Why is the output value a zero when it should be 1 for this program?

This function takes a matrix representing a 4x4 Sudoku board and returns true if the board is a valid Sudoku solution and false if it is not. The conditions for a valid board are: the numbers on the board should only be one of 1,2,3,4, also a number can not not be repeated on a row or column of the board or within any of the four 2x2 sub-blocks. Here is my code:

function out=issudoku(m)
[R,C]=size(m);
%Find if any number on the board is not a 1, 2, 3 or 4
for i=1:R
    for j=1:C
        if m(i,j)~=1||2||3||4 
            out=0;
%%%see if any number is repeated within the individual squares
    elseif m(1,1)==m(2,1)||m(1,2)||m(2,2)
            out=0;
    elseif m(3,1)==m(4,1)||m(3,2)||m(4,4)
            out=0;
    elseif m(1,3)==m(2,3)||m(1,4)||m(2,4)
            out=0;
    elseif m(3,3)==m(4,3)||m(3,4)||m(4,4)
            out=0;
    %%repeated numbers in columns        
    elseif any(diff(m(:,1)==0))==1
            out=0;
    elseif any(diff(m(:,2)==0))==1
            out=0;
    elseif any(diff(m(:,3)==0))==1
            out=0;
    elseif any(diff(m(:,4)==0))==1
            out=0;
    %repeated numbers within rows:
    elseif any(diff(m(1,:)==0))==1
            out=0;
    elseif any(diff(m(2,:)==0))==1
            out=0;
    elseif any(diff(m(3,:)==0))==1
            out=0;
    elseif any(diff(m(4,:)==0))==1
            out=0;
        else
            out=1;
        end
    end
end

When i run issudoku([1 4 2 3; 3 2 4 1; 1 4 3 2; 2 3 1 4]) in the command window I am getting a 0 as a result when it should be 1.

[per isakson]

See Debug a MATLAB Program

Answer 1

[Jan]

The line

if m(i,j)~=1||2||3||4

does not perform, what you expect. The condtion is evaluated from right to left:

1.  m(i,j)~=1           ==> replies e.g. TRUE
2.  (m(i,j)~=1) || 2    ==> this is TRUE || 2, which is TRUE in every case
3.  TRUE || 3           ==> This is TRUE also
4.  TRUE || 4           ==> guess

I assume you want:

if ~isember(m(i,j), 1:4)

or another formulation:

if m(i,j) > 4

or

if m(i,j)~=1 && m(i,j)~=2 && m(i,j)~=3 && m(i,j)~=4

[Mohannad Abboushi]

Ok I changed that, but I am still getting false as a result for some reason

Answer 2

[Steven Lord]

In addition to what Jan said, the matrix you're testing is not a valid 4-by-4 Sudoku solution. Column 1 contains two 1's and no 4's, and column 2 contains two 4's and no 1's. Swapping the first two elements of either row 1 or row 3 will make it a valid Sudoku solution. I'd recommend swapping row 3 as then each of the main diagonal and antidiagonal will contain the digits 1 through 4 once as well.

[1 4 2 3;
 3 2 4 1;
 4 1 3 2;
 2 3 1 4]

[Mohannad Abboushi]

It is a valid Sudoku matrix, since all the conditions are satisfied in:

[1 4 2 3; 3 2 4 1; 1 4 3 2; 2 3 1 4]

[Jan]

But there are several 1s in the first column?!

Answer 3

[Jan]

Another problem:

elseif any(diff(m(1,:)==0))==1

What do you assume does this condition do?

m(1,:)==0 compares all elements of the 1st row with 0. Because the matrix contains the values 1 to 4, this is [true, true, true, true] in every case. Then you perform a diff. Because all elements are equal, this replies [0,0,0] in every case. Then any([0,0,0])==1 replies false. Note, that you can omit the "==1" part.

You see, that all these elseif any(... commands are not meaningful also.

Please fix this problem also and post your code again, such that we can search for further errors.

[Mohannad Abboushi]

Here's my new code. When I put a matrix that has duplicate elements within its columns i.e. [1 4 2 3; 3 2 4 1; 1 4 3 2; 2 3 1 4]. It is still keeping out as true. While debugging it, I saw that it skipped assigning out as false after if a~=validnumbers.

function out=issudoku(m)
  out=true;
  validnumbers=[1,2,3,4];
  [R,C]=size(m);

    %check if sudoku board is 4x4
    if R~=4||C~=4
        out=false;
    end
    %check if any elements are greater than 4
    if any(m>4)
        out=false;
    end
    %check for any repeat values in columns
    for j=1:C
            a=m(:,j);
            a=sort(a');
            if  a~=validnumbers
                out=false;
            end
    end

    %check for any repeat values in rows
    for i=1:R
            b=m(i,:);
            sort(b);
            if  b~=validnumbers
                out=false;
            end
    end
    %check if any number is repeated within the individual squares
            submatrix1=m([1 2],[1 2]);
            if sort(reshape(submatrix1,1,[]))~=[1 2 3 4]
                out=false;
            end

           submatrix2=m([3 4],[1 2]);
            if sort(reshape(submatrix2,1,[]))~=[1 2 3 4]
                out=false;
            end

           submatrix3=m([1 2],[3 4]);
            if sort(reshape(submatrix3,1,[]))~=[1 2 3 4]
                out=false;
            end

            submatrix4=m([3 4],[3 4]);
            if sort(reshape(submatrix4,1,[]))~=[1 2 3 4]
                out=false;
            end