[SalesForce] Logically comma separating address field to form a String

I am trying to create a string of address in this format: Street, City, State, Country, Zip. Assume that there is an Address object called addr which has account's shipping address.

Address addr = Account__r.ShippingAddress; // Ignore the syntax here and assume that addr has Address.

My Challenge here is I want to build a string of the addr with comma separated. Example if shipping address has

Shipping Street : 123th Street
Shipping City   : SFO
Shipping State/Province : CA
Shipping Zip/Postal Code: 12345
Shipping Country: USA

I want to form a string like String s = 123th Street, SFO, CA, 12345, USA

The catch :

There could be different possiblity that street may not be present or country may not be present in that case the String should logically display the
commas example – city, state, zip -> SFO, CA, 12345. Also I do not want to display NULL in case street/country/state/zip is not available. So it is possible that any of the data might be missing and my string should accommodate for missing data and produce the correct comma separated string.

This is what I got started with but I see the logic is getting complex:

String street; String city; String state; String country; String zip;
         Address addr = Account__r.ShippingAddress; 
          street = addr.getStreet() <> NULL ? addr.getStreet() : ''; // to make sure I do not display NULL in string
          if(street == NULL){
          city = addr.getCity() <> NULL ? addr.getCity() : '';
          }else{
          city = addr.getCity() <> NULL ? ', ' + addr.getCity() : '';
          }
          if(city == NULL){
          state = addr.getState() <> NULL ? addr.getState() : '';
          }else{
          state = addr.getState() <> NULL ? ', ' + addr.getState() : '';
          }
          if(state == NULL){
          country = addr.getCountry() <> NULL ? addr.getCountry() : '';
          }else{
          country = addr.getCountry() <> NULL ? ', ' + addr.getCountry() : '';
          }
          if(country == NULL){
          zip = addr.getPostalCode() <> NULL ? addr.getPostalCode() : '';
          }else{
          zip = addr.getPostalCode() <> NULL ? ', ' + addr.getPostalCode() : '';
          }
     String addString = street + '' + city + '' + state + '' + country + '' + zip;