Suppose that your USB flash drive has a capacity of G gigabytes. Assume that you have the following ‘n’ files that you want to copy onto the flash drive: F₁, F₂, F₃,…., F_n. The i^th file F_i takes g_i gigabytes. The problem is that your USB flash drive’s capacity, G, is less than the sum of all the g_is and also assumes that each file occupies contiguous memory in the flash drive.

That is, .

S₁: Assume that you want to maximize the number of files that you copy onto your USB flash drive. A greedy algorithm that selects files to copy in increasing size order (from smallest to largest) will produce an optimal solution.

S₂: Assume that you want to maximize the space utilization of your USB flash drive (that is, you want to use as much of your G gigabytes as possible). A greedy algorithm that selects files to copy in decreasing size order from largest to smallest) will produce an optimal solution.

Which of the following statements are true :