Question

I have a very large data set that I’m trying to find the smallest set that will satisfy all the data sets. The final set must have one value in it that is in all of the data sets

A small sample of the data looks like

[0] => Array
    (
        [0] => 21
        [1] => 21
        [2] => 21
    )

[1] => Array
    (
        [0] => 29
    )

[2] => Array
    (
        [0] => 27
    )

[3] => Array
    (
        [0] => 21
        [1] => 21
        [2] => 21
        [3] => 39
        [4] => 39
        [5] => 43
    )

[4] => Array
    (
        [0] => 29
        [1] => 33
        [2] => 33
        [3] => 43
    )

In this case I need logic to return 21, 27 and 29
The values returned needs to be be the minium number of values that match all arrays. Since I’m a PHP programmer, I writing this function in PHP.

Answer 1

You could follow this algorithm:

Updated after testing

$data=array(
            array(21,29,27,57,22),
            array(22,21,23,24,25,26),
            array(31)
            );

$map = array(); // keep a map of values and how many times they occur in other sets
foreach ($data as $setid => $set) {
    foreach (array_unique($set) as $v) {
        $map[$v][$setid] = true;
    }
}

function reverseCount(array $a, array $b)
{
    return count($b) - count($a);
}

// sort reversed on intersection count
uasort($map, 'reverseCount');

// after sorting the first number will be the one that occurs the most
// keep track of which sets have been hit
$setmap = array(); $n = count($data);
foreach ($map as $v => $sets) {
    $hits = 0;
    foreach ($sets as $setid => $dummy) {
        if (!isset($setmap[$setid])) {
            --$n;
            ++$hits;
            $setmap[$setid] = true;
        } else {
            continue;
        }
    }
    if ($hits) {
        echo "value $v\n";
        if (!$n) {
            // all sets are hit
            break;
        }
    }
}

Tested this time. It’s not proven to always get the right result, because this is considered a greedy approximation algorithm.

But I hope it gives an idea of what you could do. Let me know if anything confuses you or if I’m dead wrong about it 🙂