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package main
import (
"fmt"
"os"
"strconv"
"strings"
)
func FileRead(path string) string {
file, err := os.ReadFile(path)
if err != nil {
fmt.Println("Couldn't Read file: ", err)
}
return string(file)
}
type Machine struct {
Buttons [][]int64 // x, y cooefcients
Prize []int64 // x, y cooefcients
}
func parseInput(data string) []Machine {
var machines []Machine
lines := strings.Split(data, "\n\n")
for _, line := range lines {
var buttons [][]int64
var prize []int64
for _, subline := range strings.Split(line, "\n") {
if len(subline) > 0 {
line_splitted := strings.Split(subline, ": ")
nums_with_ops := strings.Split(line_splitted[1], ", ") // X+99 Y+44
if subline[0] == 'B' {
var button []int64
for _, coef := range nums_with_ops {
coefInt, _ := strconv.Atoi(coef[2:])
button = append(button, int64(coefInt))
}
buttons = append(buttons, button)
} else {
for _, coef := range nums_with_ops {
coefInt, _ := strconv.Atoi(coef[2:])
prize = append(prize, int64(coefInt))
}
}
}
}
machines = append(machines, Machine{
Buttons: buttons,
Prize: prize,
})
}
return machines
}
// determinant calculates the determinant of a square matrix using recursion
func determinant(matrix [2][2]int64) int64 {
return matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0]
}
// replaceColumn replaces a column in a matrix with a given vector
func replaceColumn(matrix [2][2]int64, column [2]int64, colIndex int) [2][2]int64 {
var newMatrix [2][2]int64
for i := range matrix {
newMatrix[i] = matrix[i]
newMatrix[i][colIndex] = column[i]
}
return newMatrix
}
func cramerSolve(coefficients [2][2]int64, constants [2]int64) ([2]int64, error) {
n := len(coefficients)
detA := determinant(coefficients)
if detA == 0 {
return [2]int64{}, fmt.Errorf("no unique solution exists (determinant is zero)")
}
solutions := [2]int64{}
for i := 0; i < n; i++ {
modifiedMatrix := replaceColumn(coefficients, constants, i)
detModified := determinant(modifiedMatrix)
if detModified%detA != 0 {
return [2]int64{}, fmt.Errorf("no integer solution exists")
}
solutions[i] = detModified / detA
}
return solutions, nil
}
func solve_part_one(data string) int64 {
machines := parseInput(data)
var coefficients [][]int64
var constants []int64
for _, machine := range machines {
for i := 0; i < len(machine.Buttons); i++ {
var machine_coeffs []int64
for j := 0; j < len(machine.Buttons[0]); j++ {
machine_coeffs = append(machine_coeffs, machine.Buttons[j][i])
}
coefficients = append(coefficients, machine_coeffs)
constants = append(constants, machine.Prize[i])
}
}
var ans int64 = 0
for i := 0; i < len(constants); i += 2 {
coeffs := [2][2]int64{{coefficients[i][0], coefficients[i][1]}, {coefficients[i+1][0], coefficients[i+1][1]}}
consts := [2]int64{constants[i], constants[i+1]}
sol, err := cramerSolve(coeffs, consts)
if err == nil {
ans += sol[0]*3 + sol[1]
}
}
return ans
}
func solve_part_two(data string) int64 {
machines := parseInput(data)
var coefficients [][]int64
var constants []int64
for _, machine := range machines {
for i := 0; i < len(machine.Buttons); i++ {
var machine_coeffs []int64
for j := 0; j < len(machine.Buttons[0]); j++ {
machine_coeffs = append(machine_coeffs, (machine.Buttons[j][i]))
}
coefficients = append(coefficients, machine_coeffs)
constants = append(constants, (machine.Prize[i] + 10000000000000))
}
}
var ans int64 = 0
for i := 0; i < len(constants); i += 2 {
coeffs := [2][2]int64{{coefficients[i][0], coefficients[i][1]}, {coefficients[i+1][0], coefficients[i+1][1]}}
consts := [2]int64{constants[i], constants[i+1]}
sol, err := cramerSolve(coeffs, consts)
if err == nil {
ans += sol[0]*3 + sol[1]
}
}
return ans
}
func main() {
test := FileRead("../input/day13.test")
prod := FileRead("../input/day13.prod")
fmt.Println("Part_1 test: ", solve_part_one(test))
fmt.Println("Part_1 prod: ", solve_part_one(prod))
fmt.Println("Part_2 test: ", solve_part_two(test))
fmt.Println("Part_2 prod: ", solve_part_two(prod))
}
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