In the bin-packing problem, we are given n metal objects, each weighing between zero and one kilogram. Our goal is to find the smallest number of bins that will hold the n objects, with each bin holding one kilogram at most. A. The best-fit heuristic for bin packing is as follows. Consider the objects in the order in which they are given. For each object, place it into the partially filled bin with the smallest amount of extra room after the object is inserted.. If no such bin exists, start a new bin. Design an algorithm that implements the best-fit heuristic (taking as input the n weights w1,w2,...,wn and outputting the number of bins used) in O(nlogn) time. B. Repeat the above using the worst-fit heuristic, where we put the next object in the partially filled bin with the largest amount of extra room after the object is inserted.

You have a linux system that has a 1000gb hard disk drive, which has a 90gb partition containing an ext4 filesystem mounted to the / directory and a 4gb swap partition. currently, this linux system is only used by a few users for storing small files; however, the department manager wants to upgrade this system and use it to run a database application that will be used by 100 users. the database application and the associated data will take up over 200gb of hard disk space. in addition, these 100 users will store their personal files on the hard disk of the system. each user must have a maximum of 5gb of storage space. the department manager has made it very clear that this system must not exhibit any downtime as a result of hard disk errors. how much hard disk space will you require, and what partitions would you need to ensure that the system will perform as needed? where would these partitions be mounted? what quotas would you implement? what commands would you need to run and what entries to /etc/fstab would you need to create? justify your answers.