# Time:  O(nlogn)
# Space: O(n)

# N cars are going to the same destination along a one lane road.
# The destination is target miles away.
#
# Each car i has a constant speed speed[i] (in miles per hour),
# and initial position position[i] miles towards the target along the road.
#
# 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 distance between these two cars is ignored - 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.
#
# How many car fleets 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 and 8 become a fleet, meeting each other at 12.
# The car starting at 0 doesn't catch up to any other car, so it is a fleet
# by itself.
# The cars starting at 5 and 3 become a fleet, meeting each other at 6.
# Note that no other cars meet these fleets before the destination,
# so the answer is 3.
#
# Note:
# - 0 <= N <= 10 ^ 4
# - 0 < target <= 10 ^ 6
# - 0 < speed[i] <= 10 ^ 6
# - 0 <= position[i] < target
# - All initial positions are different.


class Solution(object):
    def carFleet(self, target, position, speed):
        """
        :type target: int
        :type position: List[int]
        :type speed: List[int]
        :rtype: int
        """
        times = [float(target-p)/s for p, s in sorted(zip(position, speed))]
        result, curr = 0, 0
        for t in reversed(times):
            if t > curr:
                result += 1
                curr = t
        return result