Consider the greedy algorithm for the bin-packing problem, which is called the first-fit (FF) algorithm: place each of the items in the order given into the first bin the item fits in; when there are no such bins, place the item in a new bin and add this bin to the end of the bin list.
a. Apply FF to the instance
and determine whether the solution obtained is optimal.
b. Determine the worst-case time efficiency of FF.
c. Prove that FF is a 2-approximation algorithm.