Suppose you wish to make an application that traverses a computer's filesystem and an- alyzes the amount of space (in megabytes) used by all of the various files and directories. Your application must store the following information: • The amount of space used by each individual file. • The total amount of space used by the contents of each directory (folder). For each directory, you need to store the total amount of space used by all files in that directory and all of the files in all of its sub-directories (sub-folders), sub-sub-directories, and so forth. For example: if the only files in the filesystem are: /Users/Mark/Documents/exam.tex (0.014 Mb) /Users/Mark/Documetns/exam.pdf (0.3Mb Mb) /Users/Mark/piratesong.mp4 (2.9 Mb) Then the stored size for /Users/Mark/Documents would be 0.314 Mb (sum of the sizes of the two files in the Documents directory), and the stored size for the directories /Users/Mark, /Users, and / would be 3.214 (sum of the sizes of all three files because they are all stored somewhere under /Users/Mark). This data must be stored in a data structure that you design. That data structure should, as efficiently as possible, support the following operations on the data: • Given the absolute path to a file (e.g. /usr/mark/Documents/exam.pdf), look up the amount of space used by that file. • Given the absolute path to a directory (e.g. /usr/Mark/Documents/ amount of space used by all files in that directory and all of it's sub-directories. videos), look up the • Calculate the total amount of space used by all files with a given extension (e.g. jpeg or .mp3). In your own words, describe a data structure design that would be suitable for storing this data and supporting the operations on it. Justify your design choices. For example, if you choose to use a particular ADT, explain why you think it is the best choice both in terms of why it is appropriate for storing the data and why it will efficiently support the required operations on the data. Do not write Java code. We will not read code and it will not be considered a part of your answer. Describe your data structure in prose. You are encouraged to draw schematic diagrams to illustrate your design and aid in the understanding of its description. Do not rush the composition of your answers. The quality of the logic and reasoning of your iustifications are factore in the assessment of vour ans wers