**PLEASE IMPLEMENT IN JAVA**

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.

Chapter 2 Algorithm Analysis

(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++;