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Lab 17: Conditionals

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 lab17 
$ cd lab17

Practice 1

Write a function sum_powers(n), which computes the sum of the numbers in the set:

$$\{x^{x} \mid 0 < x \leq n\}$$
Which in sigma notation is:
$$ \sum\limits_{x=1}^{n} x^x = 1^1 + 2^2 + 3^3 + \ldots + n^n$$ 
















  
Practice 2



   Write a function called compute_product(n), which
    computes the series:
    

      \[\prod\limits_{x=2}^{n} \frac{x}{x-1} = \frac{2}{1} \times
      \frac{3}{2} \times \frac{4}{3} \times \ldots \times
      \frac{n}{n-1}\]
    




  

    
  

  

    
  

  















  
Practice 3




    Write a function called clamp_even(n, minimum,
    maximum), which
    returns the value of n "clamped" to the range \([minimum,
    maximum]\) only if n is even.  If n is odd,it
    should return n. 
    Clamping is a process where values less than the specified minimum
    get set to the minimum, and values greater than the maximum get
    set to the maximum.  Any value in the range stays the same.


  

    
  

  

    
  

  







Date Validation



The reason we have leap years added to our calendar is because they
do not take into account the fact that the Earth actually takes
(about) 365.25 days to revolve once around the sun.  While it sounds
like this should be an easy thing to account for, there's actually some fairly 
complex math involved in dealing with this inconsistency.  This
causes havoc when trying to validate a date, but we can simplify
things by adding functions and using our conditionals wisely.




Details



  Copy for file called date_validation.py from the last lab.



$ cd ~/cs120/labs/lab17
$ cp ../lab16/date_validation.py .




  In this, write an additional
  function days_in_month(month, year), which takes a
  integer parameter in the range \([0, 12)\) which specifies the
  month, and an integer that specifies the year.  Your function should
  return the number of days in the month.  Recall:




30 days hath September, April,
June, and November
 
All the rest have 31

Except for February, the only one.





  
    Test this function before you go on.
  





  Once you have tested your days_in_month function, you
  can write the validate_date(month, day, year) function.
  This function takes 3 integers: The first specifies the month, the
  second specifies the day, and the final specifies the year.  This
  function should return True if the date specified is valid, and
  False otherwise.





  Make sure you test this function with various parameters before you
  have it checked.  Make sure you also follow all of the course's
  style guidelines.




Sample Test Cases



  
    

      Function Parameters
      Expected Output
    

  
  
    

      2, 29, 2004
      True
    

    

      2, 29, 2015
      False
    

  



Hint



  
  

    
    
      
  • 
	
    
	  You need to make sure that you don't send any parameters
	  to days_in_month function that are outside of
	  the ranges.  If you operate under this assumption, you can
	  write this function using only 4 conditionals: one for
	  months with 31 days, one for months with 30 days, one for
	  February non-leap year (28), and one for February leap years (29).
	  You will need to use your is_leap_year function
	  here.
	
    
      
    • 
      
  • 
	
    
	  Validate date needs to check to make sure the month is a
	  valid integer for a month and the day specified is within
	  the ranges for the month they specified.  If both of these
	  conditions are satisfied, then the date is valid.
	
    
      
    • 
      
  • 
	
    
	  Dont forget that you can use your logical constructs to
	  reduce the complexity of the condition checks.
	
    
      
    • 
  






  
Challenge

  

    Write an additional function
    called validate_date_time(month, day, year, hours,
    minutes).  This function should validate the date AND the
    time specified.  Assume the time is specified as two integers,
    and their values should be in the ranges
    \([0, 12]\) and \([0, 60]\).