CPSC120B
Fundamentals of Computer Science I

Lab 30

Two-dimensional Lists

Write a function called sum_column(a_matrix, col_index), which takes a 2-dimensional list and a positive integer as parameters. Your function should return the sum of all of the values along the specified column of the list. 






Magic Squares



  One interesting application of multidimensional lists are magic
  squares.  Magic squares are a mathematical structure that has been
  studied for centuries.  
  A magic square is an \(n \times n\) 2-dimensional list such that the
  sum of each row, the sum of each column, and the sum of each
  diagonal are exactly the same.
  Constructing an magic square is a little bit complicated, but
  determining if a specified square is magic is not super complicated.





Details



  Write a function check_magic_square(a_square), in a
  file called square.py.  This function takes some \(n \times
  n\) 2-dimensional list of integers.  It should return True
  if the parameter is a magic square, and False otherwise.




Example


  >>> square = [[8, 1, 6], [3, 5, 7], [4, 9, 2]]
  >>> print(check_magic_square(square))
  True
  >>> square = [[8, 1, 10], [3, 5, 7], [4, 9, 2]]
  >>> print(check_magic_square(square))
  False
  >>> square = [[17, 24, 1, 8, 15], [23, 5, 7, 14, 16], [4, 6, 13, 20, 22], [10, 12, 19, 21, 3], [11, 18, 25, 2, 9]]
  >>> print(check_magic_square(square))
  True



Hint



  
  

    
    
      
  • 
	
    
	  You can use the built in sum
	  function to compute the sum of a particular row of the
	  square.
	
    
      
    • 

      
  • 
	
    
	  To assist your checks, you might want to write a function
	  called sum_column(a_square, column_number),
	  which will compute the sum of all of the values in the
	  specified column of the square. To sum a column, you need to
	  sum the column position from each row.
	
    
      
    • 

      
  • 
	
    
	  You might also want to write functions
	  called sum_major_diagonal(a_square),
	  and sum_minor_diagonal(a_square).  The major
	  diagonal of a square 2-dimensional list are all of the
	  values where the row identifier equals the column
	  identifier.  The minor diagonal is the opposite diagonal.
	
    
      
    • 

      
  • 
	
    
	  The check_magic_square function will need to
	  compute the sum of one of the rows in the potentially magic
	  square.  Then, sum every row and check if it's equal to the
	  magic sum.  Sum every column, check if it's equal to the
	  magic sum.  Sum the two diagonals, and check if it's equal
	  to the magic sum.  If any of them are not equal to the magic
	  sum, then you don't have a magic square.
	
    
      
    • 
    

  





 



  
Challenge

  

    One additional restriction, for an official magic square, is that
    every element in the magic square has to be unique.  [[1, 1],
    [1, 1]] is not a magic square, for example.  Add an
    additional check in your program to verify you have true magic
    squares.
  





 



  
Challenge


  

    In addition, there are some relatively straight forward algorithms
    for generating a square which is guaranteed to be magic.  Read the
    Wikipedia
    article for magic squares, and write a function
    called generate_magic_square(size) to generate a
    magic square of the specified size.
  




Submission


Please show your source code and run your programs for the instructor or lab assistant. Only a programs that have perfect style and flawless functionality will be accepted as complete.