Solving a system of linear equations with Cocoa Autolayout (Advent of Code 2024 Day 13)

AoC-2014-Day13.swift

// https://adventofcode.com/2024/day/13

import AppKit

// Button A: X+94, Y+34
// Button B: X+22, Y+67
// Prize: X=8400, Y=5400
let X: CGFloat = 8400
let Y: CGFloat = 5400
let x_a: CGFloat = 94
let x_b: CGFloat = 22
let y_a: CGFloat = 34
let y_b: CGFloat = 67

// Equation 1:
// a * x_a + b * x_b = X
// a = (X - b * x_b) / x_a
// a = X/x_a - b * x_b/x_a
// a = -x_b/x_a * b + X/x_a

// Equation 2:
// a * y_a + b * y_b = Y
// … (solve for a in the same way as eq. 1)

let va = NSView()
va.translatesAutoresizingMaskIntoConstraints = false
let vb = NSView()
vb.translatesAutoresizingMaskIntoConstraints = false
let container = NSView()
container.addSubview(va)
container.addSubview(vb)

let c1 = NSLayoutConstraint(
    item: va,
    attribute: .width,
    relatedBy: .equal,
    toItem: vb,
    attribute: .width,
    multiplier: -x_b/x_a,
    constant: X/x_a
)

let c2 = NSLayoutConstraint(
    item: va,
    attribute: .width,
    relatedBy: .equal,
    toItem: vb,
    attribute: .width,
    multiplier: -y_b/y_a,
    constant: Y/y_a
)

NSLayoutConstraint.activate([c1, c2])
container.layoutSubtreeIfNeeded()
va.frame.width // A = 80 ✅
vb.frame.width // B = 40 ✅
// A = 80 and B = 40 is the correct solution:
// "The cheapest way to win the prize is by pushing the A button 80 times and the B button 40 times."
//
// (This code only shows that A = 80 and B = 40 is a valid solution, not that it's the cheapest.
// But it's good enough for a proof of concept.)