mod_rewrite check public folder before passing to php - apache

Question

What I am trying to achieve (with mod_rewrite) is on request check if a file/directory exists in the public folder, if it does, serve it, if not, route the request to the index.php file. Also if no extension provided in the URL then default to .html.
Below is my folder structure:
/.htaccess
/index.php
/public
/test.html
/test.xml
/a_folder
/index.html
/test.html
So for example here are a few requests and responses:
example.com/test.xml >>> /public/test.xml
example.com/a_folder/ >>> /public/a_folder/index.html
example.com/a_folder/test >>> /public/a_folder/test.html
example.com/not_in_public >>> /index.php
Any pointers on this would be amazing, thanks in advance.

Answer 1

Something like this: (Heavily cribbed from my WordPress .htaccess file)
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)^(\.\w+) $1.html [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
The $1.html line is off the top of my head and may need some tweaking. Note that this is a dumb check that the requested URL ends in a dot followed by one or more word characters.

Answer 2

<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^(|index\.php)$ - [L]
RewriteRule ^public/(.*)$ - [L]
RewriteRule ^(.*)$ public/$1
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . index.php [R]
</IfModule>
This should do the trick.
Basically, if it's / or /index.php it won't do anything, if it's /public/whateveryouwant it won't do anything, if it's anything else it will rewrite to /public/whateveryouwant and check if it's either a file or a directory. If it's not it will redirect to index.php.

Answer 3

Thanks to #jxpx777 and #N1xx1 after a bit of juggling made it work.
Options -Indexes
RewriteEngine On
RewriteBase /
RewriteRule ^public/(.*)$ - [L]
# Check public cache
RewriteRule ^(.*)$ public/$1
RewriteRule (.*)/$ $1/index
# Add .html if not extension provided
RewriteCond %{REQUEST_URI} !\..*$
RewriteRule ^(.*)$ $1.html
# Push through stack in not in cache
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . index.php [L]