N= Problem Size Complexity Class Time to Solve on Old M Solvable in the same Time Machine (secs) on a New Machine 2x as Fast 106 O(Log2 N) 1 106 O(N) 1 2 x 10° 10 O(N Log2 N) 1 106 O(N) 1
Fill in the last line (for each complexity class), which shows the size of a problem (M) that can be solved in the same amount of time on a new machine that runs twice as fast as the old machine. Solve by hand when you can, use Excel or a calculator when you must: I used external tools only for O(N Log2 N) and O(N2 ) solving those to 3 significant figures. Solving a problem in the same amount of time on the new/faster machine is equivalent to solving a problem that takes ten times the amount of time on the old machine. See the O(N) for an example. Check that your answers aren’t crazy. Hint: write a formula equating problem sizes N and M using the speedup and complexity class. For linear complexity: 2*c*N = c*M; then solve for M.
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