Solution for 2023, day 24 + vendor

Author: lucianoq

2023/24/Makefile

@@ -0,0 +1,17 @@
+main1:
+	go build -o main1 main1.go common.go
+
+main2:
+	go build -o main2 main2.go common.go
+
+.PHONY: run1 run2 clean
+
+run1: main1
+	./main1 <input
+
+run2: main2
+	./main2 <input
+
+clean:
+	rm -f main1 main2
+

2023/24/common.go

@@ -0,0 +1,31 @@
+package main
+
+import (
+	"bufio"
+	"fmt"
+	"os"
+)
+
+type P struct{ x, y, z float64 }
+
+type HailStone struct{ Pos, Vel P }
+
+func parse() []HailStone {
+	hail := []HailStone{}
+	scanner := bufio.NewScanner(os.Stdin)
+	for scanner.Scan() {
+		ice := HailStone{}
+		_, _ = fmt.Sscanf(
+			scanner.Text(),
+			"%f, %f, %f @ %f, %f, %f",
+			&ice.Pos.x,
+			&ice.Pos.y,
+			&ice.Pos.z,
+			&ice.Vel.x,
+			&ice.Vel.y,
+			&ice.Vel.z,
+		)
+		hail = append(hail, ice)
+	}
+	return hail
+}

2023/24/main1.go

@@ -0,0 +1,74 @@
+package main
+
+import "fmt"
+
+const (
+	Min = 200000000000000
+	Max = 400000000000000
+)
+
+func main() {
+	hail := parse()
+
+	count := 0
+	for i := 0; i < len(hail)-1; i++ {
+		for j := i + 1; j < len(hail); j++ {
+			p, intersect := findIntersection(hail[i], hail[j])
+
+			if intersect {
+				if p.x >= Min && p.x <= Max && p.y >= Min && p.y <= Max {
+					count++
+				}
+			}
+		}
+	}
+
+	fmt.Println(count)
+}
+
+func findIntersection(h1, h2 HailStone) (P, bool) {
+	// (1)  xf = x0 + vx*t   ==>   t = (xf-x0)/vx
+	// (2)  yf = y0 + vy*t
+	//
+	// Combining (1) and (2)
+	// yf = y0 + vy * (xf-x0)/vx
+	// yf = y0 + (vy/vx)(xf-x0)
+	// yf = (vy/vx) * xf + [ y0 - (vy/vx)*x0 ]
+	// y  =    m    *  x +        q
+	//
+	// m = vy/vx
+	// q = y0 - m*x0
+
+	m1 := h1.Vel.y / h1.Vel.x
+	m2 := h2.Vel.y / h2.Vel.x
+
+	if m1 == m2 {
+		// parallel lines
+		return P{}, false
+	}
+
+	q1 := h1.Pos.y - m1*h1.Pos.x
+	q2 := h2.Pos.y - m2*h2.Pos.x
+
+	xf := (q2 - q1) / (m1 - m2)
+	yf := m1*xf + q1
+
+	// they meet in (xf,yf)
+	// need to check if this was in the past
+
+	// From (1)
+	t1 := (xf - h1.Pos.x) / h1.Vel.x
+	if t1 < 0 {
+		// past
+		return P{}, false
+	}
+
+	// From (1)
+	t2 := (yf - h2.Pos.y) / h2.Vel.y
+	if t2 < 0 {
+		// past
+		return P{}, false
+	}
+
+	return P{xf, yf, 0}, true
+}

