2. For each of the following three program fragments, give an analysis of the running time. First, give the total number of times of each statement being executed. Then give the summed/total time in Big- O notation using function with the least order of magnitude. Basically don't say the complexity is O(N9) if it is also O(N2). (21 pts) (a) Sum = 0; for(i= 1; i N; i++) Sum Sum + i; (b) Sum= 0; for(i=1;i < N;i++) for(j= 1; j N; j++) for(k = 1; k < N; k++) Sum Sum + 1; (c) Sum = 0; for (i = 1; i N; i++) for(j= 1; ji; j++) Sum Sum + 1; (d) x = 100; y = 0; for(i= 1; i N; i = 2 * i) x = x + i; for(j= 1; j < N; j++) if(x > y/j) y = y + i/j; else y = y - 1; 2