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Lab 30: 2-d lists

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 lab30 
    $ cd lab30 



Practice 1

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.