For each of the following six program fragments:
a. Give an analysis of the running time (Big-Oh will do).
b. Implement the code in Java, and give the running time for several values of N.
c. Compare your analysis with the actual running times.
(1) sum = 0;
for( i = 0; i < n; i++ )
sum++;
(2) sum = 0;
for( i = 0; i < n; i++ )
for( j = 0; j < n; j++ )
sum++;
(3) sum = 0;
for( i = 0; i < n; i++ )
for( j = 0; j < n * n; j++ )
sum++;
(4) sum = 0;
for( i = 0; i < n; i++ )
for( j = 0; j < i; j++ )
sum++;
(5) sum = 0;
for( i = 0; i < n; i++ )
for( j = 0; j < i * i; j++ )
for( k = 0; k < j; k++ )
sum++;
(6) sum = 0;
for( i = 1; i < n; i++ )
for( j = 1; j < i * i; j++ )
if( j % i == 0 )
for( k = 0; k < j; k++ )
sum++;