Contents:

1. (5 points)
   Many things in our daily lives involve written instructions (e.g., preparing food, setting the clock on the microwave, ordering a product from a catalog). We want you to look around for such instructions so that we can see whether these constitute an algorithm based on the definition given in Figure 4.1 on page 169 of the Brookshear text.

   Find something in your life that contains written instructions and type these instructions, exactly as they appear (please select something so that your instructions take up at least a third of a page, but at most one whole page when typed.)

   Now, consider the definition of an algorithm, as given in Figure 4.1 on page 169 of the Brookshear text. Evaluate whether or not you feel that the instructions constitute an "algorithm" by this definition, explaining your thoughts.

2. (5 points)
   Suppose the insertion sort as presented in Figure 4.11 (p. 194 [Br]) was applied to the list

     Frank
     Bob
     Carol
     George
     Alice
     Elaine
   

   Describe the organization of the list at the end of each execution of the body of the outer while structure.

3. (5 points)
   Imagine that we are searching the list {A, B, C, D, E, F, G}. Please fill in the following table specifying the number of list items which are compared to the Target for each search:

   target	sequential search	binary search
   A
   B
   C
   D
   E
   F
   G

4. (5 points)
   Consider the following sorted list of numbers:

   1

   2

   9

   11

   12

   13

   15

   26

   23

   24

   29

   34

   35

   41

   43

   What sequence of 'middle' values in considered when running the binary search algorithm (Figure 4.14 of [Br]) with target 6?

   What sequence of 'middle' values in considered when running the binary search algorithm (Figure 4.14 of [Br]) with target 11?

   What sequence of 'middle' values in considered when running the binary search algorithm (Figure 4.14 of [Br]) with target 12?

   What sequence of 'middle' values in considered when running the binary search algorithm (Figure 4.14 of [Br]) with target 19?

   What sequence of 'middle' values in considered when running the binary search algorithm (Figure 4.14 of [Br]) with target 41?

The recursive solution to the problem can be expressed with the following pseudocode:

  procedure Transfer(numRings, startPeg, endPeg, tempPeg)
    if (numRings > 0) 
      then
        [
         Apply Transfer(numRings-1, startPeg, tempPeg, endPeg)
        ]
        Move single Ring #numRings from startPeg to endPeg
        [
         Apply Transfer(numRings-1, tempPeg, endPeg, startPeg)
        ]

For example, if we called Transfer(2,A,C,B) the process is:

  Move ring #1 from A to B
  Move ring #2 from A to C
  Move ring #1 from B to C