magic squars
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function iain_magic(n::Int) | |
if n % 2 == 1 | |
# Odd-order magic square | |
# http://en.wikipedia.org/wiki/Magic_square#Method_for_constructing_a_magic_square_of_odd_order | |
M = zeros(Int, n, n) | |
for I = 1:n, J = 1:n # row, column | |
@inbounds M[I,J] = n*((I+J-1+div(n,2))%n) + ((I+2J-2)%n) + 1 | |
end | |
return M | |
elseif n % 4 == 0 | |
# Doubly-even order magic square | |
# http://en.wikipedia.org/wiki/Magic_square#A_method_of_constructing_a_magic_square_of_doubly_even_order | |
# http://hal.archives-ouvertes.fr/docs/00/94/51/29/PDF/magicsquarev2.pdf | |
M = [(i-1)*n+j for i = 1:n, j = 1:n] | |
for outer_col = 1:4:n, outer_row = 1:4:n | |
# Sides | |
for i in (1,2), j in (0,3) | |
@inbounds M[outer_row+i,outer_col+j] = n^2 - M[outer_row+i,outer_col+j] | |
end | |
# Top and bottom | |
for i in (0,3), j in (1,2) | |
@inbounds M[outer_row+i,outer_col+j] = n^2 - M[outer_row+i,outer_col+j] | |
end | |
end | |
return M | |
end | |
end |
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