Can you give examples of the LDAP connection string for Active Directory?

You need the server name for the AD placement - then the syntax will be like this:

For Contoso.com

LDAP://[ServerName]/dc=contoso,dc=com

For test.contoso.com

LDAP://[ServerName]/dc=test,/dc=contoso,dc=com

I don't know if this is useful for you, but here is a connection example in a C # application

    DirectoryEntry de = new DirectoryEntry("LDAP://[ServerName]/dc=test,/dc=contoso,dc=com");
    de.Username = "username";
    de.Password = "password";