2023/24/main2.go

@@ -0,0 +1,130 @@
+package main
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+// Given:
+// (1) p¹ = p₀¹ + v¹⋅t
+// (2) p² = p₀² + v²⋅t
+// (3) p³ = p₀³ + v³⋅t
+// ...
+//
+// Find:
+// p = p₀ + v⋅t
+//
+// such as:
+// p¹=p when t¹=t
+// p²=p when t²=t
+// p³=p when t³=t
+// ...
+//
+// where
+// pⁿ = [pₓⁿ, pᵧⁿ, pₛⁿ]
+// p₀ⁿ = [pₓ₀ⁿ, pᵧⁿ, pₛ₀ⁿ]
+// vⁿ = [vₓⁿ, vᵧⁿ, vₛⁿ]
+
+// p¹ + v¹⋅t = p + v⋅t
+// p² + v²⋅t = p + v⋅t
+// p³ + v³⋅t = p + v⋅t
+// pⁿ + vⁿ⋅t = p + v⋅t
+//
+// (p - p¹) = (v¹ - v)t¹
+// (p - p²) = (v² - v)t²
+// (p - p³) = (v³ - v)t³
+// (p - pⁿ) = (vⁿ - v)tⁿ
+// and so:
+// (p - pⁿ) ⋅ (v-vⁿ) = 0
+func main() {
+	hail := parse()
+
+	// Ax = b
+	//
+	// A = [         0,  -v⁰ₛ +v¹ₛ,   v⁰ᵧ - v¹ᵧ,          0,  -p¹ₛ +p⁰ₛ,   p¹ᵧ -p⁰ᵧ
+	//		  v⁰ₛ -v¹ₛ,          0,  -v⁰ₓ + v¹ₓ,   p¹ₛ -p⁰ₛ,          0,  -p¹ₓ +p⁰ₓ
+	//		 -v⁰ᵧ +v¹ᵧ,   v⁰ₓ -v¹ₓ,           0,  -p¹ᵧ +p⁰ᵧ,   p¹ₓ -p⁰ₓ,          0
+	//               0,  -v⁰ₛ +v²ₛ,   v⁰ᵧ - v²ᵧ,          0,  -p²ₛ +p⁰ₛ,   p²ᵧ -p⁰ᵧ
+	//		  v⁰ₛ -v²ₛ,          0,  -v⁰ₓ + v²ₓ,   p²ₛ -p⁰ₛ,          0,  -p²ₓ +p⁰ₓ
+	//		 -v⁰ᵧ +v²ᵧ,   v⁰ₓ -v²ₓ,           0,  -p²ᵧ +p⁰ᵧ,   p²ₓ -p⁰ₓ,          0 ]
+	//
+	// x = [ pₓ
+	//       pᵧ
+	//       pₛ
+	//       vₓ
+	//       vᵧ
+	//       vₛ ]
+	//
+	// b = [ p¹ᵧ⋅v¹ₛ -p¹ₛ⋅v¹ᵧ -p⁰ᵧ⋅v⁰ₛ +p⁰ₛ⋅v⁰ᵧ,
+	//		 p¹ₛ⋅v¹ₓ -p¹ₓ⋅v¹ₛ -p⁰ₛ⋅v⁰ₓ +p⁰ₓ⋅v⁰ₛ,
+	//		 p¹ₓ⋅v¹ᵧ -p¹ᵧ⋅v¹ₓ -p⁰ₓ⋅v⁰ᵧ +p⁰ᵧ⋅v⁰ₓ,
+	//       p²ᵧ⋅v²ₛ -p²ₛ⋅v²ᵧ -p⁰ᵧ⋅v⁰ₛ +p⁰ₛ⋅v⁰ᵧ,
+	//		 p²ₛ⋅v²ₓ -p²ₓ⋅v²ₛ -p⁰ₛ⋅v⁰ₓ +p⁰ₓ⋅v⁰ₛ,
+	//		 p²ₓ⋅v²ᵧ -p²ᵧ⋅v²ₓ -p⁰ₓ⋅v⁰ᵧ +p⁰ᵧ⋅v⁰ₓ ]
+	//
+
+	// hail[0] with hail[1]
+	// (p0 - p[1]) x (v0 - v[1]) == 0
+	A00 := diff(crossMatrix(hail[0].Vel), crossMatrix(hail[1].Vel))
+	A03 := diff(crossMatrix(hail[1].Pos), crossMatrix(hail[0].Pos))
+
+	// hail[0] with hail[2]
+	// (p0 - p[2]) x (v0 - v[2]) == 0
+	A30 := diff(crossMatrix(hail[0].Vel), crossMatrix(hail[2].Vel))
+	A33 := diff(crossMatrix(hail[2].Pos), crossMatrix(hail[0].Pos))
+
+	A := mat.NewDense(6, 6, []float64{
+		A00[0], A00[1], A00[2], A03[0], A03[1], A03[2],
+		A00[3], A00[4], A00[5], A03[3], A03[4], A03[5],
+		A00[6], A00[7], A00[8], A03[6], A03[7], A03[8],
+		A30[0], A30[1], A30[2], A33[0], A33[1], A33[2],
+		A30[3], A30[4], A30[5], A33[3], A33[4], A33[5],
+		A30[6], A30[7], A30[8], A33[6], A33[7], A33[8],
+	})
+
+	b0 := diff(hail[1].Pos.cross(hail[1].Vel).toF(), hail[0].Pos.cross(hail[0].Vel).toF())
+	b3 := diff(hail[2].Pos.cross(hail[2].Vel).toF(), hail[0].Pos.cross(hail[0].Vel).toF())
+
+	b := mat.NewVecDense(6, []float64{b0[0], b0[1], b0[2], b3[0], b3[1], b3[2]})
+
+	var x mat.VecDense
+	_ = x.SolveVec(A, b)
+
+	rock := HailStone{
+		Pos: P{x.At(0, 0), x.At(1, 0), x.At(2, 0)},
+		Vel: P{x.At(3, 0), x.At(4, 0), x.At(5, 0)},
+	}
+
+	fmt.Printf("%.0f\n", rock.Pos.x+rock.Pos.y+rock.Pos.z)
+}
+
+func crossMatrix(p P) []float64 {
+	return []float64{
+		0, -p.z, p.y,
+		p.z, 0, -p.x,
+		-p.y, p.x, 0,
+	}
+}
+
+func diff(a, b []float64) []float64 {
+	res := make([]float64, len(a))
+	for i := 0; i < len(a); i++ {
+		res[i] = a[i] - b[i]
+	}
+	return res
+}
+
+// https://wikimedia.org/api/rest_v1/media/math/render/svg/3242bd71d63c393d02302c7dbe517cd0ec352d31
+// https://en.wikipedia.org/wiki/Cross_product#Coordinate_notation
+func (p P) cross(p2 P) P {
+	return P{
+		p.y*p2.z - p.z*p2.y,
+		p.z*p2.x - p.x*p2.z,
+		p.x*p2.y - p.y*p2.x,
+	}
+}
+
+func (p P) toF() []float64 {
+	return []float64{p.x, p.y, p.z}
+}

