Question

I have written an algorithm for generating a Sudoku board but it is failing. I have written it based on this though it does differ as I had written a lot of my code before I stumbled upon this.

The Code

I have a multidimensional array set up for holding the values called matrix. matrix consists of 9 arrays which are the rows and each of these hold the 9 columns. So to get the value at row 4 column 7 I would use

matrix[3][6];

The function for solving all the squares:

var populateMatrix = function() {
    var possibles = generatePossibleNumbersArray();
    var found = false;
    for(var i=0; i< matrix.length; i++) {
        for(var j=0; j< matrix[i].length; j++) {
            while(possibles[i][j].length > 0) {
                var rnd = Math.floor(Math.random() * possibles[i][j].length);
                var num = possibles[i][j].splice(rnd, 1)[0];
                if(isValid(i, j, num)) {
                    matrix[i][j] = num;
                    found = true;
                    break;
                } else {
                    found = false;
                    continue;
                }
            }
            if(!found) {
                possibles[i][j] = [1,2,3,4,5,6,7,8,9];
                j -= 2;
            }
        }
    }
}   

The generatePossibleNumbersArray() is just a helper function for creating a multidimensional array exactly like matrix except it is initialised to hold an array of integers 1-9 for each cell. During the populateMatrix() function these possible numbers get whittled down for each cell.

The Problem

It fails before completing the matrix every time because j ends up being -1. This is because as more cells get solved it becomes harder for the algorithm to find a value for a cell so it backtracks. But it eventually ends up backtracking all the way back until j == -1.

I really thought this algorithm would work and I’ve spent all day trying to get my head around this but I’m stumped so any light anyone could shed on this would be very much appreciated.

I thought ‘I know, I’ll write a javascript function for solving Sudoku. How hard can it be?’. How wrong I was.

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[SOLUTION]

Based on a comment by @Steve314 (which he’s now deleted!) I added matrix[i][j] = undefined into the if(!found) { ... and the algorithm now works and is lightening fast.

If anyone is interested, here is the complete code.

Answer 1

Backtracking algorithms usually restore the state if a branch fails and do the next possible move. So if the random filling of a field creates a failed branch just write back what was originally there.