Advent-of-Code-2023/day24/lines.go

package day24

import (
	"log"
	"os"
	"strconv"
	"strings"
)

const (
	// CoordMin int = 7
	// CoordMax int = 27
	CoordMin int = 200000000000000
	CoordMax int = 400000000000000
)

type Point struct {
	x, y, Z int
}

type HailParam struct {
	p0, p1     Point
	Dx, Dy, Dz int
	line       string
	// for 2d : ay + bx = 0
	a, b, c int
	// for 2d : y = slope*x + shift
	slope, shift float64
}


func CheckPairwiseIntersections(hails []HailParam) (totalIntersections int) {
	for i, hail := range hails {
		for j := i + 1; j < len(hails); j++ {
			otherHail := hails[j]
			intersect := CheckTaskIntersection(hail, otherHail)
			if intersect {
				totalIntersections += 1
			}
		}
	}
	return
}

func CheckTaskIntersection(h1, h2 HailParam) (doIntersect bool) {
	log.Printf("intersecting %+v and %+v\n", h1, h2)
	// x, y, intersectAtAll := IntersectByLineEquasions(h1, h2)
	// x, y, intersectAtAll := IntersectByTwoPoints(h1, h2)
	// x, y, intersectAtAll := IntersectByTwoPointsAttempt2(h1, h2)
	// x, y, intersectAtAll := IntersectByTwoPointsAttempt3(h1, h2)
	x, y, intersectAtAll := IntersectBySlopeAndShift(h1, h2)
	if !intersectAtAll {
		log.Println("no intersection at all\n", x, y)
		return false
	}
	isH1Future := h1.FloatPointInFuture(x, y)
	isH2Future := h2.FloatPointInFuture(x, y)

	if !isH1Future {
		log.Printf("point %f, %f in the past for h1\n", x, y)
	}
	if !isH2Future {
		log.Printf("point %f, %f in the past for h2\n", x, y)
	}
	if !isH1Future || !isH2Future {
		return false
	}

	if x < float64(CoordMin) || x > float64(CoordMax) ||
		y < float64(CoordMin) || y > float64(CoordMax) {
		log.Printf("intersect at %f %f but outside of area\n", x, y)
		return false // outside of area
	}

	log.Println("> intersect inside of the area! ", x, y)
	return true
}

// WRONG
func IntersectByLineEquasions(h1, h2 HailParam) (intersectionX, intersectionY float64, isIntersecting bool) {
	D := h1.a*h2.b - h1.b*h2.a
	if D == 0 {
		return 0, 0, false
	}
	Dx := h1.c*h2.b - h1.b*h2.c
	Dy := h1.a*h2.c - h1.b*h2.a
	intersectionX = float64(Dx) / float64(D)
	intersectionY = float64(Dy) / float64(D)
	isIntersecting = true
	return
}

// WRONG
// in 2d only
func IntersectByTwoPoints(h1, h2 HailParam) (intersectionX, intersectoinY float64, isIntersecting bool) {
	p1 := h1.p0
	p2 := h1.p1
	p3 := h2.p0
	p4 := h2.p1

	denominator := (p1.x-p2.x)*(p3.y-p4.y) - (p1.y-p2.y)*(p3.x-p4.x)
	if denominator == 0 {
		return 0, 0, false
	}

	divisibleX := (p1.x*p2.y-p1.y*p2.x)*(p3.x-p4.x) - (p1.x-p2.x)*(p3.x*p4.y-p3.y*p4.x)
	divisibleY := (p1.x*p2.y-p1.y*p2.x)*(p3.y-p4.y) - (p1.y-p2.y)*(p3.x*p4.y-p3.y*p4.x)

	x := float64(divisibleX) / float64(denominator)
	y := float64(divisibleY) / float64(denominator)

	return x, y, true
}

func IntersectByTwoPointsAttempt2(h1, h2 HailParam) (intersectionX, intersectionY float64, isIntersecting bool) {
	x1 := h1.p0.x
	y1 := h1.p0.y
	x2 := h1.p1.x
	y2 := h1.p1.y
	x3 := h2.p0.x
	y3 := h2.p0.y
	x4 := h2.p1.x
	y4 := h2.p1.y
	divisor :=  (x1-x2)*(y3-y4)-(y1-y2)*(x3-x4)
	if divisor == 0 {
		return
	}
	intersectionX = float64((x1*y2-y1*x2)*(x3-x4)-(x1-x2)*(x3*y4-y3*x4)) / float64(divisor)
	intersectionY = float64((x1*y2-y1*x2)*(y3-y4)-(y1-y2)*(x3*y4-y3*x4)) /  float64(divisor)
	isIntersecting = true
	return
}

