Due: Friday, Jan. 30, 2004

Chapter 1 problems: 4, 11, 22, 25, and the following problems:

A) Analyze the below algorithm to determine the obvious big-oh (upper-bound), then trace the algorithm to determine its theta notation, ( ).

i := n
while i > 0 do
     j := 1
     while j < i do
	< something of >
	j := j * 2
     end while
     i := i / 2
end while

B) Analyze the below algorithm to determine the obvious big-oh (upper-bound), then trace 
the algorithm to determine its theta notation, ( ).
 for i := 1 to n do
      for j := 1 to i do
           for k := j to (i + j) do
   	     some code that takes   time
            end for k
      end for j
 end for i

C) Analyze the below algorithm to determine the obvious big-oh (upper-bound), then trace 
the algorithm to determine its theta notation, ( ).
 i := n 
while (i >= 1) do 
     for j := 1 to i do 
          for k := 1 to n do 
               something that takes O(1) 
          end for k 
     end for j 
     i := i / 2 
end while