To get rid of the /public you can either:
A) Upload vender, bootstrap, and app folders on directory higher than the htdocs or www folder. Then place all files in the public folder to the into htdocs or www.

B) Move files in public directory one folder higher, modify index.php removing the up directory “../” from the includes.

C) Make an .htaccess file in the root something to the effect of

RewriteEngine On

RewriteRule ^(.*)$ public/$1 [L]