Sudoku Solver - SciLab

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//////////////////////////   Check Sudoku   ///////////////////////////////
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function r=OneToNine(V) // function checks if the given vector V contains 1 to 9
    r = %T              // this works
    u = %F
    index = 1
    while r == %T & index < 10
        for i=1 : length(V)
            if V(i)==index then 
                u = %T
            end
        end
        index=index+1
        if u == %F then r = %F
            else u = %F
        end          
    end
    if length(V) > 9 then r = %F
    end
endfunction

function y=check(M) // Checks if the given matrix M is a solved sudoku
    y = %T          // this works too
    
    if size(M,1)<>9 | size(M,2)<>9 then // if it has more or less than 9 rows and columns
        y = %F                          // we return false
    end
    
    for i=1 : size(M,1)                 // if not all rows have 1-9 we return false
        if OneToNine(M(i,:)) == %F then
            y = %F
        end
    end
endfunction


function P=PossibilitiesPosition(board, x, y)
    // this one works
    // we fill the vector possibilites with 9 zeros
    // 0 means empty, 1 means it already has a value, so we don't need to change it
    
    possibilities = []      // a vector that stores the possible values for position(x,y)
    for t=1 : 9            // sudoku has 9 values
        possibilities(t)=0
    end
    
    // Check row f the value (x,y) for possibilities
    // we fill the possibilities further by puttin '1' where the value is not possible 
    for i=1 : 9            // sudoku has 9 values
        if board(x,i) > 0 then
            possibilities(board(x,i))=1
        end
    end
    
    // Check column of the value (x,y) for possibilities
    // we fill the possibilities further by puttin '1' where the value is not possible
    for j=1 : 9            // sudoku has 9 values
        if board(j, y) > 0 then
            possibilities(board(j, y))=1
        end
    end
    
    // Check the 3x3 matrix of the value (x,y) for possibilities
    // first we see which 3x3 matrix we need
    k=0
    m=0
       if x >= 1 & x <=3 then
           k=1
       else if x >= 4 & x <= 6 then
               k = 4
       else k = 7
           end
       end
       if y >= 1 & y <=3 then
           m=1
       else if y >= 4 & y <= 6 then
               m = 4
       else m = 7
           end
       end
       
       // then we fill the possibilities further by puttin '1' where the value is not possible
       for i=k : k+2
           for j=m : m+2
               if board(i,j) > 0 then
                   possibilities(board(i,j))=1
               end
           end           
       end       
       P = possibilities
       
       // we want to see the real values of the possibilities. not just 1 and 0
       for i=1 : 9            // sudoku has 9 values
           if P(i)==0 then
               P(i) = i
           else P(i) = 0
           end
       end
    
endfunction





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//////////////////////////   Solve Sudoku   ///////////////////////////////
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function S=solve(board) // the real solving function, here must be a problem somewhere
    x=1
    y=1
    possibilities = [] // an empty vector to put in the possible value later on
    
    if check(board) == %T then // if it's a fully solved sudoku the function gives the solution
        S = board
        
    else
        for i=1 : 9                   // sudoku has 9 values
            for j=1 : 9               // sudoku has 9 values
                if board(i,j)==0 then // if the value board(i,j) is empty so 0
                    x=i               // we put the coordinates in x and y
                    y=j               // break means stop the loop
                    break
                end
            end
        end
        possibilities = PossibilitiesPosition(board,x,y) //we check the possibilities
        
        for p=1 : 9                             // sudoku has 9 values
            if possibilities(p) > 0 then        // if this is a possibility
                board(x,y) = possibilities(p)   // we put in that value
                solve(board)                    // and we repeat until check(board) gives true
            end
        end
        board(x,y)=0                            // if we went trough al the possibilities
    end                                         // and there is still no solution we have to put that value back to 0
                                                // this is called backtracking
endfunction


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