Advent of Code - 2024 - Day 13

var input = await File.ReadAllTextAsync("input.txt");
var machineRecords = input.Split($"{Environment.NewLine}{Environment.NewLine}");

List<(int, int, int, int, int, int)> machines = [];

foreach (var record in machineRecords)
{
    var lines = record.Split(Environment.NewLine);

    var buttonA = lines[0][10..].Split(", ");
    var ax = int.Parse(buttonA[0][2..]);
    var ay = int.Parse(buttonA[1][2..]);

    var buttonB = lines[1][10..].Split(", ");
    var bx = int.Parse(buttonB[0][2..]);
    var by = int.Parse(buttonB[1][2..]);

    var prize = lines[2][7..].Split(", ");
    var px = int.Parse(prize[0][2..]);
    var py = int.Parse(prize[1][2..]);

    machines.Add((ax, ay, bx, by, px, py));
}

for (var part = 1; part <= 2; part++)
{
    var correction = (part - 1) * 10000000000000L;
    var result = 0L;

    foreach (var (ax, ay, bx, by, px0, py0) in machines)
    {
        var px = px0 + correction;
        var py = py0 + correction;

        // We want to solve the following system of equations,
        // where x is the number of presses for button A,
        // and y is the number of presses for button B:
        // ax*x + bx*y = px
        // ay*x + by*y = py
        // We solve it by applying Cramer's rule:
        // x = (px*by - py*bx) / (ax*by - ay*bx)
        // y = (ax*py - ay*px) / (ax*by - ay*bx)

        var d = ax * by - ay * bx;
        var dx = px * by - py * bx;
        var dy = ax * py - ay * px;

        if (dx % d != 0 || dy % d != 0)
        {
            // There is no integer solution, hence the prize is not reachable.
            continue;
        }

        var x = dx / d;
        var y = dy / d;

        if (part == 1 && (x > 100 || y > 100))
        {
            continue;
        }

        result += x * 3 + y;
    }

    Console.WriteLine($"Part {part}: {result}");
}