Consider the following java-like code for a recursive sorting algorithm: // sorts the items from l[i] through l[j] void threewaysort(int[ ] l, int i, int j) { if (l[i] > l[j]) swap (i, j); if ((j - i + 1) > 2) { t = (j - i + 1)/3; threewaysort(l, i, j-t); threewaysort(l, i+t, j); threewaysort(l, i, j-t); } } (a) prove that this algorithm is correct, that is, that the call threewaysort(l, 0, l. length-1) actually has the side effect of making l sorted. (b) let f(n) be the running time of threewaysort(l, i,j) when j − i + 1 = n. write a recurrence for f(n). (c) solve your recurrence to determine the worst-case running time of threewaysort on lists of size n. how does it compare to other sorting algorithms you know?