1) Suppose that you have an algorithm that required 10 seconds to run on a problem size of 1000. How long would you expect the algorithm to run on a problem size of 10,000?

2) Determine the (a) obvious big-oh notation, (b) trace the algorithm, and then (c) determine the theta notation for the following algorithm:

     i := n
     while (i >= 1) do
          for j := 1 to i do
                 some code that takes  time
          end for j
          i := i / 2
     end while

3) Determine the (a) obvious big-oh notation, (b) trace the algorithm, and then (c) determine the theta notation for the following algorithm:

     for i := 1 to n do
          for j := 1 to i do
	   k = 1
               while (k < n) do
                    some code that takes  time
	        k = k * 2
               end while
          end for j
     end for i

4) Determine the (a) obvious big-oh notation, (b) trace the algorithm, and then (c) determine the theta notation for the following algorithm:

     i := n
     while i > 0 do
          j = n
          while j > i do
                for k = 1 to n do
        	         some code that takes   time
                end for
                j = j / 2
          end while
          i := i / 2
     end while