Consider a file system that uses the index$-$allocation technique, with block size of $1$ KB $($file block size and disk block size are the same$).$ The disk partition holding the file system has size $200$KB$.$ The file system keeps one i$-$node for each file and one d$-$node for each directory. Each i$-$node has some file attributes $,6$ direct blocks $,3$ single indirect block $,2$ double indirect block and $1$ triple indirect block. Each d$-$node has some directory attributes and linear list of files$/$subdirectories under it$.$ The maximum file$/$directory name size is $15$ character. The maximum number of files and sub directories under a single directory is $50.$ The maximum number of directories in the system can be $500.$However, the maximum number of files in the system can be $20000.$ The file system support read$/$write$/$execute permission for each file and directory, and hard links for both file and directories.

$($a$)$ Compare and contrast different file allocation technique.

$($b$)$ What is the maximum size of the file that can be supported?

$($c$)$ Implement how the file system components are organized in the disk partition $($showing the exact size and order of the components$).$ Assume that bit method is used to manage free space for i$-$nodes $d-$nodes and data blocks.

$($d$)$ List the steps that occur when the call write $($fd$,$ buff, size$)$ is made, which write size bytes starting from memory address buff to the end of an already open file with file descriptor fd$.$ Assume that the system supports both a peer process and a system widen $-$open file table. The file and directory attributes you choose must support the above operation efficiently. Align all the fields in the data structure define to byte boundaries. You can assume that routine read$/$write block from $/$to disk already exit that you can call.