853.car-fleet.py

#  Tag: Array, Stack, Sorting, Monotonic Stack
#  Time: O(NlogN)
#  Space: O(N)
#  Ref: -
#  Note: -

#  There are n cars at given miles away from the starting mile 0, traveling to reach the mile target.
#  You are given two integer array position and speed, both of length n, where position[i] is the starting mile of the ith car and speed[i] is the speed of the ith car in miles per hour.
#  A car cannot pass another car, but it can catch up and then travel next to it at the speed of the slower car.
#  A car fleet is a car or cars driving next to each other. The speed of the car fleet is the minimum speed of any car in the fleet.
#  If a car catches up to a car fleet at the mile target, it will still be considered as part of the 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 fleet forms at target.
#  The car starting at 0 (speed 1) 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.
#  
#  
#  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 car starting at 4 (speed 1) travels to 5.
#  Then, the fleet at 4 (speed 2) and the car at position 5 (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
#  
#  

class Solution:
    def carFleet(self, target: int, position: List[int], speed: List[int]) -> int:
        n = len(position)
        time = {position[i] : (target - position[i]) / speed[i] for i in range(n)}
        position.sort()

        stack = []
        for p in position:
            while len(stack) > 0 and time[p] >= time[stack[-1]]:
                stack.pop()
                    
            stack.append(p)
        
        return len(stack)