$1.(40$pts$).$ For the following languages, the alphabet is $($a$,$ b$).$ Draw the DFA diagrams for the following four languages:

$(1)$ L $=\{$w $|$ w has even length$\}.$

$(2)$ L $=\{$w$|$ w has at most one b$\}.$

$(3)$ L $=[$w $|$ w has even length and has at most one b$).$

$(4)$ L $=($w $|$ w does not have ab as its substring$).$