From 2fc909f9c76c8a43e5990d3f7064cedbe2ede5d8 Mon Sep 17 00:00:00 2001
From: Max <git@maximhutz.me>
Date: Wed, 24 Dec 2025 13:59:58 -0500
Subject: [PATCH] feat: works

---
 pkg/car_fleet/main.go | 90 ++++++++++++++++++++++++++-----------------
 1 file changed, 55 insertions(+), 35 deletions(-)

diff --git a/pkg/car_fleet/main.go b/pkg/car_fleet/main.go
index 8322be9..184a24d 100644
--- a/pkg/car_fleet/main.go
+++ b/pkg/car_fleet/main.go
@@ -1,84 +1,104 @@
 package car_fleet
 
 import (
-	"fmt"
 	"math"
 	"slices"
 )
 
 type Car struct {
-	position int
-	speed    int
+	Position float64
+	Speed    float64
 }
 
+// The TIME at which the two cars will collide with each other.
 func (c Car) CollidesInto(o Car) float64 {
-	if c.speed == o.speed {
+	if c.Speed == o.Speed {
 		return math.Inf(1)
 	}
-	return float64(c.position-o.position) / float64(o.speed-c.speed)
+	return float64(c.Position-o.Position) / float64(o.Speed-c.Speed)
 }
 
-func (c Car) At(time int) int {
-	return c.position + c.speed*time
+// The DISTANCE the car will be at a point in time.
+func (c Car) At(time float64) float64 {
+	return c.Position + c.Speed*time
 }
 
-type CarSpace struct {
-	car  Car
-	from float64
-	to   float64
+// The TIME the car will reach a certain distance.
+func (c Car) Reaches(target float64) float64 {
+	if c.Speed == 0 {
+		return math.Inf(1)
+	}
+
+	return (target - c.Position) / c.Speed
 }
 
-func (s CarSpace) Contains(point float64) bool {
-	return point >= float64(s.from) && point <= float64(s.to)
+type Interval struct {
+	From float64
+	To   float64
+}
+
+func (i Interval) Contains(point float64) bool {
+	return point >= i.From && point <= i.To
+}
+
+func (i Interval) Intersect(o Interval) Interval {
+	return Interval{
+		From: max(i.From, o.From),
+		To:   min(i.To, o.To),
+	}
+}
+
+type Trajectory struct {
+	Car
+	Interval
 }
 
 func sortByInversePosition(a Car, b Car) int {
-	return b.position - a.position
+	return int(b.Position - a.Position)
 }
 
 func CarFleet(target int, position []int, speed []int) int {
 	cars := []Car{}
-	ends := map[int]bool{}
+	ends := map[float64]bool{}
 
 	for i := range position {
 		cars = append(cars, Car{
-			position: position[i],
-			speed:    speed[i],
+			Position: float64(position[i]),
+			Speed:    float64(speed[i]),
 		})
 	}
 
 	slices.SortFunc(cars, sortByInversePosition)
-	stack := []CarSpace{}
+	stack := []Trajectory{}
 
 	for _, car := range cars {
+		fastest_trajectory := Trajectory{
+			Car: car,
+			Interval: Interval{
+				From: 0,
+				To:   car.Reaches(float64(target)),
+			},
+		}
+
 		for {
-			fmt.Println(car, stack)
 			if len(stack) == 0 {
-				stack = append(stack, CarSpace{
-					car:  car,
-					from: 0,
-					to:   float64(target),
-				})
+				stack = append(stack, fastest_trajectory)
 				break
 			}
 
-			top := stack[len(stack)-1]
-			time := car.CollidesInto(top.car)
-			if top.Contains(time) {
-				stack[len(stack)-1].from = time
-				stack = append(stack, CarSpace{
-					car:  car,
-					from: 0,
-					to:   time,
-				})
+			first_trajectory := stack[len(stack)-1]
+			collision_time := car.CollidesInto(first_trajectory.Car)
+			if fastest_trajectory.Intersect(first_trajectory.Interval).Contains(collision_time) {
+				first_trajectory.From = collision_time
+				fastest_trajectory.To = collision_time
+				stack = append(stack, fastest_trajectory)
 				break
 			}
 
 			stack = stack[:len(stack)-1]
 		}
 
-		ending_at := stack[0].car.At(target)
-		ends[ending_at] = true
+		ends[stack[0].To] = true
 	}
 
 	return len(ends)