['min' => 20, 'max' => 30],
        '17-22' => ['min' => 25, 'max' => 40],
        '23-24' => ['min' => 10, 'max' => 15],
    ];


    $spread = [];
    foreach ($rules as $time => $rule) {
        $value = rand($rule['min'], $rule['max']);

        while ($this->getNewSum($spread, $value) > 100) {
            $value = $value - 1;
        }

        $spread[$time] = $value;
    }

    return $spread;
}

private function getNewSum($spread, $value) {
    $sum = 0 + $value;
    foreach ($spread as $s) {
        $sum = $sum + $s;
    }
    return $sum;
}

Results:

array:5 [
  "00-07" => 5
  "08-12" => 24
  "13-18" => 30
  "19-22" => 32
  "23-24" => 9
]
array:5 [
  "00-07" => 8
  "08-12" => 29
  "13-18" => 29
  "19-22" => 27
  "23-24" => 7
]
array:5 [
  "00-07" => 8
  "08-12" => 28
  "13-18" => 21
  "19-22" => 33
  "23-24" => 10
]
array:5 [
  "00-07" => 9
  "08-12" => 20
  "13-18" => 21
  "19-22" => 25
  "23-24" => 15
]
array:5 [
  "00-07" => 8
  "08-12" => 28
  "13-18" => 20
  "19-22" => 29
  "23-24" => 10
]
array:5 [
  "00-07" => 9
  "08-12" => 20
  "13-18" => 22
  "19-22" => 28
  "23-24" => 15
]
array:5 [
  "00-07" => 5
  "08-12" => 23
  "13-18" => 23
  "19-22" => 40
  "23-24" => 9
]

Any way to optimize this and make it more "random", id like to be able to increase the min, max rules, but if i do this, the end element suffers, and always becomes a 0

Id would actually be optimal to create this by the hour, rather then a from - to hour.

You could use [`mt_rand()`](http://www.php.net/manual/en/function.mt-rand.php) for better randomness — Xorifelse, Jan 26 '17 at 10:39

score 1 · Accepted Answer · answered Jan 26 '17 at 19:48

You need to use the proper conditional probabilities. Sorry for the Python 3.

import collections
import random


def sample(total, intervals):
    counts = [collections.Counter({0: 1})]
    for interval in reversed(intervals):
        counts.append(collections.Counter())
        for x in interval:
            for tot, n in counts[-2].items():
                counts[-1][x + tot] += n
    samp = []
    for interval in intervals:
        outcome = random.randrange(counts.pop()[total])
        for x in interval:
            outcome -= counts[-1][total - x]
            if outcome < 0:
                samp.append(x)
                break
        else:
            assert False
        total -= samp[-1]
    return samp


for i in range(20):
    print(sample(100, [
        range(5, 11),
        range(20, 31),
        range(20, 31),
        range(25, 41),
        range(10, 16),
    ]))

Sample output:

[10, 21, 20, 39, 10]
[7, 27, 26, 29, 11]
[6, 28, 21, 31, 14]
[7, 22, 27, 34, 10]
[10, 21, 29, 27, 13]
[9, 23, 24, 34, 10]
[7, 24, 30, 26, 13]
[7, 22, 20, 39, 12]
[10, 28, 25, 27, 10]
[9, 22, 20, 38, 11]
[5, 26, 30, 29, 10]
[7, 25, 22, 33, 13]
[5, 27, 21, 37, 10]
[9, 23, 25, 28, 15]
[6, 28, 25, 28, 13]
[7, 30, 23, 30, 10]
[7, 21, 20, 38, 14]
[6, 26, 22, 34, 12]
[8, 24, 23, 30, 15]
[9, 29, 25, 25, 12]

Issue creating better random algorithm - daily spread

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