# Car Fleet

*There are **n** cars going to the same destination along a one-lane road*. The destination is `target`

miles away.

You are given two integer array `position`

and `speed`

, both of length `n`

, where `position[i]`

is the position of the `ith`

car and `speed[i]`

is the speed of the `ith`

car (in miles per hour).

A car can never pass another car ahead of it, but it can catch up to it and drive bumper to bumper **at the same speed**. The faster car will **slow down** to match the slower car’s speed. The distance between these two cars is ignored (i.e., they are assumed to have the same position).

A **car fleet** is some non-empty set of cars driving at the same position and same speed. Note that a single car is also a car fleet.

If a car catches up to a car fleet right at the destination point, it will still be considered as one car fleet.

Return *the **number of car fleets** that will arrive at the destination*.

**Example 1:**

**Input:** target = 12, position = [10,8,0,5,3], speed = [2,4,1,1,3]

**Output:** 3

**Explanation:**

The cars starting at 10 (speed 2) and 8 (speed 4) become a fleet, meeting each other at 12.

The car starting at 0 does not catch up to any other car, so it is a fleet by itself.

The cars starting at 5 (speed 1) and 3 (speed 3) become a fleet, meeting each other at 6. The fleet moves at speed 1 until it reaches target.

Note that no other cars meet these fleets before the destination, so the answer is 3.

**Example 2:**

**Input:** target = 10, position = [3], speed = [3]

**Output:** 1

**Explanation:** There is only one car, hence there is only one fleet.

**Example 3:**

**Input:** target = 100, position = [0,2,4], speed = [4,2,1]

**Output:** 1

**Explanation:**

The cars starting at 0 (speed 4) and 2 (speed 2) become a fleet, meeting each other at 4. The fleet moves at speed 2.

Then, the fleet (speed 2) and the car starting at 4 (speed 1) become one fleet, meeting each other at 6. The fleet moves at speed 1 until it reaches target.

**Constraints:**

`n == position.length == speed.length`

`1 <= n <= 105`

`0 < target <= 106`

`0 <= position[i] < target`

- All the values of
`position`

are**unique**. `0 < speed[i] <= 106`

**Algorithm:**

The key point here is that, once a car catches another car, it can’t pass it but drives in a fleet(because in the problem its given its a one-lane road and no one can overtake before one). That means the car that’s in the front will decide what speed to drive and what time of arrival. Any car behind that can catch up to that car before it arrives and becomes fleet. So in the test example, we order the car by position:

**Algorithm in Steps -**

1. Calculate time needed to arrive the target.

2. Sort by the start position.

3. Loop on each car from the end to the beginning.

4. update **maxTime** with the current biggest time (the slowest).

5. If another car needs less or equal time than **maxTime**, it can catch up this car. Otherwise it will become the new slowest car, that is new lead of a car fleet.