We can apply this knowledge to the board by marking cell5 and clearing cell1 and cell2. Since a cell can either be a mine (1) or safe (0), the only solution to this system is that cell1 and cell2 (from columns1 and 2) are safe, and that cell5 is a mine. Note this yields two additional solutions. If our 1 - the cell that defines the first column - was touching two other unknown cells (which did not touch the 2), we'd have the following system instead: 1 1 1 1 0 | 1Īs before, subtracting row1 from row2 we get: -1 -1 0 0 1 | 1 Using Gaussian elimination, or the even more informative Gauss-Jordan elimination method, we can partially solve this system: subtracting row1 from row2 yields the following: 0 0 1 | 1Īnd this indicates that the cell represented by column3 is a mine. The second row is our 2, adjacent to three cells. In the above example, then, the first row is our 1 (from the last column), adjacent to two cells (columns 1 and 2), but not adjacent to the third cell (hence its value of 0). Each column represents a cell in this system of cells, and we assign a 1 to the column if this row's cell is adjacent to the cell for that column, and a 0 if is not.
Each row in the matrix represents an exposed cell, with that cell's value as the last value (behind the pipe symbol) in the row. We construct the matrix as follows: 1 1 0 | 1Īgain, this is the simplest case of a 1-2 pattern. Cell1 has an exposed value of 1, and cell2 has an exposed value of 2. In it, we have cell1 adjacent to two or more unknown cells, and cell2 adjacent to three cells. I'll provide a simple case, the 1-2 pattern. The linear algebra approach captures exposed cells adjacent to unknown cells, and constructs an augmented linear matrix. There are two very good approaches I rather like: linear algebra, and sets. See if you can identify the defining characteristics of them in a way that you can capture with code. Please don't take offense - it's an error most of us make, and it's how we learn, but you may want to temper your expectations a bit, at least at first. Coding a solver is much more complicated than coding a playable Minesweeper clone, but suffice it to say that you'll have to consider just how you can identify solvable cases and provide that information to your players.īased on your question, I wonder if you've bitten off more than you can chew.
0 kommentar(er)
