多次元 PHP 配列のキーと値のペアに基づいてサブ配列を効率的に見つけるにはどうすればよいですか?

function search($array, $key, $value)
{
    $results = array();

    if (is_array($array)) {
        // Check if the current subarray matches
        if (isset($array[$key]) && $array[$key] == $value) {
            $results[] = $array;
        }

        // Recursively search inner subarrays
        foreach ($array as $subarray) {
            $results = array_merge($results, search($subarray, $key, $value));
        }
    }

    return $results;
}

$arr = array(0 => array(id => 1, name => "cat 1"),
             1 => array(id => 2, name => "cat 2"),
             2 => array(id => 3, name => "cat 1"));

$found = search($arr, 'name', 'cat 1');
print_r($found);

Array
(
    [0] => Array
        (
            [id] => 1
            [name] => cat 1
        )

    [1] => Array
        (
            [id] => 3
            [name] => cat 1
        )

)

function search_optimized($array, $key, $value)
{
    $results = [];
    search_r($array, $key, $value, $results);
    return $results;
}

function search_r($array, $key, $value, & $results)
{
    if (!is_array($array)) {
        return;
    }

    if (isset($array[$key]) && $array[$key] == $value) {
        $results[] = $array;
    }

    foreach ($array as $subarray) {
        search_r($subarray, $key, $value, $results);
    }
}