% solving Sudoku using CVX
% loading data
X = [5 3 0 0 7 0 0 0 0
6 0 0 1 9 5 0 0 0
0 9 8 0 0 0 0 6 0
8 0 0 0 6 0 0 0 3
4 0 0 8 0 3 0 0 1
7 0 0 0 2 0 0 0 6
0 6 0 0 0 0 2 8 0
0 0 0 4 1 9 0 0 5
0 0 0 0 8 0 0 7 9];
% CVX solution
cvx_begin quiet
variable cube(9, 9, 9);
minimize ( sum(sum(sum(abs(cube)))) );
subject to
% if X(i, j) == k, then constrain c(i, j, k) == 1, otherwise 0
for i = 1 : 9
for j = 1 : 9
if X(i,j) ~= 0
cube(i, j, X(i,j)) == 1;
end
end
end
% constrain number 1-9 appears only one time in each row and colume
sum(cube, 1) == 1;
sum(cube, 2) == 1;
sum(cube, 3) == 1;
% 1 - 9 appears only one time in each 3*3 square
for i = 1 : 3
for j = 1 : 3
for k = 1 : 9
sum(sum(cube((i-1)*3+(1:3), (j-1)*3+(1:3), k))) == 1;
end
end
end
cvx_end
% converting Cube to Result
Result = zeros(9, 9);
for i = 1 : 9
Result = Result + i*cube(:,:,i);
end
display(uint8(Result));
