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How to generate a set covering the maximum number of results?
There is the following task
We have a condition for forming a set of sets (or a table):
- The number of rows (elements of the set)
- For each column, the percentage of the Null value is set (for example (10,20,50) - the first column is 10% zeros, the second is 20 and the third is 50 )
It is necessary to generate such a set of a given length that it optimally covers all possible combinations of zeros and non-zeros
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1. Calculate the total number of combinations ("masks" of zeros/non-zeros: from "all zeros" to "all non-zeros" on a given set: the number of rows). This will be 100% of the entire range.
2. 10%, 20%, 50% - every 10th, every 5th, every 2nd, respectively.
3. Let's start with the most frequent (50%) and after 1 (every 2nd) we will make a list.
4. Take the next one (20%) and apply it to the remaining half (also evenly, considering half - for 100%) and add it to the list.
5. Take the remaining percentage (10%) and apply to the remaining 30% - this will be every 3rd element and also add to the list.
The resulting list will be what was required.
And what's the problem then?
$nullPercents = [10, 20, 50];
$totalRows = 11;
$result = [];
for ($i = 1; $i <= $totalRows; $i++) {
$row = [];
foreach ($nullPercents as $percent) {
if ($i <= $totalRows*$percent/100) {
$row[] = null;
} else {
$row[] = $i;
}
}
$result[] = $row;
}
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