Php random number total 3000 [closed] - php

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i want to generate 630 random numbers between 1 and 20. So far, so good. However, the sum of the numbers between 1 and 20 of these 630 produced should not exceed 3000. I could not write such an algorithm. Could you help?

Answer 1

Your problem is that 3000 / 630 = 4.76 which is far from the average number between 1-20. What we can do is constrain the random numbers' ranges to accommodate this, and get a distribution slant with an average sum approximate to the maximum sum.
Given the required maximum average of 4.76, we can for example generate 1/4 of the random numbers as between 1-20, and 3/4 as between 1-4 to slant the distribution:
function get_slanted_rands() {
$rands = [];
for($i = 1; $i <= 630; $i++) {
// For every 4th iteration, get random from the full range
$rands[] = $i % 4 === 0
? mt_rand(1,20)
: mt_rand(1,4);
}
$sum = array_sum($rands);
// If the sum is over the max, recall:
if($sum > 3000) {
return get_slanted_rands();
}
// Log the average for debugging:
$avg = round($sum / count($rands), 2);
return compact('sum', 'avg', 'rands');
}
Notice that the function checks the sum and recalls itself on the odd occasion that the sum exceeds 3000. On a typical call, the sum 3000 isn't exceeded with the above "calibration" — since we split 1:3 in favor of the lower range. But random is random, so there's no "average" guaranteed.
Let's test-drive this contraption for 100 iterations and see what we get:
$test = [];
for($t = 1; $t <= 100; $t++) {
$test[] = get_slanted_rands();
}
$sums = array_column($test, 'sum');
rsort($sums);
echo "==== SUMS ====\n" . implode(', ', $sums) . "\n\n";
$avgs = array_column($test, 'avg');
rsort($avgs);
echo "==== AVGS ====\n" . implode(', ', $avgs);
This yields for the following (reverse sorted), sums between 2600+ and 3000 and averages between 4.75 and 4.19. (On average, ~1:100 iterations exceeds 3000 and is recalled.)
==== SUMS ====
2993, 2985, 2975, 2969, 2959, 2947, 2941, 2933, 2926, 2919, 2919, 2917, 2911, 2909, 2908, 2904, 2903, 2901, 2894, 2894, 2892, 2886, 2884, 2884, 2882, 2881, 2879, 2876, 2871, 2869, 2867, 2863, 2861, 2853, 2852, 2852, 2851, 2851, 2850, 2848, 2844, 2843, 2842, 2838, 2838, 2837, 2837, 2837, 2836, 2834, 2834, 2826, 2826, 2825, 2820, 2814, 2813, 2812, 2802, 2801, 2799, 2799, 2799, 2798, 2796, 2795, 2792, 2789, 2789, 2787, 2784, 2784, 2784, 2783, 2778, 2778, 2776, 2768, 2767, 2764, 2762, 2754, 2754, 2747, 2743, 2737, 2736, 2728, 2727, 2724, 2723, 2721, 2719, 2718, 2707, 2706, 2690, 2673, 2642
==== AVGS ====
4.75, 4.74, 4.72, 4.71, 4.7, 4.68, 4.67, 4.66, 4.64, 4.63, 4.63, 4.63, 4.62, 4.62, 4.62, 4.61, 4.61, 4.6, 4.59, 4.59, 4.59, 4.58, 4.58, 4.58, 4.57, 4.57, 4.57, 4.57, 4.56, 4.55, 4.55, 4.54, 4.54, 4.53, 4.53, 4.53, 4.53, 4.53, 4.52, 4.52, 4.51, 4.51, 4.51, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.49, 4.49, 4.48, 4.48, 4.47, 4.47, 4.46, 4.45, 4.45, 4.44, 4.44, 4.44, 4.44, 4.44, 4.44, 4.43, 4.43, 4.43, 4.42, 4.42, 4.42, 4.42, 4.42, 4.41, 4.41, 4.41, 4.39, 4.39, 4.39, 4.38, 4.37, 4.37, 4.36, 4.35, 4.34, 4.34, 4.33, 4.33, 4.32, 4.32, 4.32, 4.32, 4.31, 4.3, 4.3, 4.27, 4.24, 4.19
You can always tweak the slanting condition if you feel it should on average be closer to 3000... Or simply add a recall condition with a "minimum sum" check and "brute force" it. But this suffices to give you the general idea: You need to generate random numbers of a limited range in proportion to what your "average for target sum" demands. Demo at 3v4l: https://3v4l.org/fG74X
Finally, a sample of the sort of distribution you get. Given as "number" => "instances" in a set of 630. It's heavily slanted to 1, 2, 3, 4 there — and that's how it must be to meet your specs!
$nums = get_slanted_rands();
$distribution = array_count_values($nums['rands']);
arsort($distribution);
print_r($distribution);
// yields:
[3] => 143
[4] => 125
[2] => 125
[1] => 110
[8] => 13
[9] => 12
[18] => 12
[19] => 10
[11] => 9
[5] => 8
[17] => 8
[14] => 7
[12] => 7
[10] => 7
[16] => 7
[6] => 7
[15] => 6
[7] => 6
[20] => 5
[13] => 3

Answer 2

$result = [];
$sumCurrent = 0;
$barrier = 3000 / 630;
for ($i = 1; $i <= 630; $i++) {
$sumBarrier = intval($i * $barrier);
while (true) {
$number = random_int(1, 20);
if ($sumCurrent + $number <= $sumBarrier) {
break;
}
}
$result[] = $number;
$sumCurrent += $number;
}
$sum = array_sum($result);
$occurrences = array_count_values($result);
uksort($occurrences, fn($key1, $key2) => $key1 <=> $key2);
print_r($result); echo "\n";
print_r($sum); echo "\n";
print_r($occurrences); echo "\n";