go.mod

@@ -2,4 +2,7 @@ module github.com/lucianoq/adventofcode
 
 go 1.23.4
 
-require github.com/lucianoq/container/set v0.0.0-20220318183130-8a364c4afb3e
+require (
+	github.com/lucianoq/container/set v0.0.0-20220318183130-8a364c4afb3e
+	gonum.org/v1/gonum v0.15.1
+)

go.sum

@@ -1,2 +1,6 @@
 github.com/lucianoq/container/set v0.0.0-20220318183130-8a364c4afb3e h1:22MyLR3FQpLZGoCTyvD05lbVOptCgY4U+uAGVdPf3OQ=
 github.com/lucianoq/container/set v0.0.0-20220318183130-8a364c4afb3e/go.mod h1:MQlqJvLUYtP+m6YG0x7FteiDO0QQCN0i0d1KqFtxO/c=
+golang.org/x/exp v0.0.0-20231110203233-9a3e6036ecaa h1:FRnLl4eNAQl8hwxVVC17teOw8kdjVDVAiFMtgUdTSRQ=
+golang.org/x/exp v0.0.0-20231110203233-9a3e6036ecaa/go.mod h1:zk2irFbV9DP96SEBUUAy67IdHUaZuSnrz1n472HUCLE=
+gonum.org/v1/gonum v0.15.1 h1:FNy7N6OUZVUaWG9pTiD+jlhdQ3lMP+/LcTpJ6+a8sQ0=
+gonum.org/v1/gonum v0.15.1/go.mod h1:eZTZuRFrzu5pcyjN5wJhcIhnUdNijYxX1T2IcrOGY0o=