Code:

<?php
$rootPath = realpath('../public');   // path do root foldera za skidanje

$zip = new ZipArchive(); // kreiranje zip-a
$zip_file = 'file.zip';
$zip->open($zip_file, ZipArchive::CREATE | ZipArchive::OVERWRITE);

$files = new RecursiveIteratorIterator(
    new RecursiveDirectoryIterator($rootPath),
    RecursiveIteratorIterator::LEAVES_ONLY
);

foreach ($files as $name => $file)      {
    if (!$file->isDir())        {
        $filePath = $file->getRealPath();
        $relativePath = substr($filePath, strlen($rootPath) + 1);
        $zip->addFile($filePath, $relativePath);
    }
}
$zip->close();

// DOWNLOAD kreiranog zipa
header('Content-type: application/zip');
header('Content-Disposition: attachment; filename="'.basename($zip_file).'"');
header("Content-length: " . filesize($zip_file));
header("Pragma: no-cache");
header("Expires: 0");
ob_clean();
flush();
readfile($zip_file);

unlink($zip_file);      // Obrisi zip da ne zauzima prostor
exit;