1. Give an analysis of the running time (Big-Oh notation) for each of the following 4 program fragments. You must provide calculate the computational cost of each line of code that shows how you estimated the code snippets running time. Note that the running time corresponds here to the number of times the operation sum++ is executed. sqrt is the function that returns the square root of a given number.

(a

)sum = 0; for(i=0;i

b)

sum = 0;

for(i=0;i

for(j=i;j<8+i;j++)

for(k=j;k<8+j;k++)

sum++;

(c)

sum = 0; for(i=1;i<2*n;i++) for(j=1;j

if (j % i == 1)

sum++;

(d)

sum = 0; for(i=1;i<2*n;i++) for(j=1;j

2. If it takes 10ms to run program (b) for n=100, how long will it take to run for n=400