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Lab 12: Functions

As usual, create a directory to hold today's files. All programs that you write today should be stored in this directory. 

    $ cd ~/cs120/labs
    $ mkdir lab12 
    $ cd lab12

Practice 1

Write a function called multiply_integers(a, b), which takes two integers as parameters. Your function should return the result of multiplying the integers a and b together.








Practice 2











  
Write a function called
    average_four(value1, value2, value3,
      value4), which takes 4 floating point
    values as parameters. Your function should
    return the arithmetic mean (standard
    average) of the four values.

  


  

  

    
  

  









Coin Counting



  There are many people that would call me a lazy person.  I don't
  find that offensive, but I think it's not a valid description.  It's
  not that I'm lazy, I just try to be as efficient as possible.  For
  example, in college a group of friends and I deduced the fewest
  amount of coins to carry that would produce any arbitrary amount of
  change.  While a computation like that is still a little too
  complex, figuring out the fewest amount of coins for a fixed amount
  of change is possible.



Details



  Create the function count_coins(cents) in a file
  called change.py. This function should take as a parameter
  the number of cents (an integer in the range 0 to 100) and returns
  the smallest number of coins (using the American monetary system
  consisting of quarters, dimes, nickles and pennies) necessary to
  make that amount of change.




  Test your function by calling the function multiple times with
  different parameters.  Make sure your code follows the course's code
  conventions.



Test Cases





  
    

      Function Parameters
      Expected Output
    

  
  
    

      0
      0
    

    

      1
      1
    

    

      2
      2
    

    

      5
      1
    

    

      10
      1
    

    

      15
      2
    

    

      16
      3
    

    

      25
      1
    

    

      50
      2
    

  





Hint



  
  

    
    
      
  • 
	While it might seem like you are going to use a loop for this
	function, you actually won't use a single loop.
      
    • 

      
  • 
	You can use integer division (//) to determine how many times
	a coin goes into the change amount evenly.
      
    • 

      
  • 
	Recall that you can use the mod (%) operator to determine the
	remainder of an integer division operator.  Use this to
	determine the change amount the rest of the coins need to cover.
      
    • 

      
  • 
	Start with the largest coin first (quarters) and work
	your way down.  This is known as a greedy approach, and is
	very common in Computer Science.
      
    • 
    

  






  
Challenge

  

    Going back to my inspiration for this activity, the perfect amount
    of change is going to be the maximum number that this function
    will produce on inputs in the range [0,
    100).  Once your function is written and tested well,
    compute the number of coins for all possible change values.  Use
    the max function to find the largest number of coins.