Every time a proble joins the agency, NCIS $($Naval Criminal Investigative Service$)$ assigns a case to them from the requested range $[$F$,$ L$]$ out of total N cases. As and when a case is solved it will be marked. BN $90280104011-8838$

Which data structure you will use to execute the following operations most efficiently?

$[1$M$]$

Give and explain an algorithm to implement each with reasoning for the time complexity.

Returns the number of unsolved cases in $[$FL$]$

Return the first unsolved case in $[$F$,$ L$],$ mark it as TAKEN' or return 'NONE' if all cases in $[$F$,$ L$]$ are solved.

Most efficient algorithm fetches maximum credit.