distribute, Php - rextester

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<?php //php 7.0.8

$testData = [
    'AAAAABBBCC',
    'AAAAABBBCCC',
    'ABBCCC',
    'AAAAAABBC',
    'AAAAAABBBBCCD',
    'AAAAAAAAAABC',
    'hpp',
    'stackoverflow',
    'ACCD', // :-)
];

$results = [];

foreach ($testData as $dataStr) {
    $a = str_split($dataStr);
    $data = [];
    foreach ($a as $type) {
        $data[] = ['type' => $type];
    }
    $result = distribute($data);
    $resultStr = implode(array_column($result, 'type'));
    $results[$dataStr] = $resultStr;
}
var_export($results);

###############################################################

function distribute($data) {
    $groups = [];
    foreach ($data as $row) {
        $groups[$row['type']][] = $row;
    }
    $groupSizes = array_map('count', $groups);
    asort($groupSizes);

$result = [];
    foreach ($groupSizes as $type => $groupSize) {
        if (count($result) == 0) {
            $result = $groups[$type];
        } elseif (count($result) >= count($groups[$type])) {
            $result = merge($result, $groups[$type]);
        } else {
            $result = merge($groups[$type], $result);
        }
    }
    return $result;
}

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