A disk contains a B blocks, F of which are free. A bitmap needs 1 bit for each block, both free and occupied. A linked list needs 2 integers for each free block to link together all free blocks. The bitmap and linked list occupy a dedicated portion of the disk. (a) Determine what fraction of blocks must be free such that the bitmap and the linked list occupy the same amount of disk space.
(b) Determine the same fraction as above when the linked-list method connects groups of adjacent blocks, rather than individual blocks. The average group size is 10 blocks. Each group needs 2 integers for the link and 1 integer to record the number of blocks in the group.