What is the optimal time complexity of solving Car Fleet?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Car Fleet?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Car Fleet?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Car Fleet?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Car Fleet

Learn how to solve the 'Car Fleet' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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 arrays 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 (they are assumed to be at the same position).

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

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

Write a function carFleet(target: int, position: List[int], speed: List[int]) -> int.

Constraints

•n == len(position) == len(speed)
•1 <= n <= 10^5
•0 < target <= 10^6
•0 <= position[i] < target
•0 < speed[i] <= 10^6
•All positions are unique

Examples

Example 1

Input

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

Output

Explanation

Cars at positions 10 and 8: car at 8 catches car at 10 (both arrive at time 1), forming 1 fleet. Car at 0: arrives at time 12. Car at 5: arrives at time 7. Car at 3: arrives at time 3, catches car at 5 at time 7, but car at 5 arrives at 7 too. Cars at 3 and 5 form a fleet. Total: 3 fleets.

Example 2

Input

target = 10, position = [3], speed = [3]

Output

Explanation

Only one car, so one fleet.

Example 3

Input

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

Output

Explanation

All cars eventually form a single fleet.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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