Given is a set of activities $A_1,A_2,$dots,$A_n$ with each activity Ai consisting of start time si$,$ finish time fi and enrollment count wi$.$ We need to find out what is the maximum number of parking slots that are required $($considering all the activities are happening in the same building and no one carpools$).$ This is equivalent to finding a subset of overlapping activities $($which all overlap with each other$)$ such that sum of their enrollment count is the maximum. Give an algorithm for this and analyse its complexity. Answer should be explained as a step$-$wise algorithm in plain English aided by a pseudocode as necessary for clarity. The algorithm should be the most efficient one to achieve full credits.