= = 2. (4 marks) Suppose that we have four algorithms whose running times are expressed by the functions f(n) = 1000 log2 n, g(n) 100n, h(n) 10na, j(n) 2. You should interpret these functions to mean the number of operations (or steps) it takes to run the algorithms on an input of size n. Suppose we also have three different machines. On Machine A, we can execute 1000 of these operations per second. On Machine B, we can execute 10 000 operations per second. On Machine C, we can execute 100 000 operations per second. Fill in the table below. For each function and each machine, determine the largest (integer) size n of a problem that can be solved in one minute by each machine using each algorithm. (In some cases, you might get answers like 2100; it's fine to leave your answers in that form.) Please show your calculations. Machine A | Machine B Machine C f(n) = 1000 log2 n g(n) = 100n h(n) = 10n2 j(n) = 21