Calculate magic square¶
Calculate magic square.
A magic square is an arrangement of distinct numbers
(i.e., each number is used once), usually integers, in a square grid,
where the numbers in each row, and in each column,
and the numbers in the main and secondary diagonals,
all add up to the same number, called the “magic constant.”
A magic square has the same number of rows as it has columns,
and in conventional math notation, “n” stands for the number of rows
(and columns) it has. Thus, a magic square always contains n2 numbers,
and its size (the number of rows [and columns] it has) is described
as being “of order n”.
def magic_square_test(M):
iSize = len(M[0])
sum_list = []
# horizontal part
sum_list.extend([sum(lines) for lines in M])
# vertical part
for col in range(iSize):
sum_list.append(sum(row[col] for row in M))
# diagonals Part
result1 = 0
for i in range(0, iSize):
result1 += M[i][i]
sum_list.append(result1)
result2 = 0
for i in range(iSize-1, -1, -1):
result2 += M[i][i]
sum_list.append(result2)
if len(set(sum_list)) > 1:
return False
return True
# test
m = [
[7, 12, 1, 14],
[2, 13, 8, 11],
[16, 3, 10, 5],
[9, 6, 15, 4],
]
print(magic_square_test(m)) # True
m = [
[2, 7, 6],
[9, 5, 1],
[4, 3, 8],
]
print(magic_square_test(m)) # True
m = [
[2, 7, 6],
[9, 5, 1],
[4, 3, 7],
]
print(magic_square_test(m)) # False