A 1024 x 1024 array of 32-bit numbers is to be "normalized" as follows. For each column, the largest element is found and all elements of the column are divided by this maximum value. Assume that each page in the virtual memory consists of 4K bytes, and that 1M bytes of the main memory are allocated for storing data during this computation. Suppose that it takes 40 ms to load a page from the disk into the main memory when a page fault occurs.

(a) How many page faults would occur if the elements of the array are stored in column order in the virtual memory?

(b) How many page faults would occur if the elements are stored in row order?

(c) Estimate the total time needed to perform this normalization for both arrangements

(a) and (b).