Question: Do a complexity analysis on each of the loops below and determine its complexity class. Confirm your results using empirical analysis where necessary. (1)

Do a complexity analysis on each of the loops below and determine its complexity class. Confirm your results using empirical analysis where necessary. (1) Sum = 0; for(i=0; i < N; i++ ) (2) Sum = 0; Sum++; for(i=0; i < N; i++) for(j = 0; j < N; j++) (3) Sum = 0; Sum++; 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 < 1; 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++; Turn in a written report showing the analysis of each algorithm and, where necessary, a table of results for various values of N (at least five) showing the correctness of your analysis. The report should be no more than one page in length. Example:

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