For each of the following code fragments, give an analysis of the running time (Big-Oh notation). Be sure to show your work.

sum = 0;

for (int i = 0; i < n + 2; i++)

sum++;

sum = 0;

for (int i = 0; i < n; i++)

for (int j = 0; j < n; j++)

sum++;

sum = 0;

for (int i = 0; i < n; i++)

for (int j = 0; j < i; j++)

sum++;

sum = 0;

for (int i = 0; i < n*n; i++)

for (int j = 0; j < i; j++)

sum++;

sum 0;

for (int i = 0; i < n*n; i++)

for (int j = 0; j < i; j++)

for (int k = 0; k < j; k++)

sum++;

sum = 0;

for (int i = 0; i < n; i++)

for (int j = 0; j < i*i; j++)

if (j % i == 0)

for (k = 0; k < j; k++)

sum++;