Question

I’m writing a 4D 4-in-a-row game in javascript. You can see it here. I’d like to implement checking of a win.

To save time, I intend to build a list of all posible winning patterns beforehand, which makes checking for a win the trivial job of iterating over this list.

The trouble I’m having is how to construct this list. The sets of winning lines include:

[[0, x, y, z], [1, x, y, z], [2, x, y, z], [3, x, y, z]] for all x, y, and z
[[w, 0, y, z], [w, 1, y, z], [w, 2, y, z], [w, 3, y, z]] for all w, y, and z
[[w, x, 0, z], [w, x, 1, z], [w, x, 2, z], [w, x, 3, z]] for all w, x, and z
[[w, x, y, 0], [w, x, y, 1], [w, x, y, 2], [w, x, y, 3]] for all w, x, and y

And then

[[0, 0, y, z], [1, 1, y, z], [2, 2, y, z], [3, 3, y, z]] for all y, and z
[[0, 3, y, z], [1, 2, y, z], [2, 1, y, z], [3, 0, y, z]] for all y, and z

As you can guess, the list goes on and on. Essentially, the rule is that one set of ordinates (for example, the x-ordinate) in the set must be the sequence [1, 2, 3, 4], and the others are either the sequence [1, 2, 3, 4], [4, 3, 2, 1], or [n, n, n, n].

How the heck can I construct this list?
….

Answer 1

Solved!

var winningLines = (function() {
    var validCoordSets = (function() {
        var a = [];

        //Build sequences, such as [1, 2, 3, 4] and [4, 3, 2, 1]
        var sequence = [];
        for(var i = 0; i < size; i++) {
            sequence.push(i);
        }
        a.push(sequence);
        a.push(sequence.slice().reverse());

        //Build constants, such as [1, 1, 1, 1], [2, 2, 2, 2]
        for(var i = 0; i < size; i++) {
            var straight = [];
            for(var j = 0; j < size; j++) {
                straight.push(i);
            }
            a.push(straight);
        }
        return a;
    })();

    var n = validCoordSets.length;

    var a = [];

    var w = validCoordSets[0];
    for(var i = 0; i < n; i++)
    for(var j = 0; j < n; j++)
    for(var k = 0; k < n; k++) {
        var x = validCoordSets[i];
        var y = validCoordSets[j];
        var z = validCoordSets[k];

        line = [];
        for(var l = 0; l < size; l++) {
            line.push([w[l], x[l], y[l], z[l]]);
        }
        a.push(line);
    }

    var x = validCoordSets[0];
    for(var i = 1; i < n; i++)
    for(var j = 0; j < n; j++)
    for(var k = 0; k < n; k++) {
        var w = validCoordSets[i];
        var y = validCoordSets[j];
        var z = validCoordSets[k];

        line = [];
        for(var l = 0; l < size; l++) {
            line.push([w[l], x[l], y[l], z[l]]);
        }
        a.push(line);
    }

    var y = validCoordSets[0];
    for(var i = 1; i < n; i++)
    for(var j = 1; j < n; j++)
    for(var k = 0; k < n; k++) {
        var w = validCoordSets[i];
        var x = validCoordSets[j];
        var z = validCoordSets[k];

        line = [];
        for(var l = 0; l < size; l++) {
            line.push([w[l], x[l], y[l], z[l]]);
        }
        a.push(line);
    }

    var z = validCoordSets[0];
    for(var i = 1; i < validCoordSets.length; i++)
    for(var j = 1; j < validCoordSets.length; j++)
    for(var k = 1; k < validCoordSets.length; k++) {
        var w = validCoordSets[i];
        var x = validCoordSets[j];
        var y = validCoordSets[k];

        line = [];
        for(var l = 0; l < size; l++) {
            line.push([w[l], x[l], y[l], z[l]]);
        }
        a.push(line);
    }

    return a;
})()