advent-of-code-2024/day13/clawmachine.go

package main

import (
    "fmt"
    "os"
    "math"
    "errors"
    "strings"
    "regexp"
    "strconv"
)


// data types

type Vec struct {
    x uint32
    y uint32
}

func (v Vec) Sub(other Vec) Vec {
    return Vec{x: v.x - other.x, y: v.y - other.y}
}

func (v Vec) Mul(skalar uint32) Vec {
    return Vec{x: v.x * skalar, y: v.y *skalar}
}

func (v Vec) VecDiv(other Vec) (float64, error) {
    /* Returns an error if v and other do not lie on a staight line.
     * It holds: v.VecDiv(other).Abs() = v.Abs() / other.Abs()
    */
    cx := float64(v.x) / float64(other.x)
    cy := float64(v.y) / float64(other.y)

    if abs(cx - cy) > 10e-5 { return 0, errors.New("vectors do not lie in a straight line") }

    return cx, nil
}

func (v Vec) Abs() float64 {
    return math.Sqrt(float64(v.x * v.x + v.y * v.y))
}


type ClawMachine struct {
    buttonA Vec
    buttonB Vec
    price Vec
}

func (cm ClawMachine) FindPath(max_presses_per_button uint32) ([2]uint32, error) {
    /* Find all combinations of cm.buttonA and cm.buttonB that result in cm.price .
     * => x1 * cm.buttonA + x2 * cm.buttonB = cm.price
     * where x1, x2 are of type uint and x1,x2 <= max_presses_per_button
     *
     * Returns a list of all the [x1, x2] where the equation is solvable with the 
     * restrictions above.
     */

    for i := range max_presses_per_button {
        x1, err := cm.price.Sub( cm.buttonB.Mul(i + 1) ).VecDiv( cm.buttonA )
        if err != nil || uint32(x1 - 10e-5) > max_presses_per_button { continue }

        x2, err := cm.price.Sub( cm.buttonA.Mul(uint32(x1)) ).VecDiv( cm.buttonB )

        if err == nil && i + 1 == uint32(x2) {
            return [2]uint32{uint32(x1), uint32(x2)}, nil
        }
    }

    return [2]uint32{0,0}, errors.New("no path found")
}


// general util
func check(e error) {
    if e != nil { panic(e) }
}

func abs(n float64) float64 {
    if n < 0 { return -n }
    return n
}


// main loop
func main() {

    // read in file
    dat, err := os.ReadFile("data.txt")
    check(err)
    dat_str := strings.TrimSpace(string(dat))

    cms := make([]ClawMachine, 0)
    pattern := regexp.MustCompile(`\d+`)
    numbers := [6]uint32{}
    for _, machine_str := range strings.Split(dat_str, "\n\n") {
        // collect numbers as ints
        for i, match := range pattern.FindAllString(machine_str, -1) {
            numInt, err := strconv.Atoi(match)
            check(err)
            numbers[i] = uint32(numInt)
        }
        // construct ClawMachines
        cms = append(cms, ClawMachine{
            Vec{numbers[0],numbers[1]}, 
            Vec{numbers[2], numbers[3]},
            Vec{numbers[4],numbers[5]},
        })
    }
    
    // calculate cost
    cost := 0
    for _, cm := range cms {
        path, err := cm.FindPath(100)
        if err == nil {
            cost += int(path[0]) * 3 + int(path[1])
        }
    }
    fmt.Println(cost)
}