Q4

CPSC 110 Spring 2012 Quiz 4

Instructions: The first problem asks you to read a function and determine what it does. The secon problem asks you to write a function given a description.

What value would function(4) return? Show your work.

# Comment: A function with 1 parameter

To function(N):
  Set global Var to 1
  While N > 0 do:
     Set Var to Var × N
     Set N to N - 1
  Return Var

  N    Var          Var × N
 ----------------------------------
  4     1           4
  3     4           12
  2     12          24
  1     24          24
  0     24          -            Var = 24 = 4 × 3 × 2 × 1 = 4!

Define a function named countMs(aList, M) that counts the number of occurrences of M in the list aList. For example, if we call the function with the list [1,2,2,3,3,2,1,4,1,2] and 2, as in
```
    countMs( [1,2,2,3,3,2,1,4,1,2], 2)
```
it will return 4 because there are four 2s in the list.
```
To countMs (aList, M):
   Set global Count to 0
   For each item in aList do:
      If item = M do:
         Set Count to Count + 1
   Return Count
```
Instructions: The next two problems ask you to define a function in Pseudocode or write a loop algorithm. Model your answers after the Pseudocode algorithms in the first 2 questions. Be careful about indentation.

Suppose you have a variable named list that contains the following values: [1,2,3,4,5,6,7,8,9]. What would be the final value of Var as a result of the following algorithm?

# Comment: What is the final value of Var

   Set global Var to 0
   For each item in list do:
   If remainder(item, 4) = 0
      Set global Var to Var + item * item

Var    Item         Remainder(Item, 4)    Var + Item * Item
-----------------------------------------------------------
0       1                1               
0       2                2               
0       3                3  
0       4                0                0 + 4 × 4 = 16
16      5                1               
16      6                2   
16      7                3
16      8                0                16 + 8 × 8 = 80
80      9                1

Convert the loop algorithm in problem #3 (above) to an equivalent while loop.

Set global Var to 0
Set global Index to 1
While Index ≤ length(list) do:
   Set Item to list element at Index
   If remainder(Item, 4) = 0
      Set global Var to Var + Item × Item
  Set global Index to Index + 1