CPSC 110 Q3 Practice

CPSC 110 Fall 2011 Quiz 3 Practice Questions

Instructions: The first three problems ask you to read a Pseudocode algorithm. Trace through each of them by hand, keeping track of the variables, to determine the answer to the question.

What value would functionA(5) return?

Problem	Solution
# Comment: A function definition that takes 1 parameter To functionA(a): Return: a + 100	Trace: functionA(5) returns 5 + 100 = 105

What value would functionB(3,5) return?

Problem	Solution
# Comment: A function with 2 parameters To functionB(m,n): Set Var to m Set m to m + 1 While M <= N do: Set Var to Var + m Set m to m + 1 Return Var	m n Var Return ------------------------------------ 3 5 3 4 7 5 12 6 12

Problem

Solution

# Comment: A function with 2 parameters

To functionB(m,n):
  Set Var to m
  Set m to m + 1
  While M <= N do:
     Set Var to Var + m
     Set m to m + 1
  Return Var

m            n         Var    Return
------------------------------------
3            5          3
4                       7
5                      12
6                                12

What value would mystery(3,2) return? What value would mystery(3,3) return?

Problem	Solution
# Comment: A mystery function To mystery(x, y): Set M to x If y < x then do: Set M to y Return M	x y M Return -------------------------------- 3 2 3 2 2 mystery(3,2) returns 2 3 3 3 3 mystery(3,3) returns 3

Problem

Solution

# Comment: A mystery function

To mystery(x, y):
   Set M to x
   If y < x then do:
      Set M to y
   Return M

x        y        M       Return
--------------------------------
3        2        3
                  2         2      mystery(3,2) returns 2


3        3        3         3      mystery(3,3) returns 3

Instructions: The next three problems ask you to define a function in Pseudocode. Model your answers after the Pseudocode algorithms in the first 3 questions.

Define a function named add3 that will compute and return the sum of any three numbers.

# A function that returns the sum of its 3 arguments.

To sum3(a, b, c):
   Return a + b + c

Define a function named average that will compute the average of the numbers from 1 to N, where N is a parameter.

Algorithm	Trace
# A function to compute the average of the numbers from 1 to N To average(N): Set global Sum to 0 Set global Index to 1 While Index <= N do: Set Sum to Sum + Index Set Index to Index + 1 Return Sum / N	N Sum Index Return --------------------------------- 4 0 1 1 2 3 3 6 4 10 5 10/4 = 2.5

Algorithm

Trace

# A function to compute the average of the numbers from 1 to N

To average(N): 
   Set global Sum to 0
   Set global Index to 1
   While Index <= N do:
      Set Sum to Sum + Index
      Set Index to Index + 1
   Return Sum / N

N      Sum       Index     Return
---------------------------------
4       0          1
        1          2
        3          3
        6          4
        10         5       10/4 = 2.5

To compute 2⁵ you can multiply 2 by itself 5 times. In general to compute 2ⁿ you can multiply 2 by itself n times. Write a function named powerOf2, which takes 1 parameter, n and computes 2ⁿ.

Algorithm	Trace
# A function to compute 2^n by repeated multiplication To powerOf2(n): Set global Product to 1 # Multiplication so initialize with 1 Set global Index to 1 While Index <= n do: Set Product to Product * 2 # Repeatedly multiply the product by 2 Set Index to Index + 1 Return Product	n Product Index Return ------------------------------------- 4 1 1 2 2 4 3 8 4 16 5 16 = 2^4

Algorithm

Trace

# A function to compute 2^n by repeated multiplication

To powerOf2(n):
   Set global Product to 1           # Multiplication so initialize with 1
   Set global Index to 1
   While Index <= n do:
      Set Product to Product * 2     # Repeatedly multiply the product by 2
      Set Index to Index + 1
   Return Product

n     Product       Index      Return
-------------------------------------
4         1           1 
          2           2
          4           3
          8           4
          16          5         16 = 2^4