day24: why slope&shift work, while points dont?

day24/lines.go

@@ -22,13 +22,12 @@ type HailParam struct {
 	p0, p1     Point
 	Dx, Dy, Dz int
 	line       string
-	// for 2d : ay + bx + c = 0
+	// for 2d : ay + bx = 0
 	a, b, c int
+	// for 2d : y = slope*x + shift
+	slope, shift float64
 }
 
-func (h HailParam) String() string {
-	return "(" + h.line + ")"
-}
 
 func CheckPairwiseIntersections(hails []HailParam) (totalIntersections int) {
 	for i, hail := range hails {
@@ -47,9 +46,11 @@ 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 := IntersectByTwoPointsAttempt2(h1, h2)
+	// x, y, intersectAtAll := IntersectByTwoPointsAttempt3(h1, h2)
+	x, y, intersectAtAll := IntersectBySlopeAndShift(h1, h2)
 	if !intersectAtAll {
-		log.Printf("no intersection at all\n")
+		log.Println("no intersection at all\n", x, y)
 		return false
 	}
 	isH1Future := h1.FloatPointInFuture(x, y)
@@ -71,7 +72,7 @@ func CheckTaskIntersection(h1, h2 HailParam) (doIntersect bool) {
 		return false // outside of area
 	}
 
-	log.Println("> intersect inside of the area!")
+	log.Println("> intersect inside of the area! ", x, y)
 	return true
 }
 
@@ -130,6 +131,38 @@ func IntersectByTwoPointsAttempt2(h1, h2 HailParam) (intersectionX, intersection
 	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
@@ -157,14 +190,21 @@ func ReadHailLine(line string) (h HailParam) {
 	h.Dy = AtoIOrPanic(fields[4])
 	h.Dz = AtoIOrPanic(fields[5])
 
-	h.p1.x = h.p0.x + h.Dx
-	h.p1.y = h.p0.y + h.Dy
-	h.p1.Z = h.p0.Z + h.Dz
+	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
 }
 

day24/lines_test.go

@@ -19,6 +19,19 @@ func TestReadLine(t *testing.T) {
 
 }
 
+func TestReadLineInput(t *testing.T) {
+	lines := `147847636573416, 190826994408605, 140130741291716 @ 185, 49, 219
+287509258905812, 207449079739538, 280539021150559 @ -26, 31, 8
+390970075767404, 535711685410735, 404166182422876 @ -147, -453, -149
+306391780523937, 382508967958270, 264612201472049 @ -24, -274, 28
+278063616684570, 510959526404728, 288141792965603 @ -18, -441, -6`
+	for _, line := range strings.Split(lines, "\n") {
+		hail := ReadHailLine(line)
+		t.Logf("%+v\n", hail)
+	}
+
+}
+
 func TestSecondPointIsInFuture(t *testing.T) {
 	lines := `19, 13, 30 @ -2,  1, -2
 18, 19, 22 @ -1, -1, -2

day24/notes.org

@@ -31,3 +31,5 @@ should be easy
 day24 result: 8406
 * another formula gives
 day24 result: 8406
+* another formula
+12938