Car lane assignment algorithm

Fun problem. This algorithm should work in all cases.

const cars = [
    { name: "car0blue", start: 0, end: 3 },
    { name: "car1red", start: 1, end: 4 },
    { name: "car2yellow", start: 3, end: 7 },
    { name: "car3green", start: 3, end: 6 },
    { name: "car4purple", start: 4, end: 7 },
    { name: "car5grey", start: 5, end: 11 },
];

const lanes = [];
cars.forEach(placeInFreeLane);
console.log( cars );

// Algorithm:

function placeInFreeLane(car) {
    let lane = 0;
    while (!tryFitInLane(car, lane)) lane++;
    car.lane = lane;
}

function tryFitInLane(car, laneNumber) {
    const lane = lanes[laneNumber];
    if (lane === undefined) {
        lanes[laneNumber] = [car];
        return true;
    } else {
        const intersectsWithAny = lane.some(otherCar => intersects(car, otherCar));
        if (!intersectsWithAny) {
            lane.push(car);
            return true;
        }
    }
    return false;
}

function intersects(a, b) { return a.start < b.end && a.end > b.start; }

Output given your case (matches the desired output):

[
  { "name": "car0blue", "start": 0, "end": 3, "lane": 0 },
  { "name": "car1red", "start": 1, "end": 4, "lane": 1 },
  { "name": "car2yellow", "start": 3, "end": 7, "lane": 0 },
  { "name": "car3green", "start": 3, "end": 6, "lane": 2 },
  { "name": "car4purple", "start": 4, "end": 7, "lane": 1 },
  { "name": "car5grey", "start": 5, "end": 11, "lane": 3 }
]

EDIT: for the fun of it here is another version written in a more functional manner. This one is self contained and doesn't mutate the original or global state. It copies the input data and has no side effects.

// Algorithm:

const intersects = (a, b) => a.start < b.end && a.end > b.start;
const hasNoIntersectionsWith = (car) => (lane) => !lane.some((other) => intersects(car, other));
const getPacked = (cars) => {
    const lanes = [];
    return cars.map((car) => {
        let freeLaneIndex = lanes.findIndex(hasNoIntersectionsWith(car));
        if (freeLaneIndex < 0) freeLaneIndex = lanes.push([]) - 1;
        lanes[freeLaneIndex].push(car);
        return { ...car, lane: freeLaneIndex };
    });
};

// Example:

var cars = [
    { name: "car0blue", start: 0, end: 3 },
    { name: "car1red", start: 1, end: 4 },
    { name: "car2yellow", start: 3, end: 7 },
    { name: "car3green", start: 3, end: 6 },
    { name: "car4purple", start: 4, end: 7 },
    { name: "car5grey", start: 5, end: 11 },
];

console.log(getPacked(cars));

Tags:

Javascript

Recent Posts