func determinant(a, b Point) int {
	return a.x * b.y - a.y * b.x
}
func IntersectByTwoPointsAttempt3(h1, h2 HailParam) (intersectionX, intersectionY float64, isIntersecting bool) {
	xdiff := Point{ h1.p0.x - h1.p1.x, h2.p0.x - h2.p1.x, 0 }
	ydiff := Point { h1.p0.y - h1.p1.y, h2.p0.y - h2.p1.y , 0 }

	div := determinant(xdiff, ydiff)
	if div == 0 {
		return
	}
	d := Point { determinant(h1.p0, h1.p1), determinant(h2.p0, h2.p1), 0}
	x := float64(determinant(d, xdiff)) / float64(div)
	y := float64(determinant(d, ydiff)) / float64(div)

	return x, y, true
}

func IntersectBySlopeAndShift(h1, h2 HailParam) (intersectionX, intersectionY float64, isIntersecting bool) {
	if h1.slope == h2.slope {
		return
	}
	// y = slope * x + shift
	// slope1 * x + shift1 = slope2 * x + shift2
	// x = ( shift2 - shift1 ) / (slope1 - slope2)
	
	x := (h2.shift - h1.shift) / (h1.slope - h2.slope)
	y := h1.slope * x + h1.shift

	return x, y, true
}

func (h HailParam) PointInFuture(p Point) bool {
	xPositiveSteps := (p.x-h.p0.x)*h.Dx >= 0
	yPositiveSteps := (p.y-h.p0.y)*h.Dy >= 0
	zPositiveSteps := (p.Z-h.p0.Z)*h.Dz >= 0
	return xPositiveSteps && yPositiveSteps && zPositiveSteps
}
func (h HailParam) FloatPointInFuture(x, y float64) bool {
	xPositiveSteps := (x-float64(h.p0.x))*float64(h.Dx) >= 0
	// yPositiveSteps := (y - float64(h.p0.y)) * float64(h.Dy) >= 0
	// return xPositiveSteps && yPositiveSteps
	return xPositiveSteps
}

// 19, 13, 30 @ -2,  1, -2
func ReadHailLine(line string) (h HailParam) {
	h.line = line
	line = strings.ReplaceAll(line, "@", "")
	line = strings.ReplaceAll(line, ",", "")
	fields := strings.Fields(line)

	h.p0.x = AtoIOrPanic(fields[0])
	h.p0.y = AtoIOrPanic(fields[1])
	h.p0.Z = AtoIOrPanic(fields[2])
	h.Dx = AtoIOrPanic(fields[3])
	h.Dy = AtoIOrPanic(fields[4])
	h.Dz = AtoIOrPanic(fields[5])

	countP1AfterMillis := 1

	h.p1.x = h.p0.x + countP1AfterMillis * h.Dx
	h.p1.y = h.p0.y + countP1AfterMillis * h.Dy
	h.p1.Z = h.p0.Z + countP1AfterMillis * h.Dz

	h.a = h.p0.y - h.p1.y
	h.b = h.p1.x - h.p0.x
	h.c = -(h.p0.x*h.p1.y - h.p1.x*h.p0.y)

	h.slope = float64(h.Dy) / float64(h.Dx)
	// y = slope * x + shift
	// shift = y - slope * x // for some point
	h.shift = float64(h.p0.y) - h.slope * float64(h.p0.x)
	
	return
}

func ReadHailFile(filename string) []HailParam {
	bytes, err := os.ReadFile(filename)
	if err != nil {
		panic(err)
	}
	text := strings.TrimSpace(string(bytes))
	lines := strings.Split(text, "\n")
	result := make([]HailParam, len(lines))

	for i, line := range lines {
		result[i] = ReadHailLine(line)
	}

	return result
}

func AtoIOrPanic(str string) (num int) {
	num, err := strconv.Atoi(str)
	if err != nil {
		panic(err)
	}
	return
}