Checking for a Magic Square Python

Question

i'm trying to make a function that checks whether or not a matrix is a magic square. i only need to check the vertical and horizontal (not diagonal). sometimes it passes and sometimes it fails. i was hoping that someone could help me solve the issue. this is my code:

for i in range(len(m)):
     if len(m[i]) != len(m):
          return False
return True

and this is the one that fails. it returns false:

m = [ [1,2,3,4]
    , [5,6,7,8]
    , [9,10,11,12]
    , [13,14,15,16]
    ]
print(magic_square(m)) == False)

Answer 1

The code you provide does not check if a matrix is a magic square, it only checks if a matrix (in this case, a list of lists) is square. After this check, you need to calculate the sums of each row, each column and each diagonal (although for some reason you said you don't need those) and compare if all of them are equal.

Answer 2

If you are ok with using numpy then you can use

m = np.array(m)
len(np.unique(np.concatenate([m.sum(axis=1), m.sum(axis=0)]))) == 1

Test cases:

m = [ [1,2,3,4]
    , [5,6,7,8]
    , [9,10,11,12]
    , [13,14,15,16]
    ]
m = np.array(m)
print (len(np.unique(np.concatenate([m.sum(axis=1), m.sum(axis=0)]))) == 1)


m = [ [2,7,6]
    , [9,5,1]
    , [4,3,8]    
    ]
m = np.array(m)
print (len(np.unique(np.concatenate([m.sum(axis=1), m.sum(axis=0)]))) == 1)

Output:

False
True

Meaning:

• m.sum(axis=1) : Sum the numpy array along the rows
• m.sum(axis=0) : Sum the numpy array along the columns
• np.concatenate([m.sum(axis=1), m.sum(axis=0)]) : Combine both the sums (along rows and columns) into t single numpy array
• np.unique(x) : Find the number of unique elements in the numpy array x
• len(np.unique(np.concatenate([m.sum(axis=1), m.sum(axis=0)]))) == 1) : Check the number of unique elements in the row wise sum and columns wise sum is 1. ie all the row wise sum and column wise sums are same.

Answer 3

This is not as clever as the numpy answer, but it works

def magic_square(m):
    # check size
    for i in range(len(m)):
       if len(m[i]) != len(m):
          return False
          
    # check row sums
    for r in m:
       if sum(r) != sum(m[0]):
          return False
    
    # check column sums
    cols = [[r[c] for r in m] for c in range(len(m[0]))]
    for c in cols:
       if sum(c) != sum(m[0]):
          return False
       
    return True


m = [ [1,2,3,4]
    , [5,6,7,8]
    , [9,10,11,12]
    , [13,14,15,16]
    ]
print(magic_square(m))  # False
 
m = [ [8,11,14,1]
    , [13,2,7,12]
    , [3,16,9,6]
    , [10,5,4,15]
    ]
print(magic_square(m))  # True